Solution of three‐dimensional viscous incompressible flows by a multi‐grid method

Abstract

Abstract The three‐dimensional Navier‐Stokes equations for viscous incompressible fluids are discretized on staggered or non‐staggered grids. The system of finite‐difference equations is solved by a multi‐grid method. The method and some possible sources of difficulties and their remedies are described. The numerical algorithm has been applied to the computations of flows in ducts for a range of Reynolds numbers up to 2000. As outflow boundary conditions, either the fully developed flow profile (Dirichlet condition) or parabolic conditions have been applied. The multi‐grid method has a fast rate of convergence (with both types of boundary conditions), and it is not sensitive to the number of mesh points and the Reynolds number. The numerical solution, using parabolic boundary conditions, is insensitive to the location of the outflow boundary, even for large Reynolds numbers, in contrast to the solution with Dirichlet boundary conditions.