Parallel CUDA implementation of the algorithm for solving the Navier-Stokes equations using the fictitious domain method (Journal of Mathematics Mechanics and Computer Science, 2021)
An important direction in the development of numerical simulation methods is the study of approximate methods for solving problems of mathematical physics in complex multidimensional fields. To solve many applied problems in irregular areas, the method of fictitious areas is widely used, which is characterized by a high degree of automation of programming. The main idea of the method of fictitious domains is that the problem is solved not in the original complex domain, but in some other, simpler domain. This allows you to create software immediately for a fairly wide class of problems with arbitrary computational domains. The possibilities of applying the method of fictitious domains to the problems of hydrodynamics in the variables “stream function, velocity vortex” have been considered in many works. In this paper, we study a numerical method for solving the Navier-Stokes equations in doubly connected domains. To solve the two-dimensional Navier-Stokes equations in irregular domains, an approximate method based on the method of fictitious domains is proposed. A computational finite difference algorithm for solving an auxiliary problem of the method of fictitious domains has been developed. The results of numerical simulation of two-dimensional Navier-Stokes equations by the method of fictitious domains with continuation by the lowest coefficient are presented. For this problem, a parallel algorithm was developed using CUDA technologies, which was tested on various mesh dimensions
Keywords: Navier-Stokes equations; stream function; velocity vortex; fictitious domains method; boundary conditions; CUDA; parallel algorithm; high performance computing