Mass Conservative and Energy Stable Finite Difference Methods for the Quasi-incompressible Navier-Stokes-Cahn-Hilliard system: Primitive Variable and Projection-Type Schemes
| Autor: | Zhenlin Guo, Steven M. Wise, John Lowengrub, Ping Lin |
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| Rok vydání: | 2017 |
| Předmět: |
Mechanical Engineering
Computational Mechanics Finite difference method Mathematics::Analysis of PDEs General Physics and Astronomy Context (language use) 010103 numerical & computational mathematics Numerical Analysis (math.NA) 01 natural sciences Instability Projection (linear algebra) Computer Science Applications 010101 applied mathematics Physics::Fluid Dynamics Multigrid method Flow (mathematics) Mechanics of Materials Compressibility Projection method FOS: Mathematics Applied mathematics Mathematics - Numerical Analysis 0101 mathematics Mathematics |
| DOI: | 10.48550/arxiv.1703.06606 |
| Popis: | In this paper we describe two fully mass conservative, energy stable, finite difference methods on a staggered grid for the quasi-incompressible Navier–Stokes–Cahn–Hilliard (q-NSCH) system governing a binary incompressible fluid flow with variable density and viscosity. Both methods, namely the primitive method (finite difference method in the primitive variable formulation) and the projection method (finite difference method in a projection-type formulation), are so designed that the mass of the binary fluid is preserved, and the energy of the system equations is always non-increasing in time at the fully discrete level. We also present an efficient, practical nonlinear multigrid method – comprised of a standard FAS method for the Cahn–Hilliard equation, and a method based on the Vanka-type smoothing strategy for the Navier–Stokes equation – for solving these equations. We test the scheme in the context of Capillary Waves, rising droplets and Rayleigh–Taylor instability. Quantitative comparisons are made with existing analytical solutions or previous numerical results that validate the accuracy of our numerical schemes . Moreover, in all cases, mass of the single component and the binary fluid was conserved up to 1 0 − 8 and energy decreases in time. |
| Databáze: | OpenAIRE |
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