STABILITY AND ACCURACY ANALYSES FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON THE STAGGERED TRIANGULAR GRID

摘要

Stability and accuracy analyses for the discretized incompressible Navier-Stokes equations on the staggered triangular grid are performed in this article. The discretized equations are derived by a finite-volume procedure with a term-by-term consideration of flow convection, pressure gradient, and diffusion contributions, which results in a highly comprehensible solution procedure. The staggered grid where pressure is calculated at the cell center and velocity on the cell faces, is adopted to eliminate the pressure checkerboard problem, which may occur in a nonstaggered grid. Stability study based on Fourier analysis provides the mathematical explanation for the prevention of the unphysical pressure field. Accuracy of the discretized equations is depicted with the truncation error term derived from Taylor series expansion. A previous formulation is proven to be conditionally consistent, and therefore a modified version is proposed to provide rm unconditionally consistent discretization regardless of the grid stretching or distortion. The present work supplies a stringent mathematical foundation for further applications of incompressible flow calculations with the staggered triangular grid. [References: 24]