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Zh. Vychisl. Mat. Mat. Fiz., 2007, Volume 47, Number 12, Pages 2055–2075 (Mi zvmmf211)  

This article is cited in 25 scientific papers (total in 25 papers)

Piecewise parabolic method on local stencil for gasdynamic simulations

M. V. Popov, S. D. Ustyugov

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia

Abstract: A numerical method based on piecewise parabolic difference approximations is proposed for solving hyperbolic systems of equations. The design of its numerical scheme is based on the conservation of Riemann invariants along the characteristic curves of a system of equations, which makes it possible to discard the four-point interpolation procedure used in the standard piecewise parabolic method (PPM) and to use the data from the previous time level in the reconstruction of the solution inside difference cells. As a result, discontinuous solutions can be accurately represented without adding excessive dissipation. A local stencil is also convenient for computations on adaptive meshes. The new method is compared with PPM by solving test problems for the linear advection equation and the inviscid Burgers equation. The efficiency of the methods is compared in terms of errors in various norms. A technique for solving the gas dynamics equations is described and tested for several one-and two-dimensional problems.

Key words: numerical methods in gas dynamics, local stencil, Riemann invariants, numerical methods, hyperbolic systems of equations, PPM, PPML.

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English version:
Computational Mathematics and Mathematical Physics, 2007, 47:12, 1970–1989

Bibliographic databases:

UDC: 519.633
Received: 30.05.2007
Revised: 05.06.2007

Citation: M. V. Popov, S. D. Ustyugov, “Piecewise parabolic method on local stencil for gasdynamic simulations”, Zh. Vychisl. Mat. Mat. Fiz., 47:12 (2007), 2055–2075; Comput. Math. Math. Phys., 47:12 (2007), 1970–1989

Citation in format AMSBIB
\by M.~V.~Popov, S.~D.~Ustyugov
\paper Piecewise parabolic method on local stencil for gasdynamic simulations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 12
\pages 2055--2075
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 12
\pages 1970--1989

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
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    2. Popov M.V., Ustyugov S.D., “Piecewise Parabolic Method on a Local Stencil for Gas Dynamics and MHD”, Numerical Analysis and Applied Mathematics, AIP Conference Proceedings, 1048, 2008, 436–439  crossref  mathscinet  adsnasa  isi  scopus
    3. Ustyugov S.D., “Realistic Simulation of Local Solar Supergranulation”, Exploring the Solar System and the Universe, AIP Conference Proceedings, 1043, 2008, 234–237  crossref  adsnasa  isi  scopus
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    5. Popov M.V., Ustyugov S.D., “Piecewise parabolic method on a local stencil for hyperbolic conservation laws”, Hyperbolic Problems: Theory, Numerics and Applications, Part 2, Proceedings of Symposia in Applied Mathematics, 67, no. 2, 2009, 869–878  crossref  mathscinet  zmath  isi
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    10. Ray M.P., Puranik B.P., Bhandarkar U.V., “Development and Assessment of Several High-Resolution Schemes for Compressible Euler Equations”, Int. J. Comput. Methods, 11:1 (2014), 1350049  crossref  mathscinet  zmath  isi  elib  scopus
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    16. Kulikov I. Vorobyov E., “Using the PPML approach for constructing a low-dissipation, operator-splitting scheme for numerical simulations of hydrodynamic flows”, J. Comput. Phys., 317 (2016), 318–346  crossref  mathscinet  zmath  isi  elib  scopus
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