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KIAM Preprint № 8, Moscow, 2019
Authors: Bragin M.D., Rogov B.V.
A conservative limiting method for bicompact schemes
Abstract:
In this work, a new limiting method for bicompact schemes is proposed that preserves them conservative. The method is based upon a finite-element treatment of the bicompact approximation. An analogy between Galerkin schemes and bicompact schemes is established. The proposed method is tested on one-dimensional gasdynamics problems that include the Sedov problem, the Riemann 'peak' problem, and the Shu-Osher problem. It is shown on these examples that bicompact schemes with conservative limiting are significantly more accurate than hybrid bicompact schemes.
Keywords:
bicompact schemes, conservative schemes, monotonicity preserving schemes, hyperbolic equations, discontinuous solutions
Publication language: russian/english,  pages: 26/25
Research direction:
Mathematical problems and theory of numerical methods
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About authors:
  • Bragin Mikhail Dmitrievich,  orcid.org/0000-0002-3990-9583KIAM RAS
  • Rogov Boris Vadimovich,  orcid.org/0000-0001-7664-5866KIAM RAS