Driss Yakoubi

@article{el-amrani_3162,

title = {A fractional time-stepping method for unsteady thermal convection in non-Newtonian fluids},

author = {Mofdi El-Amrani and Anouar Obbadi and Mohammed Seaid and Driss Yakoubi},

url = {https://www.sciencedirect.com/science/article/pii/S1007570424005355},

year  = {2025},

date = {2025-01-01},

journal = {Communications In Nonlinear Science And Numerical Simulation},

volume = {140},

number = {Part 1},

pages = {108350},

abstract = {We propose a fractional-step method for the numerical solution of unsteady thermal convection in non-Newtonian fluids with temperature-dependent physical parameters. The proposed method is based on a viscosity-splitting approach, and it consists of four uncoupled steps where

the convection and diffusion terms of both velocity and temperature solutions are uncoupled while a viscosity term is kept in the correction step at all times. 

This fractional-step method maintains the same boundary conditions imposed in the original problem for the corrected velocity solution, and it eliminates all inconsistencies related to boundary conditions for the

treatment of the pressure solution. In addition, the method is unconditionally stable, and it allows the temperature to be transported by a non-divergence-free velocity field. In this case, we introduce a methodology to handle the subtle temperature convection term in the error analysis

and establish full first-order error estimates for the velocity and the temperature solutions and 1?2-order estimates for the pressure solution in their appropriate norms. Three numerical examples are presented to demonstrate the theoretical results and examine the performance of the proposed method for solving unsteady thermal convection in non-Newtonian fluids. The computational results obtained for the considered examples confirm the convergence, accuracy, and applicability of the proposed time fractional-step method for unsteady thermal convection in non-Newtonian fluids.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{deteix_3161,

title = {An iterative split scheme for steady flows with heterogeneous viscosity},

author = {Jean Deteix and Driss Yakoubi},

url = {https://www.sciencedirect.com/science/article/pii/S0045782524006467},

year  = {2024},

date = {2024-12-01},

journal = {Computer Methods In Applied Mechanics And Engineering},

volume = {423},

number = {Part A},

pages = {117391},

abstract = {This paper proposes a numerical scheme for the approximation of the solution of the Stokes or steady Navier-Stokes system for fluids with heterogeneous viscosity (generic bounded viscosity or shear thinning fluids). The scheme is based on a velocity-pressure splitting resembling

a Uzawa approach combined with a grad-div stabilizing term. We establish the validity, convergence and a priori estimates for this strategy. A simpler mixed approach is also presented and studied. Numerical tests using a manufactured solution are provided, giving estimates for the accuracy order and sensitivity to the stabilizing coefficient. For more realistic numerical

experiments, we present results for the lid-driven cavity.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{jaffal-moutarda_3134,

title = {Convergence analysis of an efficient scheme for the steady state second grade fluid model},

author = {Basma Jaffal-Moutarda and Driss Yakoubi},

url = {https://doi.org/10.1016/j.cnsns.2024.108254},

year  = {2024},

date = {2024-11-01},

journal = {Communications In Nonlinear Science And Numerical Simulation},

volume = {138},

pages = {108254},

abstract = {We are interested in studying the stationary second grade fluid model in a bounded domain in R2. To approximate the solution of the continuous model, we propose a fully decoupled numerical scheme based on a splitting method combined with the use of the Grad-Div operator. This approach allows the complete decoupling of the three variables: velocity, pressure and vorticity. Each variable is computed using an iterative procedure, with the pressure step involving a simple L2-projection. We provide a proof of the convergence of the scheme to the continuous problem under smallness assumptions on the data. This theoretical analysis ensures the reliability of our method in approximating the behavior of the stationary second grade fluid model. Finally, we present several numerical tests to validate our approach. These tests illustrate the effectiveness and efficiency of our scheme in various scenarios, highlighting its potential applicability to a wide range of problems involving second grade fluids.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{boussoufa_3174,

title = {Numerical analysis for backward Euler spectral discretization for Stokes equations with boundary conditions involving the pressure: part II},

author = {Oussama Boussoufa and Yasmina Daikh and Driss Yakoubi},

url = {https://link.springer.com/article/10.1007/s10092-024-00620-1},

year  = {2024},

date = {2024-10-01},

journal = {Calcolo},

volume = {61},

number = {64},

pages = {1-24},

abstract = {In this study, we provide a nonconforming spectral approach for the Stokes equations with nonstandard boundary conditions on a single domain. The discrete spaces are defined in such a way that the discrete approximations for the velocity are exactly divergence-free. We provide a novel discrete inf-sup condition from which pressure error estimates are derived. Several numerical experiments are provided to demonstrate the method's interest.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{el-amrani_3046,

title = {A time viscosity-splitting method for incompressible flows with temperature-dependent viscosity and thermal conductivity},

author = {Mofdi El-Amrani and Anouar Obbadi and Mohammed Seaid and Driss Yakoubi},

url = {https://www.sciencedirect.com/science/article/pii/S0045782524003591?dgcid=coauthor},

year  = {2024},

date = {2024-09-01},

journal = {Computer Methods In Applied Mechanics And Engineering},

volume = {429},

pages = {117103},

abstract = {A fractional-step method is proposed and analyzed for solving the incompressible thermal Navier-Stokes equations coupled to the convection-conduction equation for heat transfer with a generalized source term for which the viscosity and thermal conductivity are temperature dependent under the Boussinesq assumption. The proposed method consists of four steps all based on a viscosity-splitting algorithm where the convection and diffusion terms of both velocity and temperature solutions are separated while a viscosity term is kept in the correction step at all times. This procedure preserves the original boundary conditions on the corrected

velocity and it removes any pressure inconsistencies. As a main feature, our method allows the temperature to be transported by a non-divergence-free velocity, in which case we show how to handle the subtle temperature convection term in the error analysis and establish full

first-order error estimates for the velocity and the temperature solutions and 1?2-order estimates

for the pressure solution in their appropriate norms. The theoretical results are examined by an accuracy test example with known analytical solution and using a benchmark problem of Rayleigh-Bénard convection with temperature-dependent viscosity and thermal conductivity.

We also apply the method for solving a problem of unsteady flow over a heated airfoil. The obtained results demonstrate the convergence, accuracy and applicability of the proposed time viscosity-splitting method.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{obbadi_3021,

title = {An improved splitting algorithm for unsteady generalized Newtonian fluid flow problems with natural boundary conditions},

author = {Anouar Obbadi and Mofdi El-Amrani and Mohammed Seaid and Driss Yakoubi},

url = {https://www.sciencedirect.com/science/article/pii/S0898122124002165?dgcid=coauthor},

year  = {2024},

date = {2024-08-01},

journal = {Computers & Mathematics With Applications},

volume = {167},

pages = {92-109},

abstract = {Generalized Newtonian fluids are challenging to solve using the standard projection or fractional-step methods which split the diffusion term from the incompressibility constraint during the time integration process. Most of this class numerical methods already suffer from some inconsistencies, even in the Newtonian case, due to unphysical pressure boundary conditions which deteriorate the quality of approximations especially when open boundary conditions are prescribed in the problem under study. The present study proposes an improved viscosity-splitting approach for solving the generalized Newtonian fluids in which the viscosity follows a nonlinear generic rheological law. This method consists of decoupling the convective effects from the incompressibility while keeping a diffusion term in the last step allowing to enforce consistent boundary conditions. We provide a full algorithmic description of the method accounting for both Dirichlet and Neumann boundary conditions. To evaluate the computational performance of the proposed viscosity-splitting algorithm, we present numerical results for an example with manufactured exact solution and for the benchmark problems of lid-driven cavity flow and flow past a circular cylinder. We also assess the accuracy of the method for an unsteady flow around an arrangement of two cylinders in tandem and comparisons with results obtained using a monolithic approach reveal good general agreement.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{el-amrani_2513,

title = {Error estimates for a viscosity-splitting scheme in time applied to non-Newtonian fluid flows},

author = {Mofdi El-Amrani and Anouar Obbadi and Mohammed Seaid and Driss Yakoubi},

url = {https://www.sciencedirect.com/science/article/pii/S0045782523007636?dgcid=coauthor},

year  = {2024},

date = {2024-02-01},

journal = {Computer Methods In Applied Mechanics And Engineering},

volume = {419},

pages = {116639},

abstract = {A time fractional-step method is presented for numerical solutions of the incompressible non-Newtonian fluids for which the viscosity is non-linear depending on the shear-rate magnitude according to a generic model. The method belongs to a class of viscosity-splitting procedures and it consists of separating the convection term and incompressibility constraint into two time steps. Unlike the conventional projection methods, the viscosity is not dropped in the last step allowing to enforce the full original boundary conditions on the end-of-step velocity which eliminates any concerns about the numerical boundary layers. We carry out a rigorous error analysis and provide a full first-order error estimate for both the velocity and pressure solutions in the relevant norms. Numerical results are presented for two test examples of non-

Newtonian fluid flows to demonstrate the theoretical analysis and confirm the reliability of this viscosity-splitting scheme.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{salhi_2456,

title = {Convergence analysis of a class of iterative methods for propagation of reaction fronts in porous media},

author = {Loubna Salhi and Mohammed Seaid and Driss Yakoubi},

url = {https://www.sciencedirect.com/science/article/pii/S0045782523006485?dgcid=author},

year  = {2024},

date = {2024-01-01},

journal = {Computer Methods In Applied Mechanics And Engineering},

volume = {418},

number = {Part A},

pages = {116524},

abstract = {We present an iterative scheme for the numerical analysis of propagating reaction front problems in porous media satisfying an Arrhenius-type law. The governing equations consist of the Darcy equations for the pressure and flow field coupled to two convection-diffusion-reaction equations for the temperature and depth of conversion.

 Well-posedness, existence and uniqueness of the weak solution are first studied using a fixed-point approach and then, analysis of the proposed iterative scheme is investigated. Numerical results are also presented in order

to validate the theoretical estimates and to illustrate the performance of the proposed scheme.

The obtained results are in line with our expectations for a good numerical resolution with high accuracy and stability behaviors.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{belhamadia_2366,

title = {Existence and uniqueness for a convective phase change model with temperature-dependent viscosity},

author = {Youssef Belhamadia and Jean Deteix and Basma Jaffal-Moutarda and Driss Yakoubi},

url = {https://www.sciencedirect.com/science/article/pii/S0022247X23005620?via%3Dihub},

year  = {2023},

date = {2023-11-01},

journal = {Journal Of Mathematical Analysis And Applications},

volume = {527},

number = {2},

pages = {127559},

abstract = {In this article, we consider a class of phase change model with temperature-dependent viscosity, convection and mixed boundary conditions on a bounded domain that reflect melting and solidification in a variety of real-world applications, such as metal casting and crystal growth. The mathematical model, which is based on the enthalpy formulation, takes into consideration the thermophysical differences between the liquid and solid states. The moving liquid-solid interface is explicitly fulfilled as the energy and momentum equations are solved over the full physical domain. Under particular assumptions, we derive various a priori estimates and prove well-posedness results. Numerical simulation of the model employed in the

paper is presented as an illustration of an example of a melting problem.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{fortin_2280,

title = {High accuracy breaking point detection for stiff DDEs},

author = {André Fortin and Driss Yakoubi},

url = {https://www.sciencedirect.com/science/article/abs/pii/S0893965923000976#d1e179},

year  = {2023},

date = {2023-09-01},

journal = {Applied Mathematics Letters},

volume = {143},

pages = {108665},

abstract = {We have recently introduced a very high order Discontinuous Galerkin (DG) method for the solution of stiff ordinary differential equations (ODEs) and delay differential equations (DDEs). In this communication we focus on the detection of breaking points frequently arising in the solution of stiff DDEs. Breaking points are discontinuities appearing in the solution of DDEs and/or in some of its derivatives. Breaking points affect the efficiency of the numerical method by forcing very small time steps in their vicinity. They also locally affect the solution accuracy. We therefore introduce a very simple breaking point detection algorithm in order to further improve the efficiency our DG method.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yakoubi_2302,

title = {Enhancing the viscosity-splitting method to solve the time-dependent Navier-Stokes equations},

author = {Driss Yakoubi},

url = {https://www.sciencedirect.com/science/article/abs/pii/S100757042300182X},

year  = {2023},

date = {2023-08-01},

journal = {Communications In Nonlinear Science And Numerical Simulation},

volume = {123},

pages = {107264},

abstract = {The viscosity-splitting (VS) scheme for solving the incompressible time-dependent Navier-Stokes equations consists to decouple the full problem into two easy subproblems to resolve.

This method splits the nonlinearity (convection term) and the incompressibility into two different steps. As a result, every subproblem is easier to solve than the Navier-Stokes system. The semi-implicit approach is mostly used in the first step for the nonlinearity term and the intermediate velocity is calculated by dropping the pressure gradient. We then resolve a linear Stokes problem in the next step.

We present a modified viscosity-splitting scheme (Incremental viscosity-splitting) (IVS) to improve this method. This scheme adds the gradient of the pressure (calculated at the previous time step) in the first step and modifies the Stokes equations in the second step to

predict a better value of the intermediate velocity. A manufactured solution and two well-known benchmarks will be used to demonstrate the effectiveness of the suggested strategy.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{bousbia_2353,

title = {Augmented spectral formulation for the Stokes problem with variable viscosity and mixed boundary conditions},

author = {Chaima Bousbia and Yasmina Daikh and Sarra Maarouf and Driss Yakoubi},

url = {https://link.springer.com/article/10.1007/s10092-023-00530-8},

year  = {2023},

date = {2023-06-01},

journal = {Calcolo},

volume = {60},

number = {3},

pages = {36},

abstract = {This paper deals with the analysis of a new augmented formulation in terms of vorticity, velocity and pressure for the Stokes equations with variable viscosity and mixed boundary conditions. The well-posedness of the continuous problem holds under assumptions on the viscosity. When the domain is a parallelepiped, the spectral discretization is proposed using the Galerkin method with numerical integration. Then, we prove the well-posedness of the obtained discrete problem under the same type of conditions on the viscosity. A priori error estimates is then derived for the three

unknowns. Finally, numerical experiments are presented that confirm the interest of

the discretization.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{fortin_2076,

title = {A very high order discontinuous Galerkin method for the numerical solution of stiff DDEs},

author = {André Fortin and Driss Yakoubi},

url = {https://www.sciencedirect.com/science/article/pii/S0096300322008359},

year  = {2023},

date = {2023-04-01},

journal = {Applied Mathematics And Computation},

volume = {443},

pages = {127767},

abstract = {We present a high order discontinuous Galerkin (DG) method for the numerical solution of systems of delay differential equations (DDEs). The method is based on Legendre orthogonal polynomials of high degree k (typically k=10) in each subinterval and is a generalisation to DDEs of a similar method which proved to be very efficient for ordinary differential equations (ODEs). We show how the error can be estimated allowing to control the size of the time step. We also propose a particularly efficient quasi Newton method for the solution of the resulting non linear systems based on a very accurate approximation of the Jacobian matrix that is very easy to implement and with excellent convergence properties. The method is then applied to very stiff systems of DDEs.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{boussoufa_2305,

title = {Numerical analysis for backward Euler spectral discretization for Stokes equations with boundary conditions involving the pressure: part I},

author = {Oussama Boussoufa and Yasmina Daikh and Driss Yakoubi},

url = {https://link.springer.com/article/10.1007/s10092-023-00520-w},

year  = {2023},

date = {2023-04-01},

journal = {Calcolo},

volume = {60},

number = {2},

pages = {1--27},

abstract = {In this paper, we address the study of the time-dependent Stokes system with boundary conditions involving the pressure. We obtain existence and uniqueness for a classof Lipschitz-continuous domains. Next, a spectral discretizations of the problem is

proposed combined with the backward Euler scheme. The discrete spaces are defined in a way to give exactly divergence-free discrete approximations for the velocity. Then, we prove the associated discrete inf-sup condition and derive a priori error estimates.

Finally, some numerical experiments are presented},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{salhi_1885,

title = {Well-posedness and numerical approximation of steady convection-diffusion-reaction problems in porous media},

author = {Loubna Salhi and Mohammed Seaid and Driss Yakoubi},

url = {https://www.sciencedirect.com/science/article/abs/pii/S0898122122003443},

year  = {2022},

date = {2022-08-01},

journal = {Computers & Mathematics With Applications},

volume = {124},

pages = {129-148},

abstract = {We study a class of steady nonlinear convection-diffusion-reaction problems in porous media. The governing equations consist of coupling the Darcy equations for the pressure and velocity fields to two equations for the heat and mass transfer. The viscosity and diffusion coefficients are assumed to be nonlinear depending on the temperature and concentration of the medium. Well-posedness of the coupled problem is analyzed and existence along with uniqueness of the weak solution is investigatedbased on a fixed-point method. An iterative scheme for solving the associated fixed-point problem is proposed and its convergence is studied. Numerical experiments are presented for two examples of coupled convection-diffusion-reaction problems. Applications to radiative heat transfer and propagation of thermal fronts in porous media are also included in this study. The obtained results show good numerical convergence and validate the established theoretical estimates.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{el-amrani_1887,

title = {An iterative scheme for solving acoupled Darcy-convection-diffusion model},

author = {Mofdi El-Amrani and Loubna Salhi and Mohammed Seaid and Driss Yakoubi},

url = {https://www.sciencedirect.com/science/article/pii/S0022247X22006175},

year  = {2022},

date = {2022-08-01},

journal = {Journal Of Mathematical Analysis And Applications},

volume = {517},

number = {2},

pages = {126603},

abstract = {We present an iterative scheme for the numerical analysis of a class of coupled Darcy-convection-diffusion problems modelling flow and heat transfer in porous media. The governing equations consist of the Darcy equations for the flow coupled to a convection-diffusion equation for heat transfer with nonlinear viscosity and diffusion coefficient depending on the temperature. Existence and uniqueness of the weak solution for the considered problem are first analyzed using a fixed-point method and then convergence study of two iterative schemes for the fixed-point algorithm is presented. Two numerical examples are selected to validate the theoretical estimates and to demonstrate the performance of the proposed algorithm. The obtained results support our theoretical expectations for a good numerical convergence with the developed estimates.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{maarouf_1803,

title = {Characteristics/finite element analysis for two incompressible fluid flows with surface tension using level set method},

author = {Sarra Maarouf and Christine Bernardi and Driss Yakoubi},

url = {https://www.sciencedirect.com/science/article/pii/S0045782522001530},

year  = {2022},

date = {2022-03-01},

journal = {Computer Methods In Applied Mechanics And Engineering},

volume = {394},

pages = {114843},

abstract = {In this paper, we present and analyze a finite element level set method based on the method of characteristics for two phase

flow. Surface tension effects are taken into account by the CSF approach. We first write the variational formulation of the problem and investigate its well-posedness. Next, for the discretization, a first order method of characteristics approach for the

evolution of the level set function and for the material derivative of the velocity is used. The velocity and pressure unknowns

are discretized by P2? P1 Taylor-Hood finite elements. Then, in each time step, the interface transport is decoupled from the

Navier-Stokes equations. Well-posedness results for subproblems in this decoupled discrete problem are derived. Furthermore,

under high regularity assumptions, we state error estimates for our scheme. Ultimately, three computational examples illustrate

the performance of the proposed method.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{deteix_1802,

title = {A new energy stable fractional time stepping scheme for the Navier-Stokes/Allen-Cahn diffuse interface model},

author = {Jean Deteix and Gerard Lionel Ndetchoua Kouamoa and Driss Yakoubi},

url = {https://www.sciencedirect.com/science/article/pii/S0045782522001104},

year  = {2022},

date = {2022-02-01},

journal = {Computer Methods In Applied Mechanics And Engineering},

volume = {393},

pages = {114759},

abstract = {In this work, we present an original time-discrete formulation of the coupled equations relating the velocity and pressure

of an unsteady flow of two immiscible fluids and the Allen-Cahn equation describing the interface between both of them. We

first prove this time-discrete formulation (based on the concept of coupled projection scheme (Deteix et al., 2014)) to be well

posed and energy stable. We then propose a new family of iterative schemes for the actual approximation of solutions. We

complete this work with numerical tests illustrating the order of accuracy and applying the new scheme on the well known

rising bubble benchmark.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{el_haddad_1795,

title = {A projection scheme for phase change problems with convection},

author = {Mireille El Haddad and Youssef Belhamadia and Jean Deteix and Driss Yakoubi},

url = {https://www.sciencedirect.com/science/article/pii/S0898122122000013},

year  = {2022},

date = {2022-01-01},

journal = {Computers & Mathematics With Applications},

volume = {108},

number = {1},

pages = {109-122},

abstract = {Numerical modeling of phase change problems with convection is known to be computationally expensive. The main challenge comes from the coupling between Navier-Stokes and heat energy equations. In this paper, we develop a new scheme for phase change problems based on a projection method. The proposed method reduces the size of the system by splitting the temperature, the velocity, and the pressure fields while preserving the accuracy of the simulations. A single-domain approach using a variant of the enthalpy-porosity formulation is employed. Incompressible Navier-Stokes problem with Boussinesq approximation for thermal effects in solid and liquid regions is considered. We regularize the discontinuous variables such as latent heat and material properties by a continuous and differentiable hyperbolic tangent function. The robustness and effectiveness of the proposed scheme are illustrated by comparing the numerical results with numerical and experimental benchmark},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yakoubi_1678,

title = {Analysis of a time--discrete scheme for the Navier-Stokes/Allen-Cahn model},

author = {Driss Yakoubi and Jean Deteix and Gerard Lionel Ndetchoua Kouamoa},

url = {https://www.sciencedirect.com/science/article/pii/S0022247X20309793?via%3Dihub},

year  = {2021},

date = {2021-04-01},

journal = {Journal Of Mathematical Analysis And Applications},

volume = {496},

number = {2},

pages = {124816},

abstract = {This paper address the existence and uniqueness, in suitable functional spaces, of the solution of a non linear system of equations originating from the implicit time discretization of the coupled unsteady Navier-Stokes and Allen-Cahn equations. This result is based on the convergence analysis of an original stabilized fixed point algorithm, from which we also get a maximum principle. Numerical experiments are performed to illustrate the influence of the implicit formulation in comparison to a simpler approach based on a semi-explicit time scheme.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{maarouf_1679,

title = {Analysis of backward Euler/spectral discretization for an evolutionary mass and heat transfer in porous medium},

author = {Sarra Maarouf and Driss Yakoubi},

url = {https://www.sciencedirect.com/science/article/pii/S0022247X20305898?via%3Dihub},

year  = {2020},

date = {2020-12-01},

journal = {Journal Of Mathematical Analysis And Applications},

volume = {492},

number = {1},

pages = {124427},

abstract = {This paper presents the unsteady Darcy's equations coupled with two nonlinear reaction-diffusion equations, namely this system describes the mass concentration and heat transfer in porous media. The existence and uniqueness of the solution are established for both the variational formulation problem and for its discrete one obtained using spectral discretization. Optimal a priori estimates are given using the Brezzi-Rappaz-Raviart theorem. We conclude by some numerical tests which are in agreement with our theoretical results.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{plasman_1680,

title = {A projection scheme for Navier--Stokes with  variable viscosity and natural boundary condition},

author = {Ludovic Plasman and Jean Deteix and Driss Yakoubi},

url = {https://onlinelibrary.wiley.com/doi/10.1002/fld.4851},

year  = {2020},

date = {2020-04-01},

journal = {International Journal for Numerical Methods in Fluids},

volume = {92},

number = {12},

pages = {1845-1865},

abstract = {Combiningthe Navier-Stokes systems with Neumann (or natural) boundary condition to characterize a fluid flow is frequent. The popular projection (or pressure

correction) methods inspired by Chorin and Temam are not well adapted to such boundary condition, which translate in loss of accuracy. If some alternative projection methods have been proposed to reduce the accuracy loss due to the Neumann condition in case of Newtonian fluids, little has been pro-

posed for generalized Newtonian fluids. In this work, we propose two methods

derived from the incremental pressure correction projection that can be used

for fluids with inhomogeneous or variable viscosity with natural boundary condition. Both time and space accuracy of the methods will be illustrated using a manufactured solution.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yakoubi_1683,

title = {An adaptive discontinuous Galerkin method for very stiff systems of ordinary differential equations},

author = {Driss Yakoubi and André Fortin},

url = {https://www.sciencedirect.com/science/article/pii/S0096300319302875?via%3Dihub},

year  = {2019},

date = {2019-10-01},

journal = {Applied Mathematics And Computation},

volume = {358},

pages = {330-347},

abstract = {We present a discontinuous Galerkin (DG) method for the numerical solution of stiff systems of ordinary differential equations (ODEs). We use a standard DG variational formulation with polynomials of degree k in each time interval. We show that the method is A-stable for every k. We then introduce a hierarchical Legendre finite element basis and we show that a whole family of approximations can be obtained simply by truncating the last p degrees of freedom from the computed solution. We show that these approximations converge to order in L2-norm and to order in supremum norm. We then show how this can be used to control the error and the time step length. We present numerical examples of solutions on very stiff problems and on stiff problems with very long time integration where the time step length can vary on many orders of magnitude.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yakoubi_1681,

title = {Shear rate projection schemes for non--Newtonian fluids},

author = {Driss Yakoubi and Jean Deteix},

url = {https://www.sciencedirect.com/science/article/pii/S0045782519303469?via%3Dihub},

year  = {2019},

date = {2019-09-01},

journal = {Computer Methods In Applied Mechanics And Engineering},

volume = {354},

number = {1},

pages = {620-636},

abstract = {The operator splitting approach applied to the Navier-Stokes equations gave rise to various numerical methods for the simulations of the dynamics of fluids. The separate work of Chorin and Temam on this subject gave birth to the so-called projection methods. The most basic of those schemes, the incremental and non-incremental variant (see Guermond et al. 2006) induce an artificial Neumann boundary condition on the pressure. The so-called rotational incremental pressure-correction scheme proposed by Timmermans et al. (1996) gives a consistent equation for the pressure in case of a Newtonian fluids with homogeneous viscosity. In this work we propose a family of projection methods for generalized Newtonian fluids based on an extension of the rotational projection scheme. Called shear rate projections, these methods produce consistent pressure when applied to generalized Newtonian fluids. Accuracy of the methods will be illustrated using a manufactured solution. Numerical experiments for the flow past a cylinder, with a Carreau rheological model, will also be presented},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yakoubi_1685,

title = {A posteriori error estimates of finite element method for the time--dependent Darcy problem in an axisymmetric domain},

author = {Driss Yakoubi and Ajmia Younes Orfi},

url = {https://www-sciencedirect-com.acces.bibl.ulaval.ca/science/article/pii/S0898122119300409?via%3Dihub},

year  = {2019},

date = {2019-05-01},

journal = {Computers & Mathematics With Applications},

volume = {77},

number = {10},

pages = {2833-2853},

abstract = {We consider the time dependent Darcy problem in a three-dimensional axisymmetric domain and, by writing the Fourier expansion of its solution with respect to the angular variable, we observe that each Fourier coefficient satisfies a system of equations on the meridian domain. We propose a discretization of these equations in the case of general solution. This discretization relies on a backward Euler's scheme for the time variable and finite elements for the space variables. We prove a posteriori error estimates that allow for an efficient adaptivity strategy both for the time steps and the meshes. Computations for an example with a known solution are presented which support the a posteriori error estimate.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yakoubi_1687,

title = {A priori error analysis of an Euler implicit,  Finite Element approximation of the unsteady Darcy problem in an axisymmetric domain},

author = {Driss Yakoubi and Ajmia Younes Orfi},

url = {https://global-sci.org/intro/article_detail/aamm/12213.html},

year  = {2018},

date = {2018-10-01},

journal = {Advances In Applied Mathematics And Mechanics},

volume = {10},

number = {2},

pages = {301-321},

abstract = {We consider the time dependent Darcy problem in a three-dimensional axisymmetric domain and, by writing the Fourier expansion of its solution with respect to the angular variable, we observe that each Fourier coefficient satisfies a system of equations on the meridian domain. We propose a discretization of these equations in the case of general solution. This discretization relies on a backward Euler's scheme for the time variable and finite elements for the space variables. We prove a priori error estimates both for the time steps and the meshes.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yakoubi_1688,

title = {Improving the pressure accuracy in a projection scheme for incompressible fluids with variable viscosity},

author = {Driss Yakoubi and Jean Deteix},

url = {https://www.sciencedirect.com/science/article/pii/S0893965917303658?via%3Dihub},

year  = {2018},

date = {2018-05-01},

journal = {Applied Mathematics Letters},

volume = {79},

pages = {111-117},

abstract = {The incremental projection scheme and its enhanced version, the rotational projection scheme are powerful and commonly used approaches producing efficient numerical algorithms for solving the Navier-Stokes equations. However, the much improved rotational projection scheme cannot be used on models with non-homogeneous viscosity, imposing the use of the less accurate incremental projection. This paper presents a projection method for the Navier-Stokes equations for fluids having variable viscosity, giving a consistent pressure and increased accuracy in pressure when compared to the incremental projection. The accuracy of the method will be illustrated using a manufactured solution.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yakoubi_1690,

title = {Spectral   discretization of  the Navier-Stokes problem with mixed boundary  conditions},

author = {Driss Yakoubi},

url = {https://www-sciencedirect-com.acces.bibl.ulaval.ca/science/article/pii/S0168927417300387?via%3Dihub},

year  = {2017},

date = {2017-08-01},

journal = {Applied Numerical Mathematics},

volume = {118},

pages = {33-49},

abstract = {We consider a variational formulation of the three dimensional Navier-Stokes equations provided with mixed boundary conditions. We write this formulation with three independent unknowns: the vorticity, the velocity and the pressure. Next, we propose a discretization by spectral methods. A detailed numerical analysis leads to a priori error estimates for the three unknowns.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yakoubi_1686,

title = {3D Model for Coupled Turbulent Fluids: Numerical Analysis of Finite Element Approximation},

author = {Driss Yakoubi and Tomas Chacon Rebollo},

url = {https://academic.oup.com/imajna/article-abstract/38/4/1927/4099779?redirectedFrom=fulltext},

year  = {2017},

date = {2017-07-01},

journal = {IMA Journal of Numerical Analysis},

volume = {38},

number = {4},

pages = {1927-1958},

abstract = {This article deals with the numerical analysis of a coupled two-fluid Reynolds-averaged Navier-Stokes (RANS) turbulence model, such as atmosphere-ocean flow. Each fluid is modeled by the coupled steady Stokes equations with the equation for the turbulent kinetic energy (TKE). In this model, the eddy viscosities for velocity and TKE depend on the TKE, the production (source) term for the TKEs is only in L1 and the boundary condition for the TKEs on the interface between the two flows depends quadratically on the difference of velocities. To overcome the lack of regularity, we approximate the initial system by a regularized system, in which the eddy viscosities and source terms for the TKEs are regularized by convolution. We perform a full finite element discretization of the regularized model, combined with a decoupled iterative linearization procedure. We prove that the discrete scheme converges to the continuous scheme for large enough eddy viscosities in natural norms. Finally, we present some numerical tests where we study the accuracy of the procedure, and simulate a realistic flow in which an imposed wind in the upper atmosphere generates an upwelling in the oceanic flow},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{abdellatif_1689,

title = {A priori error analysis of the implicit Euler, spectral discretization of a nonlinear equation for a flow in a partially saturated porous media},

author = {Nahla Abdellatif and Christine Bernardi and Moncef Touihri and Driss Yakoubi},

url = {https://www.degruyter.com/document/doi/10.1515/apam-2016-0084/html},

year  = {2016},

date = {2016-08-01},

journal = {Advances in Pure and Applied Mathematics},

volume = {9},

number = {1},

pages = {1-27},

abstract = {The aim of this work is the numerical study of a nonlinear equation, which models the water flow in a partially saturated underground porous medium under the surface. We propose a discretization of this equation that combines Euler's implicit scheme in time and spectral methods in space. We prove optimal error estimates between the continuous and discrete solutions. Some numerical experiments confirm the interest of this approach. We present numerical experiments which are in perfect coherence with the analysis.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yakoubi_1691,

title = {Spectral discretization of a model for organic pollution in waters},

author = {Driss Yakoubi},

url = {https://onlinelibrary-wiley-com.acces.bibl.ulaval.ca/doi/10.1002/mma.3899},

year  = {2016},

date = {2016-03-01},

journal = {Mathematical Methods In The Applied Sciences},

volume = {39},

number = {18},

pages = {5192-5202},

abstract = {We are interested in a mixed reaction diffusion system describing the organic pollution in stream-waters. In this work, we propose a mixed-variational formulation and recall its well-posedness. Next, we consider a spectral discretization of this problem and establish nearly optimal error estimates. Numerical experiments confirm the interest of this approach.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yakoubi_1692,

title = {Spectral discretization of an unsteady flow through a porous solid},

author = {Driss Yakoubi},

url = {https://link-springer-com.acces.bibl.ulaval.ca/article/10.1007%2Fs10092-015-0168-6},

year  = {2015},

date = {2015-12-01},

journal = {Calcolo},

volume = {53},

pages = {659-690},

abstract = {We consider the non stationary flow of a viscous incompressible fluid in a rigid homogeneous porous medium provided with mixed boundary conditions. Since the boundary pressure can present high variations, the permeability of the medium also depends on the pressure, so that the problem is nonlinear. We propose a discretization of this equation that combines Euler's implicit scheme in time and spectral methods in space. We prove optimal a priori error estimates and present some numerical experiments which confirm the interest of the discretization.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yakoubi_1693,

title = {Spectral discretization of Darcy's equations coupled with the heat equation},

author = {Driss Yakoubi},

url = {https://academic-oup-com.acces.bibl.ulaval.ca/imajna/article/36/3/1193/1751140#36218027},

year  = {2015},

date = {2015-10-01},

journal = {IMA Journal of Numerical Analysis},

volume = {36},

number = {3},

pages = {1193-1216},

abstract = {In this paper, we consider the heat equation coupled with Darcy's law with a nonlinear source term describing heat production due to an exothermic chemical reaction. The existence and uniqueness of a solution are established. Next, a spectral discretization of the problem is presented and thoroughly analysed. Finally, we present some numerical experiments which confirm the interest of the discretization.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yakoubi_1694,

title = {Finite element discretization of the Stokes and Navier--Stokes equations with boundary condition on the pressure},

author = {Driss Yakoubi},

url = {https://epubs-siam-org.acces.bibl.ulaval.ca/doi/10.1137/140972299},

year  = {2015},

date = {2015-04-01},

journal = {Siam Journal On Numerical Analysis},

volume = {53},

number = {3},

pages = {1256-1279},

abstract = {We consider the Stokes and Navier--Stokes equations with boundary conditions of Dirichlet type on the velocity on one part of the boundary and involving the pressure on the rest of the boundary. We write the variational formulations of such problems. Next we propose a finite element discretization of them and perform the a priori and a posteriori analysis of the discrete problem. Some numerical experiments are presented in order to justify our strategy.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yakoubi_1695,

title = {A Coupled prediction scheme for solving the Navier-Stokes and convection-diffusion equations,},

author = {Driss Yakoubi},

url = {https://epubs-siam-org.acces.bibl.ulaval.ca/doi/abs/10.1137/130942516},

year  = {2014},

date = {2014-10-01},

journal = {Siam Journal On Numerical Analysis},

volume = {52},

number = {5},

pages = {2415-2439},

abstract = {This paper presents a new algorithm for the numerical solution of the Navier--Stokes equations coupled with the convection-diffusion equation. After establishing convergence of the semi-discrete formulation at each time step, we introduce a new iterative scheme based on a projection method called the coupled prediction scheme. We show that even though the predicted temperature is advected by a velocity prediction which is not necessarily divergence free, the theoretical time accuracy of the global scheme is conserved. From a numerical point of view, this new approach gives a faster and more efficient algorithm compared to the usual fixed-point approaches.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yakoubi_1696,

title = {An immersed boundary method for fluid flows around rigid objects},

author = {Driss Yakoubi},

url = {https://onlinelibrary-wiley-com.acces.bibl.ulaval.ca/doi/10.1002/fld.3884},

year  = {2014},

date = {2014-02-01},

journal = {International Journal for Numerical Methods in Fluids},

volume = {75},

number = {1},

pages = {63-80},

abstract = {In this paper, we present an immersed boundary method for solving fluid flow problems in the presence of static and moving rigid objects. A FEM is used starting from a base mesh that does not represent exactly rigid objects (non?body?conforming mesh). At each time step, the base mesh is locally modified to provide a new mesh fitting the boundary of the rigid objects. The mesh is also locally improved using edge swapping to enhance the quality of the elements. The Navier-Stokes equations are then solved on this new mesh. The velocity of moving objects is imposed through standard Dirichlet boundary conditions. We consider a number of test problems and compare the numerical solutions with those obtained on classical body?fitted meshes whenever possible.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yakoubi_1697,

title = {Influence of the spray retroaction on the airflow},

author = {Driss Yakoubi},

url = {https://www.esaim-proc.org},

year  = {2010},

date = {2010-12-01},

journal = {Esaim: proceedings and surveys},

volume = {30},

pages = {153-165},

abstract = {In this work, we investigate the influence of a spray evolving in the air, in the respiration

framework. We consider two kinds of situations: a moving spray in a motionless fluid, and motionless

particles in a Poiseuille flow. We observe that the spray retroaction may not be neglected in some

situations which can really happen, for instance, when one considers rather big particles, as it is possible

for polluting particles and even for some therapeutic aerosols. The retroaction is even responsible for

increasing the deposition phenomenon.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yakoubi_1699,

title = {An Iterative Procedure to Solve a Coupled Two-Fluids Turbulence Model},

author = {Driss Yakoubi},

url = {https://www-esaim-m2an-org.acces.bibl.ulaval.ca/articles/m2an/abs/2010/04/m2an0827/m2an0827.html},

year  = {2010},

date = {2010-08-01},

journal = {Esaim-Mathematical Modelling And Numerical Analysis-Modelisation Mathematique Et Analyse Numerique},

volume = {44},

number = {4},

pages = {693 - 713},

abstract = {This paper introduces a scheme for the numerical approximation of a model for two turbulent flows with coupling at an interface. We consider the variational formulation of the coupled model, where the turbulent kinetic energy equation is formulated by transposition. We prove the convergence of the approximation to this formulation for 3D flows for large turbulent viscosities and smooth enough flows, whenever bounded in W1,p Sobolev norms for p large enough. Under the same assumptions, we show that the limit is a solution of the initial problem. Finally, we give some numerical experiments to enlighten the theoretical work.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yakoubi_1698,

title = {Numerical Model for the 2D Simulation of the Respiration},

author = {Driss Yakoubi},

url = {https://www.esaim-proc.org/articles/proc/abs/2009/03/proc092810/proc092810.html},

year  = {2009},

date = {2009-12-01},

journal = {Esaim: proceedings and surveys},

volume = {28},

pages = {162-181},

abstract = {In this article we are interested in the simulation of the air flow in the bronchial tree. The model we use has already been described in [2] and is based on a three part description of the respiratory tract. This model leads, after time discretization, to a Stokes system with non standard dissipative boundary conditions that cannot be easily and directly implemented in most FEM software, in particular in FreeFEM++ [11]. The objective is here to provide a new numerical method that could be implemented in any softwares. After describing the method, we illustrate it by two-dimensional simulations.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{yakoubi_1700,

title = {A Lower Bound for the Inf-Sup Condition's Constant for the Divergence Operator},

author = {Driss Yakoubi},

url = {https://www-sciencedirect-com.acces.bibl.ulaval.ca/science/article/pii/S1631073X08000915?via%3Dihub},

year  = {2008},

date = {2008-03-01},

journal = {Comptes Rendus Mathematique},

volume = {346},

number = {9-10},

pages = {533-538},

abstract = {The inf-sup condition plays an important role in problems from fluid mechanics. The purpose of this Note is to give, for any connected bounded open set ? with a Lipschitz-continuous boundary, a lower bound for the inf-sup condition's constant that only depends on the norm of the harmonic trace lifting on ? and on the where is a constant defined by},

keywords = {},

pubstate = {published},

tppubtype = {article}

}