PARALLEL CUDA IMPLEMENTATION OF THE ALGORITHM FOR SOLVING THE NAVIER-STOKES EQUATIONS USING THE FICTITIOUS DOMAIN METHOD

Abstract

An important direction of development of numerical modeling methods is the study of approximate methods for solving problems of mathematical physics in complex multidimensional domains. To solve many applied problems in irregular domains, the fictitious domain method is widely used, the idea of which is to solve the problem not in the original, but in a simpler domain. This approach allows to create application software packages for numerical modeling of processes in arbitrary computational domains. In this paper, we develop a computational method for solving the Navier-Stokes equations in the Boussinesq approximation in two-connected domains by the fictitious domain method with continuation by lower coefficients. The problem formulation in the current function, velocity vortex variables is considered. A computational algorithm for solving the auxiliary problem of the fictitious domain method based on the finite difference method is developed. A parallel implementation of the algorithm using the CUDA parallel computation architecture is developed, which was tested on various configurations of the computational mesh. The results of computational experiments for the problem under consideration are presented.