Energy Stability Analysis of Some Fully Discrete Numerical Schemes for Incompressible Navier–Stokes Equations on Staggered Grids
KAUST DepartmentComputational Transport Phenomena Lab
Physical Sciences and Engineering (PSE) Division
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AbstractIn this paper we consider the energy stability estimates for some fully discrete schemes which both consider time and spatial discretizations for the incompressible Navier–Stokes equations. We focus on three kinds of fully discrete schemes, i.e., the linear implicit scheme for time discretization with the finite difference method (FDM) on staggered grids for spatial discretization, pressure-correction schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations, and pressure-stabilization schemes for time discretization with the FDM on staggered grids for the solutions of the decoupled velocity and pressure equations. The energy stability estimates are obtained for the above each fully discrete scheme. The upwind scheme is used in the discretization of the convection term which plays an important role in the design of unconditionally stable discrete schemes. Numerical results are given to verify the theoretical analysis.
CitationChen H, Sun S, Zhang T (2017) Energy Stability Analysis of Some Fully Discrete Numerical Schemes for Incompressible Navier–Stokes Equations on Staggered Grids. Journal of Scientific Computing. Available: http://dx.doi.org/10.1007/s10915-017-0543-3.
SponsorsThe work of Huangxin Chen was supported by the NSF of China (Grant Nos. 11771363, 91630204, 51661135011) and Program for Prominent Young Talents in Fujian Province University. Shuyu Sun acknowledges that this work is supported by the KAUST research fund awarded to the Computational Transport Phenomena Laboratory at KAUST through the Grant BAS/1/1351-01-01.
JournalJournal of Scientific Computing