Three-Dimensional Coupling Compact Finite Difference Methods for Navier-Stokes Equations

Abstract

The higher-order three- dimensionai coupling compact finite difference methods are proposed for solving the three- dimensional time-dependent incompressible Navier-Stokes equations. In the paper, the higher-order three-dimensional coupling compact finite difference schemes for the Poisson equation and Hemholtz equation, which not only have higher accuracy and resolution, but also applies to calculate points near the boundary, are presented, thereby overcomes the difficult of the general higher-order central finite difference scheme not applied to points near the boundary. Combining these coupling compact finite difference schemes with the time splitting method, the compact finite difference methods for the time-dependent incompressible Navier-Stokes equations are constructed. This finite difference method can be apply to more general boundary conditions and flows in more general domains as compared with the general spectral methods. And then the generation, development and evolution of the turbulent spots in the channel flow are directly numerical simulated using this difference method. The results are in agreement with the experiment and prove availability of this difference method.