A Block - Matrix Iterative Numerical Method for Coupled Solving 2D Navier-Stokes Equations

Abstract

An algorithm for coupled solving 2D Navier - Stokes equations in the stream function φ - vorticity ω variables is presented. Lid driven cavity flow is computed as a test example. Implicit difference schemes on uniform grids are used for discretizing the unsteady Navier - Stokes equations. An iterative method, similar to the BLOCK-ORTHOMIN(К) method, is used for solving block-matrix set of linear algebraic equations at each time step . The non-symmetric block is reversed on each block-iteration by using approximate factorization - OR- THOMIN(1) iterative method. The difference Laplace operator is reversed by means of a direct method. The comparison of the results, provided by coupled solving Navier-Stokes equations with those provided by decoupled (consecutive) solving the equations for ω and φ demonstrate the advantages of the suggested computing technique.