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Bulletin of the Polish Academy of Sciences Technical Sciences

The Journal of Polish Academy of Sciences

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Volume 60, Issue 1 (Mar 2012)

Issues

Implementation of MUSCL-Hancock method into the C++ code for the Euler equations

K. Murawski / K. Murawski
  • Faculty of Mathematics, Physics and Informatics, UMCS, 10 Radziszewskiego St., 20-031 Lublin, Poland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ P. Stpiczyński
  • Institute of Mathematics, UMCS, 1 M. Curie-Sklodowskiej St., 20-031 Lublin, Poland
  • Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, 5 Baltycka St., 44-100 Gliwice, Poland
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2012-04-19 | DOI: https://doi.org/10.2478/v10175-012-0008-7

Implementation of MUSCL-Hancock method into the C++ code for the Euler equations

In this paper we present implementation of the MUSCL-Hancock method for numerical solutions of the Euler equations. As a result of the internal complexity of these equations solving them numerically is a formidable task. With the use of the original C++ code, we developed and presented results of a numerical test that was performed. This test shows that our code copes very well with this task.

Keywords: hyperbolic equations; numerical methods; Godunow methods

  • S. K. Godunov, "A difference scheme for numerical solution of discontinuous solution of hydrodynamic equations", Math. Sb. 47, 271-306 (1959).Google Scholar

  • E. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer, Berlin, 2009.Google Scholar

  • V. P. Kolgan, "Application of the minimum-derivative principle in the construction of finite-difference schemes for numerical analysis of discontinuous solutions in gas dynamics", Uch. Zap. TsaGI 3 (6), 68-77 (1972).Google Scholar

  • B. van Leer, "Towards the ultimate conservative difference scheme. V - A second-order sequel to Godunov method", J. Comp. Phys. 32, 101-136 (1979).Google Scholar

  • B. van Leer, "On the relation between the upwind-differencing schemes of Godunov, Engquist-Osher and Roe", SIAM J. Sci. Statist. Comput. 5 (1), 1-20 (1984).Google Scholar

  • B. van Leer, "Upwind and high-resolution methods for compressible flow: from donor cell to residual distribution schemes", Comm. Computational Physics 1 (2), 192-206 (2006).Google Scholar

  • S. A. E. G. Falle, "Self-similiar jets", MNRAS 250, 581-596 (1991).Google Scholar

  • C. Berthon, "Stability of the MUSCL schemes for the Euler equations", Comm. Math. Sciences 3, 133-158 (2005).Google Scholar

  • C. Berthon, "Why the MUSCL-Hancock scheme is L1-stable", Numer. Math. 104, 27-46 (2006).Google Scholar

  • K. Murawski and D. Lee, "Numerical methods of solving equations of hydrodynamics from perspectives of the code FLASH", Bull. Pol. Ac.: Tech. 59 (3), 81-92 (2011).Web of ScienceGoogle Scholar

  • K. Murawski, "Numerical solutions of magnetohydrodynamic equations", Bull. Pol. Ac.: Tech. 59 (2), 219-226 (2011).Google Scholar

  • P. L. Roe, "Approximate Riemann solvers, parameter vectors and difference schemes", J. Comp. Phys. 43, 357-372, (1981).Google Scholar

  • R. J. LeVeque, Finite-volume Methods for Hyperbolic Problems, Cambridge University Press, Cambridge, 2002.Google Scholar

  • D. Lee and A. E. Deane, "An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics", J. Comput. Phys. 228 (4), 952-975, (2009).Web of ScienceGoogle Scholar

  • J. M. Stone, "The Athena MHD code: extensions, applications, and comparisons to ZEUS", Numerical Modeling of Space Plasma Flows: ASTRONUM-2008 ASP Conf. Series 406, 277-281 (2009).Google Scholar

  • H.-Yu Schive, Yu-C. Tsai, T. Chiueh, "GAMER: A graphic processing unit accelerated adaptive-mesh-refinement code for astrophysics", Astrophys. J. Suppl. 186 (2), 457-484 (2010).Web of ScienceGoogle Scholar

About the article


Published Online: 2012-04-19

Published in Print: 2012-03-01


Citation Information: Bulletin of the Polish Academy of Sciences: Technical Sciences, ISSN (Print) 0239-7528, DOI: https://doi.org/10.2478/v10175-012-0008-7.

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