A UNIFIED STABILIZED FINITE VOLUME METHOD FOR STOKES AND DARCY EQUATIONS

Boukabache, Akram;Kechkar, Nasserdine

• Received : 2018.09.20
• Accepted : 2018.12.13
• Published : 2019.07.01
• 50 9

Abstract

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.

Keywords

finite volumes;collocated discretizations;Stokes equation;Darcy equation;stabilized methods

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