2016
DOI: 10.1137/15m1047891
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Stability and Convergence Analysis of a Decoupled Algorithm for a Fluid-Fluid Interaction Problem

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Cited by 28 publications
(28 citation statements)
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“…This is combined with the variational multiscale stabilization technique for treating flows at high Reynolds numbers. We prove the stability and accuracy of the method, and provide several numerical tests to assess both the quantitative and qualitative features of the computed solution.Numerical methods for solving this type of coupled problems in laminar flow regime have been investigated [3,6,27,1]. In [6], IMEX and geometric averaging (GA) time stepping methods have been proposed (and further developed in [1]) for the Navier-Stokes equations with nonlinear interface condition.The study of AO interaction has received considerable interest in the last thirty years, starting with the seminal paper of Lions, Temam and Wang, [21,22], on the analysis of full equations for AO flow.…”
mentioning
confidence: 99%
“…This is combined with the variational multiscale stabilization technique for treating flows at high Reynolds numbers. We prove the stability and accuracy of the method, and provide several numerical tests to assess both the quantitative and qualitative features of the computed solution.Numerical methods for solving this type of coupled problems in laminar flow regime have been investigated [3,6,27,1]. In [6], IMEX and geometric averaging (GA) time stepping methods have been proposed (and further developed in [1]) for the Navier-Stokes equations with nonlinear interface condition.The study of AO interaction has received considerable interest in the last thirty years, starting with the seminal paper of Lions, Temam and Wang, [21,22], on the analysis of full equations for AO flow.…”
mentioning
confidence: 99%
“…In theory, the unconditionally stable and one order time accuracy partitioned methods for a fully coupled problem is obtained. The estimate of the decoupled fractional time stepping is proved and is as good as the corresponding scheme in .…”
Section: Introductionmentioning
confidence: 86%
“…In the given experiments, the velocity and pressure are approximated by the MINI element ( P 1 b − P 1 element) with respect to the same uniform triangulation, respectively.Example In this example, the computations are carried out in the domains Ω 1 = [0, 1] × [0, 1] and Ω 2 = [0, 1] × [−1, 0]. The prescribed solutions are given by p1t,x,y=p2t,x,y=exptcosπxsinπy, u1,1t,x,y=αx2expt()x12y1, u1,2t,x,y=αitalicxyexpt6x+y3xy+2x2y4x22, u2,1()t,x,y=αxnormalexp()t()x1true(y2x()x1()μ1μ2+1μ11false/...…”
Section: Numerical Verificationmentioning
confidence: 99%
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