An implementation of the splitting scheme on staggered grids for computing nonstationary flows of viscous incompressible fluid

Abstract

Discretization of equations describing nonstationary flows of viscous incompressible fluid is considered on the basis of the finite difference method and the splitting scheme with the use of Cartesian nonuniform staggered grids. The features of boundary condition specifications for the sought-for functions and the peculiarities of construction of computational meshes are discussed. Discretization of time and spatial derivatives are analyzed in detail. A comparison of different iteration methods for solving the pressure Poisson equation is given. The possibilities of the approach developed are illustrated by the example of solving the problem of transverse flow around a circular cylinder.