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On a SAV-MAC scheme for the Cahn-Hilliard-Navier-Stokes Phase Field Model

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arxiv 1905.08504 v1 pith:MLAJKLR4 submitted 2019-05-21 math.AP

classification math.AP
keywords schemefieldphasecahn-hilliard-navier-stokeserrormodelnumericalsecond-order
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We construct a numerical scheme based on the scalar auxiliary variable (SAV) approach in time and the MAC discretization in space for the Cahn-Hilliard-Navier-Stokes phase field model, and carry out stability and error analysis. The scheme is linear, second-order, unconditionally energy stable and can be implemented very efficiently. We establish second-order error estimates both in time and space for phase field variable, chemical potential, velocity and pressure in different discrete norms. We also provide numerical experiments to verify our theoretical results and demonstrate the robustness and accuracy of the our scheme.

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Cited by 1 Pith paper

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  1. An efficient and convergent finite element scheme for Cahn--Hilliard equations with dynamic boundary conditions

    math.NA 2019-08 accept novelty 7.0 of 10

    A finite element scheme for Cahn-Hilliard equations with dynamic boundary conditions is unconditionally energy stable, mass conservative, and proven to converge to weak solutions.

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