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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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참고문헌 (15)
참고문헌 신청
S. Badia / 2009 / Unified stabilized finite element formulations for the Stokes and the Darcy problems / SIAM J. Numer. Anal 47(3):1971~2000
E. Burman / 2005 / Stabilized Crouzeix-Raviart element for the Darcy-Stokes problem / Numer. Methods Partial Di erential Equations 21(5):986~997
M. Cui / 2010 / Unified analysis of finite volume methods for the Stokes equations / SIAM J. Numer. Anal 48(3):824~839
R. Eymard / 2000 / Handbook of numerical analysis, Vol. VII / North-Holland :713~1020
R. Eymard / 2006 / On a stabilized colocated finite volume scheme for the Stokes problem / M2AN Math. Model. Numer. Anal 40(3):501~527
E. Burman / 2005 / Stabilized Crouzeix-Raviart element for the Darcy-Stokes problem / Numer. Methods Partial Di erential Equations 21(5):986~997
M. Cui / 2010 / Unified analysis of finite volume methods for the Stokes equations / SIAM J. Numer. Anal 48(3):824~839
R. Eymard / 2000 / Handbook of numerical analysis, Vol. VII / North-Holland :713~1020
R. Eymard / 2006 / On a stabilized colocated finite volume scheme for the Stokes problem / M2AN Math. Model. Numer. Anal 40(3):501~527
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