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http://dx.doi.org/10.4134/JKMS.j210211

STABILIZED-PENALIZED COLLOCATED FINITE VOLUME SCHEME FOR INCOMPRESSIBLE BIOFLUID FLOWS  

Kechkar, Nasserdine (Department of Mathematics Faculty of Exact Sciences University Freres Mentouri)
Louaar, Mohammed (Faculty of Mathematics University of Science and Technology Houari Boumediene)
Publication Information
Journal of the Korean Mathematical Society / v.59, no.3, 2022 , pp. 519-548 More about this Journal
Abstract
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 L2 and discrete H1 norms as well as robustness of the proposed scheme with respect to the choice of the given traction vector.
Keywords
Navier-Stokes equations; finite element; finite volume; stabilization;
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