An energy-stable method for solving the incompressible Navier–Stokes equations with non-slip boundary condition
- 주제(키워드) Computational fluid dynamics , Energy stability , Finite difference method , Navier–Stokes&apos , equations , Stability analysis
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 Academic Press Inc.
- 발행년도 2018
- URI http://www.dcollection.net/handler/ewha/000000149775
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.jcp.2018.01.030
초록/요약
We introduce a stable method for solving the incompressible Navier–Stokes equations with variable density and viscosity. Our method is stable in the sense that it does not increase the total energy of dynamics that is the sum of kinetic energy and potential energy. Instead of velocity, a new state variable is taken so that the kinetic energy is formulated by the L2 norm of the new variable. Navier–Stokes equations are rephrased with respect to the new variable, and a stable time discretization for the rephrased equations is presented. Taking into consideration the incompressibility in the Marker-And-Cell (MAC) grid, we present a modified Lax–Friedrich method that is L2 stable. Utilizing the discrete integration-by-parts in MAC grid and the modified Lax–Friedrich method, the time discretization is fully discretized. An explicit CFL condition for the stability of the full discretization is given and mathematically proved. © 2018 Elsevier Inc.
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