Realization of a second-order Godunovʹs method Original Research Article

A finite volume scheme of second-order accuracy in time and space and high effectiveness to calculate the problems of gas dynamics in Euler approach is presented. When approximating the system of conservative laws on the moving grid, a time splitting, piecewise linear interpolation of the functions, monotonicity algorithm and solution of the Riemann problem are used. Some dispersive properties of the scheme are considered. Results of the tests on solving the Cauchy problem for the linear advection equation and initial-boundary value problems of 1-D and 2-D flows, including the calculation on the adaptive grids, are shown.