REGULARITY ANALYSIS OF AN INCOMPRESSIBLE NAVIER-STOKES ALGORITHM FOR NON-STAGGERED GRIDS

摘要

Regularity analysis of an incompressible Navier-Stokesalgorithm recently proposed by the authors is performed. Suchan analysis is used to determine if the discrete set of equationsretains the elliptic nature of the continuum equations. Theanalysis is especially important for the incompressible equationsbecause the treatment of the velocity-pressure coupling in agiven algorithm affects the ellipticity of the discrete equations.The present algorithm uses a pressure correction approach, butemploys a non-staggered grid instead of the usual staggeredgrid. A Poisson equation for pressure is derived with therelevant compatibility constraint and the momentum equationsare integrated with an Euler-explicit scheme and second-orderaccurate finite volume discretization. The discrete equationsare examined using a discrete Fourier transform. Results showthat the algorithm remains elliptic for moderate Reynoldsnumbers and that the ellipticity of the discrete equations is not afunction of the time integration step as is the case with severalrelated algorithms. This behavior has the desirable effect ofdecoupling the dynamic stability considerations of the timeintegration scheme for the momentum equations from those ofthe Poisson equation. Time step limits can therefore beestimated purely with the standard Von-Neumann stabilityanalysis. Application of the algorithm to shear-driven cavityflow provides numerical confirmation of the analysis formoderate Reynolds numbers.