On the Accuracy of Bicompact Schemes as Applied to Computation of Unsteady Shock Waves

Abstract

Bicompact schemes that have the fourth order of classical approximation in space and a higher order (at least the second) in time are considered. Their accuracy is studied as applied to a quasilinear hyperbolic system of conservation laws with discontinuous solutions involving shock waves with variable propagation velocities. The shallow water equations are used as an example of such a system. It is shown that a nonmonotone bicompact scheme has a higher order of convergence in domains of influence of unsteady shock waves. If spurious oscillations are suppressed by applying a conservative limiting procedure, then the bicompact scheme, though being high-order accurate on smooth solutions, has a reduced (first) order of convergence in the domains of influence of shock waves.

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ACKNOWLEDGMENTS

We are grateful to N.A. Khandeeva, who kindly placed numerical results based on Rusanov’s scheme at our disposal.

Funding

This work was supported by the Russian Science Foundation, grant no. 16-11-10033.

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Correspondence to M. D. Bragin or B. V. Rogov.

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Translated by I. Ruzanova

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Bragin, M.D., Rogov, B.V. On the Accuracy of Bicompact Schemes as Applied to Computation of Unsteady Shock Waves. Comput. Math. and Math. Phys. 60, 864–878 (2020). https://doi.org/10.1134/S0965542520050061

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Keywords:

  • hyperbolic system of conservation laws
  • bicompact schemes
  • shallow water equations
  • orders of local and integral convergence