Abstract
In 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.
Original language | English (US) |
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Pages (from-to) | 427-456 |
Number of pages | 30 |
Journal | Journal of Scientific Computing |
Volume | 75 |
Issue number | 1 |
DOIs | |
State | Published - Apr 1 2018 |
Keywords
- Energy stability
- Finite difference methods
- Linear implicit scheme
- Navier–Stokes equation
- Projection method
- Staggered grids
- Upwind scheme
ASJC Scopus subject areas
- Software
- General Engineering
- Computational Mathematics
- Theoretical Computer Science
- Applied Mathematics
- Numerical Analysis
- Computational Theory and Mathematics