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

• Autorzy: Murawski K. , Stpiczyński P.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

hyperbolic equations; numerical methods; Godunow methods

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2012
• Tom: Vol. 60, nr 1
• Strony: 45--53
• Opis fizyczny: Bibliogr. 16 poz., rys., tab.

Twórcy

autor

Murawski K.

autor

Stpiczyński P.

• Institute of Informatics, UMCS, 1 M. Curie-Sklodowskiej St., 20-031 Lublin, Poland,

Bibliografia

• [1] S.K. Godunov, “A difference scheme for numerical solution of discontinuous solution of hydrodynamic equations”, Math. Sb. 47, 271–306 (1959).
• [2] E. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer, Berlin, 2009.
• [3] 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).
• [4] B. van Leer, “Towards the ultimate conservative difference scheme. V – A second-order sequel to Godunov method”, J. Comp. Phys. 32, 101–136 (1979).
• [5] 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).
• [6] 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).
• [7] S.A.E.G. Falle, “Self-similiar jets”, MNRAS 250, 581–596 (1991).
• [8] C. Berthon, “Stability of the MUSCL schemes for the Euler equations”, Comm. Math. Sciences 3, 133–158 (2005).
• [9] C. Berthon, “Why the MUSCL-Hancock scheme is L1-stable”, Numer. Math. 104, 27–46 (2006).
• [10] 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).
• [11] K. Murawski, “Numerical solutions of magnetohydrodynamic equations”, Bull. Pol. Ac.: Tech. 59 (2), 219–226 (2011).
• [12] P.L. Roe, “Approximate Riemann solvers, parameter vectors and difference schemes”, J. Comp. Phys. 43, 357–372, (1981).
• [13] R.J. LeVeque, Finite-volume Methods for Hyperbolic Problems, Cambridge University Press, Cambridge, 2002.
• [14] D. Lee and A.E. Deane, “An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics”, J. Comput. Phys. 228 (4), 952–975, (2009).
• [15] 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).
• [16] 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).