Relaxation Parameters for the IQE Iterative Procedure for Solving Semi-Implicit Navier-Stokes Difference Equations

摘要

Numerical solutions of the time-dependent Navier-Stokes equations for a thermally expandable fluid require advancing the unknown flow variables in time by either an implicit, a semi-implicit, or an explicit procedure. Explicit methods require a modest amount of computational effort per time step but require excessively small timestep lengths to ensure numerical stability. On the other hand, implicit and semi-implicit schemes allow the use of large timestep lengths but suffer from increased computational complexities. Fully-implicit methods generate coupled systems of nonlinear equations that must be solved at each point in time, whereas semi-implicit procedures generate coupled systems of linear equations. The focus of this paper is on the use of a recently formulated iterative procedure, called the IQE method, for solving the linear systems produced by a semi-implicit method. The IQE method, for solving the linear systems produced by a semi-implicit method. The IQE method requires the use of a relaxation parameter omega which must be properly chosen to obtain the greatest rate of convergence. Using heuristic arguments, we develop a numerical procedure for estimating near-optimal values of omega . Numerical test results are included. (ERA citation 10:046949)