Testing the First Order Accurate Godunov Method on Some Prototype and Applied Problems

Abstract

The Godunov method of first order accuracy continues to attract the attention of researchers both because of its simple implementation and its sufficiently high numerical accuracy subject to relatively modest resource requirements. However, it is necessary to constantly verify that the method indeed produces acceptable accuracy. We test the method on a number of one- and two-dimensional prototype problems and compare the results with analytical and numerical solutions obtained by higher accuracy schemes. The results for the method tested are quite acceptable. We also compare the solutions of applied problems on flows in supersonic, freely expanding jets and on supersonic flow past blunt bodies. The results for these problems are also positive.