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Realization of a second-order Godunov’s method. (English) Zbl 0991.76046

Summary: We present a finite volume scheme of second-order accuracy in time and space to calculate the problems of gas dynamics in Euler approach. When approximating the system of conservation laws on moving grid, we use a time splitting, piecewise linear interpolation of functions, monotonicity algorithm and solution of Riemann problem. Some dispersive properties of the scheme are considered. Finally, we show some results on solving the Cauchy problem for linear advection equation, and initial-boundary value problems for one- and two-dimensional flows including the calculation on adaptive grids.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
76L05 Shock waves and blast waves in fluid mechanics
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