2025 , Volume 30, № 6, p.76-97

In this paper, the Navier–Stokes equations of an incompressible fluid are solved using the artificial compressibility method. The Godunov scheme is implemented for calculating flows through cell boundaries. Using the Rankin–Hugonio relations and the (𝑢,𝑝)-diagram method, we find an exact solution to the one-dimensional problem of discontinuity decay between two reconstructed values. It is generalized to the multidimensional case, for which an algorithm is proposed for calculating the tangent velocity as a weighted combination of central difference and counterflow interpolations of its values in the adjacent cells. The Godunov scheme is implemented in the CADRUN software package and tested on several two-dimensional problems: the problem of inviscid flow past a cylinder, the problem of viscous stationary flow past a cylinder, the Taylor–Green vortex decay problem and the three-dimensional problem of calculating fluid flow in a hydraulic turbine. The presented results are found to be more accurate compared with the Roe scheme, especially on non-orthogonal grids.