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Description of the multi-dimensional finite volume solver EULER. (English) Zbl 1090.65532

Summary: This paper is aimed at the description of the multi-dimensional finite volume solver EULER, which has been developed for the numerical solution of the compressible Euler equations during several last years. The present overview of numerical schemes and the explanation of numerical techniques and tricks which have been used for EULER could be of certain interest not only for registered users but also for numerical mathematicians who have decided to implement a finite volume solver themselves. This solver has been used also for the computation of numerical examples presented in other papers of the authors.

MSC:

65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76N15 Gas dynamics (general theory)

Software:

ODEPACK; EULER
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References:

[1] A. C. Hindmarsh: ODEPACK, A systematized collection of ODE solvers. Scientific Computing (IMACS Transactions on Scientific Computation Volume 1), North-Holland, Amsterdam, 1983, pp. 55-64.
[2] L. R. Petzold: A description of DDASSL: A differential/algebraic system solver. Sandia Report No. Sand 82-8637, Sandia National Laboratory, Livermore, CA, 1982.
[3] K. Segeth, P. Šolín: Application of the method of lines to compressible flow (Computational aspects). Proceedings of the 10th PANM Seminar, Lázně Libverda, 2000, Mathematical Institute of the Academy of Sciences of the Czech Republic, Praha, 2000.
[4] P. Šolín, K. Segeth: Application of the method of lines to the nonstationary compressible Euler equations. Internat. J. Numer. Methods Fluids, Submitted.
[5] P. Šolín: On the method of lines (Application in fluid dynamics and a-posteriori error estimation). Doctoral dissertation, Faculty of Mathematics and Physics, Charles University, Prague, 1999.
[6] P. Šolín: Three-dimensonal Euler equations and their numerical solution by the finite volume method. Master thesis (Part 1), Faculty of Mathematics and Physics, Charles University, Prague, 1996.
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