Details

Title

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

Journal title

Bulletin of the Polish Academy of Sciences: Technical Sciences

Yearbook

2012

Numer

No 1 March

Publication authors

Divisions of PAS

Nauki Techniczne

Publisher

Polish Academy of Sciences

Date

2012

Identifier

ISSN 0239-7528, eISSN 2300-1917

References

Godunov S. (1959), A difference scheme for numerical solution of discontinuous solution of hydrodynamic equations, Math. Sb, 47, 271. ; Toro E. (2009), Riemann Solvers and Numerical Methods for Fluid Dynamics, doi.org/10.1007/b79761 ; Kolgan V. (1972), 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. ; B. van Leer (1979), Towards the ultimate conservative difference scheme. V - A second-order sequel to Godunov method, J. Comp. Phys, 32, 101, doi.org/10.1016/0021-9991(79)90145-1 ; B. van Leer (1984), On the relation between the upwind-differencing schemes of Godunov, Engquist-Osher and Roe, SIAM J. Sci. Statist. Comput, 5, 1, 1, doi.org/10.1137/0905001 ; B. van Leer (2006), Upwind and high-resolution methods for compressible flow: from donor cell to residual distribution schemes, Comm. Computational Physics, 1, 2, 192. ; Falle S. (1991), Self-similiar jets, MNRAS, 250, 581. ; Berthon C. (2005), Stability of the MUSCL schemes for the Euler equations, Comm. Math. Sciences, 3, 133. ; Berthon C. (2006), Why the MUSCL-Hancock scheme is L1-stable, Numer. Math, 104, 27, doi.org/10.1007/s00211-006-0007-4 ; Murawski K. (2011), Numerical methods of solving equations of hydrodynamics from perspectives of the code FLASH, Bull. Pol. Ac.: Tech, 59, 3, 81. ; Murawski K. (2011), Numerical solutions of magnetohydrodynamic equations, Bull. Pol. Ac.: Tech, 59, 2, 219. ; Roe P. (1981), Approximate Riemann solvers, parameter vectors and difference schemes, J. Comp. Phys, 43, 357, doi.org/10.1016/0021-9991(81)90128-5 ; LeVeque R. (2002), Finite-volume Methods for Hyperbolic Problems, doi.org/10.1017/CBO9780511791253 ; Lee D. (2009), An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics, J. Comput. Phys, 228, 4, 952, doi.org/10.1016/j.jcp.2008.08.026 ; Stone J. (2009), The Athena MHD code: extensions, applications, and comparisons to ZEUS, Numerical Modeling of Space Plasma Flows: ASTRONUM-2008 ASP Conf. Series, 406, 277. ; H.-Yu Schive (2010), GAMER: A graphic processing unit accelerated adaptive-mesh-refinement code for astrophysics, Astrophys. J. Suppl, 186, 2, 457, doi.org/10.1088/0067-0049/186/2/457

DOI

10.2478/v10175-012-0008-7

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