High order finite difference method for incompressible flow.

摘要

This work is concerned about a set of computational methods for incompressible flow, whose behavior can be governed by Navier-Stokes Equations (NSE). Finite Difference Schemes are concentrated here. The efficiency of these methods lies in the fact that only Poisson solver and heat equation solver are needed at each time stage. No Stokes-type equation needs to be solved and there is no coupling between momentum and kinematic equations. This makes the whole scheme extremely robust. Stability and convergence analysis are also documented. Some numerical examples are presented, along with perfect accuracy check with each scheme. The topics in this thesis include: Gauge formulation and the corresponding implicit gauge method; Second order scheme based on vorticity formulation, along with the choice of vorticity boundary condition; Stability and convergence analysis of Essentially Compact Fourth Order Scheme (EC4); Computation of flow on multi-connected domain; A fourth order numerical approximation to Boussinesq flow, which are discussed in each chapter, respectively.