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KIAM Preprint № 117, Moscow, 2020
Authors: Aristova E. N., Astafurov G.O.
Comparison of dissipative-dispersion properties of some conservative difference schemes
Abstract:
Schemes with a compact template are very attractive for the numerical solution of the transport equation in the presence of complex contact discontinuities and external boundaries. A numerical scheme in which the construction is based on a minimal two-point stensil in each direction is called bicompact. Without expanding the list of required values in the cell, the maximum order of approximation of the scheme is two. The class of such schemes includes the Goloviznin-Chetverushkin scheme. To increase the approximation order, it is needed to expand the list of required variables. The approximation orders can be independent in space and time, both in bicompact Rogov schemes, and consistent, as is most often the case in interpolation-characteristic methods. In this paper, the dissipative-dispersion properties of three different conservative bicompact schemes for advection equation are investigated. It is shown that a modification of the CIP (Cubic Interpolation Polynomial) scheme based on Hermitian interpolation has an extra-small variance for almost any Courant numbers, which makes it very weakly non-monotonic.
Keywords:
advection equation, transport equation, bicompact schemes, grid-characteristic schemes, conservative schemes, dispersion of the difference scheme, dissipation of the difference scheme, CIP method modification
Publication language: russian,  pages: 22
Research direction:
Mathematical problems and theory of numerical methods
Russian source text:
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About authors:
  • Aristova Elena Nikolaevna,  orcid.org/0000-0003-1653-8166KIAM RAS
  • Astafurov Gleb Olegovich,  orcid.org/0000-0002-3527-8681KIAM RAS