NUMERICAL METHODS FOR INCOMPRESSIBLE VISCOUS FLOW

One of the important problems in modern computational physics is the numerical solution of incompressible viscous flow, which, until lately, lacks the systematic difference methods and strict estimation of errors. The key problem is how to deal with nonlinear term, as well as how to describe the stability of computation.In this paper, four methods are proposed, namely, weighted conservative scheme, corrective up-wind scheme, artificial vibration method and partial explicit-implicit weighted method for nonlinear terms, baaed on the physical principle and the feature of discrete model. The definition ofgeneralized stability is given, which suits nonlinear schemes. Two classes of inequalities are proved, which help estimation of errors of multidimensional, multilevel, explicit-implicit weighted, nonlinear difference schemes.The above ideas are also applied to three-dimensional vorticity equations, n-dimenSional Navier-Stokes equations, Korteweg-de Vries-Burgers equation and so on.