Study of entropy properties of a linearized version of Godunov's method

The ideas of formulating a weak solution for a hyperbolic system of one-dimensional gas dynamics equations are presented. An important aspect is the examination of the scheme for the fulfillment of the nondecreasing entropy law, which must hold for weak solutions and is obligatory from a physics point of view. The concept of a weak solution is defined in a finite-difference formulation with the help of the simplest linearized version of the classical Godunov scheme. It is experimentally shown that this version guarantees an entropy nondecrease. As a result, the growth of entropy on shock waves can be simulated without using any correction terms or additional conditions.