Construction of the Algorithm and Computation of the Flow of an Incompressible Fluid Based on the Supporting Operators Method

Abstract

The paper is devoted to the specific problem of continuum mechanics numerical computation of the solution of two-dimensional Navier–Stokes equations for viscous incompressible fluids. The author plans to use the constructed numerical methods in hemodynamics to compute blood flow in elastic vessels. The support operators technique was chosen to construct the methods because it allows to construct conservative numerical methods, which can be relatively easy implemented on unstructured meshes. These properties are very important in hemodynamics. The whole family of such conservative methods was built. One of the methods was tested on the problem of fluid flow between two plane-parallel plates with different values of Reynolds number.