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

Stability and accuracy analyses for the discretized incompressible Nav ier-Stokes equations on the staggered triangular grid are performed in this article. The discretized equations are derived by a finite-volum e procedure with a term-by-term consideration of flow convection, pres sure gradient, and diffusion contributions, which results in a highly comprehensible solution procedure. The staggered grid where pressure i s calculated at the cell center and velocity on the cell faces, is ado pted to eliminate the pressure checkerboard problem, which may occur i n a nonstaggered grid. Stability study based on Fourier analysis provi des 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 pre vious formulation is proven to be conditionally consistent, and theref ore a modified version is proposed to provide rm unconditionally consi stent discretization regardless of the grid stretching or distortion. The present work supplies a stringent mathematical foundation for furt her applications of incompressible flow calculations with the staggere d triangular grid.