Explicit Difference Scheme N-fold Splitting For the Vortex Equation in a Viscous Incompressible Fluid

Abstract

This work is the first to consider the possibility of N-fold (n=100,200) splitting of an explicit difference scheme for the vortex equation in the system of equations of a hydrodynamic problem in a rectangular cavity with a viscous incompressible fluid and with the Reynolds number Re=1000. The algorithm proposed in the work allows us to significantly increase the maximum time step per iteration of the general problem and reduce the total calculation time by tens to hundreds of times. The splitting algorithm for the vortex equation explicit difference scheme is effective if the time spent by the program on the splitting cycle is many times less than the general problem on one iterationsolving time. It is shown numerically that the solution without splitting qualitatively coincides with the solution of the split circuit (match to five significant figures). In this case, the solution to the problem without splitting is not completely steady (the first five significant digits are constant in time after 400000 it-erations). It is shown numerically that two-layer and three-layer explicit difference schemes have steady-state solutions with fields matching in 11-12 significant signs at each node of the computational grid (velocity, vortex, stream function) after 21000 iterations.