Abstract:
A modification of the Godunov method for two-dimensional unsteady equations of gas dynamics is presented, which has a 4th order of approximation in space and a 3rd order in time. The difference scheme of the method is based on the joint discretization of equations in space and time without the use of Runge–Kutta stages, i.e. it is completely discrete. The flows are calculated as the result of solving the Riemann problem with corrections to its arguments. New versions of TVD limiters of central differences are proposed, applied to derivatives above the second order of accuracy. The results of an experimental verification of the approximation order of the method on two-dimensional smooth solutions inside Riemann and Prandtl–Meyer expansion fans are presented. A comparison has been made with other methods, both in terms of accuracy and performance.
