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Finite difference scheme of high-order convergence at a nonstationary shock wave. (Russian. English summary) Zbl 0917.76055
A finite difference scheme is constructed for the hyperbolic system of two conservation laws of the “shallow water” theory. The scheme provides at least the second-order weak convergence when calculating the nonstationary shock wave. It is not monotone; however, unlike other currently available “high-accuracy” schemes (including monotone schemes), the scheme reproduces the Hugoniot conditions with high accuracy and thus preserves the high order of the strong local convergence in the domain of nonstationary shock influence.
MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76L05 Shock waves and blast waves in fluid mechanics
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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