The experience of use the Gauss method for solving finite difference schemes of Navier–Stokes equations in the stream function-vorticity formulation

The efficiency of the use of direct methods for solving the Linear finite difference schemes for Navier–Stokes equations was studied. The software package used the Intel Math Kernel Library, which contains a parallel algorithm for LU factorization of matrices, to solve systems of linear equations with sparse matrices. The algorithms were used to solve the problem of Rayleigh–Benard convection in a rectangular region for Rayleigh numbers near critical values. Мodern methods for solving linear equations with band structure allow to construct fast and robust algorithms for the Navier–Stokes equations based on the coupled solution of the equations for the stream function and vorticity.