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RISS 인기검색어
- 검색키워드
- 저자 : Nasserdine Kechkar (검색결과 6 건)
- 무료
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STABILIZED-PENALIZED COLLOCATED FINITE VOLUME SCHEME FOR INCOMPRESSIBLE BIOFLUID FLOWS
Kechkar, Nasserdine,Louaar, Mohammed Korean Mathematical Society 2022 대한수학회지 Vol.59 No.3
In this paper, a stabilized-penalized collocated finite volume (SPCFV) scheme is developed and studied for the stationary generalized Navier-Stokes equations with mixed Dirichlet-traction boundary conditions modelling an incompressible biological fluid flow. This method is based on the lowest order approximation (piecewise constants) for both velocity and pressure unknowns. The stabilization-penalization is performed by adding discrete pressure terms to the approximate formulation. These simultaneously involve discrete jump pressures through the interior volume-boundaries and discrete pressures of volumes on the domain boundary. Stability, existence and uniqueness of discrete solutions are established. Moreover, a convergence analysis of the nonlinear solver is also provided. Numerical results from model tests are performed to demonstrate the stability, optimal convergence in the usual L<sup>2</sup> and discrete H<sup>1</sup> norms as well as robustness of the proposed scheme with respect to the choice of the given traction vector.
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Stabilized-penalized collocated finite volume scheme for incompressible biofluid flows
Nasserdine Kechkar,Mohammed Louaar 대한수학회 2022 대한수학회지 Vol.59 No.3
In this paper, a stabilized-penalized collocated finite volume (SPCFV) scheme is developed and studied for the stationary generalized Navier-Stokes equations with mixed Dirichlet-traction boundary conditions modelling an incompressible biological fluid flow. This method is based on the lowest order approximation (piecewise constants) for both velocity and pressure unknowns. The stabilization-penalization is performed by adding discrete pressure terms to the approximate formulation. These simultaneously involve discrete jump pressures through the interior volume-boundaries and discrete pressures of volumes on the domain boundary. Stability, existence and uniqueness of discrete solutions are established. Moreover, a convergence analysis of the nonlinear solver is also provided. Numerical results from model tests are performed to demonstrate the stability, optimal convergence in the usual $L^2$ and discrete $H^1$ norms as well as robustness of the proposed scheme with respect to the choice of the given traction vector.
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A UNIFIED STABILIZED FINITE VOLUME METHOD FOR STOKES AND DARCY EQUATIONS
Boukabache, Akram,Kechkar, Nasserdine Korean Mathematical Society 2019 대한수학회지 Vol.56 No.4
In this paper, we present and analyze a cell-centered collocated finite volume scheme for incompressible flows to compute solutions simultaneous to Stokes and Darcy equations by applying a pressure jump stabilization term to avoid locking. We prove that the new stabilized FV formulation satisfies a discrete inf-sup condition and error estimates for both problems. Finally, we present some numerical examples confirming this analysis.
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A unified stabilized finite volume method for Stokes and Darcy equations
Akram Boukabache,Nasserdine Kechkar 대한수학회 2019 대한수학회지 Vol.56 No.4
In this paper, we present and analyze a cell-centered collocated finite volume scheme for incompressible flows to compute solutions simultaneous to Stokes and Darcy equations by applying a pressure jump stabilization term to avoid locking. We prove that the new stabilized FV formulation satisfies a discrete inf-sup condition and error estimates for both problems. Finally, we present some numerical examples confirming this analysis.
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MINIMAL LOCALLY STABILIZED Q1-Q0 SCHEMES FOR THE GENERALIZED STOKES PROBLEM
Chibani, Alima,Kechkar, Nasserdine Korean Mathematical Society 2020 대한수학회지 Vol.57 No.5
In this paper, some novel discrete formulations for stabilizing the mixed finite element method Q1-Q0 (bilinear velocity and constant pressure approximations) are introduced and discussed for the generalized Stokes problem. These are based on stabilizing discontinuous pressure approximations via local jump operators. The developing idea consists in a reduction of terms in the local jump formulation, introduced earlier, in such a way that stability and convergence properties are preserved. The computer implementation aspects and numerical evaluation of these stabilized discrete formulations are also considered. For illustrating the numerical performance of the proposed approaches and comparing the three versions of the local jump methods alongside with the global jump setting, some obtained results for two test generalized Stokes problems are presented. Numerical tests confirm the stability and accuracy characteristics of the resulting approximations.
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Quadratic B-spline Galerkin scheme for the solution of a space-fractional Burgers' equation
Khadidja Bouabid,Nasserdine Kechkar 대한수학회 2024 대한수학회지 Vol.61 No.4
In this study, the numerical solution of a space-fractional Burgers' equation with initial and boundary conditions is considered. This equation is the simplest nonlinear model for diffusive waves in fluid dynamics. It occurs in a variety of physical phenomena, including viscous sound waves, waves in fluid-filled viscous elastic pipes, magneto-hydrodynamic waves in a medium with finite electrical conductivity, and one-dimensional turbulence. The proposed QBS/CNG technique consists of the Galerkin method with a function basis of quadratic B-splines for the spatial discretization of the space-fractional Burgers' equation. This is then followed by the Crank-Nicolson approach for time-stepping. A linearized scheme is fully constructed to reduce computational costs. Stability analysis, error estimates, and convergence rates are studied. Finally, some test problems are used to confirm the theoretical results and the proposed method's effectiveness, with the results displayed in tables, 2D, and 3D graphs.
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