On the Reliability of Kolgan Reconstruction in Godunov Method for the Numerical Solution of Hydrodynamic Equations

Abstract: This paper describes a construction of Godunov’s method with a reconstruction of the physical variables by using Kolgan’s scheme. Although this scheme has received a great deal of criticism, we have verified in detail a combination of Godunov’s method with Kolgan’s linear reconstruction using a set of one-dimensional tests for typical problems of computational gravitational hydrodynamics. These tests have shown that a major problem in reproducing various types of hydrodynamic flows is the method used to solve the Riemann problem. Kolgan’s reconstruction only makes it possible to decrease the dissipation of the numerical solution obtained by using Godunov’s classical method with linear or nonlinear discontinuity breakdown. This dissipation does not deteriorate the solution by non-physical oscillations and similar artifacts.