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Zagadnienie Riemanna : metody rozwiązań numerycznych dla potrzeb hydrodynamiki

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Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
EN
The Riemann problem : methods of numerical solutions for hydrodynamics needs
Języki publikacji
PL
Abstrakty
PL
W pracy przedstawiono przegląd obecnie stosowanych metod numerycznych przy rozwiązywaniu zagadnienia Riemanna dla potrzeb hydrodynamiki. Skupiono się na metodach dla równań Eulera, przedstawiając wyniki testów analizowanych metod. Dokonano porównań pod względem dokładności metod oraz ich kosztu obliczeiowego.
EN
The review is shown of numerical methods used presently in solutiona of the Riemann problem for hydrodynamics needs. The attention is paid on the methods for the Euler equations, presenting the test results of the analyzed methods. Comparisons were carried out with respect of the method accuracy and theirs calculation costs.
Rocznik
Strony
23--47
Opis fizyczny
Bibliogr. 26 poz.
Twórcy
autor
  • Wojskowa Akademia Techniczna, Zakład Materiałów Wybuchowych i Fizyki Wybuchu, 00-908 Warszawa, ul. S. Kaliskiego 2, akuczaj@wul.wat.waw.pl
Bibliografia
  • [1] F. Bereux, L. Sainsaulieu, A Roe-Type Riemann Solver for Hyperbolic Systems with Relaxation Based on Time-Dependent Wave Decornposition, Numerische Mathematik Vol. 77 (2) 1997, 143-485.
  • [2] Y. Brenter, S. Osher, Approximate Riemann Solvers and Numerical Flux Functions SIAM J. Numer. Anal. Vol. 23, 2 1986, 259-273,
  • [3] S. L. Brown, Approximate Riemann Solvers for Moment Models of Dilute Gases Ph.D. Dissertation, The University of Michigan, 1996.
  • [4] P. Colella, H. M. Glaz, Efficient Solution Algorithms for the Riemann Problem for Real Gases, Journal of Computational Physics, 59 (1985), 264-289.
  • [5] F. Dubois, G. Mehlman, A non-parameterized entropy correction for Roe's approximate Riemann solver, Numerische Mathematik, Vol. 73 (2) 1996, 169-208.
  • [6] B. Einfeldt, On Godunov-Type Methods For Gas Dynamics, SIAM J. Numer. Anal., Vol. 25 (2) (1988), 294-318.
  • [7] P. Glaister, An Analysis of Arithmetic Averaging in a Riemann Solver for the One-Dimensional Euler Equations, Computers Math. Applic., Vol. 30, 7 (1995 103-112.
  • [8] P. Glaister, An Analysis of Averaging Procedures in a Riemann Solver for Compressible Flows of a Real Gai, Computers Math. Applic., Vol. 33, 3 (1997), 105-11t
  • [9] P. Glaister, An Analysis of Averaging Procedures in a Riemann Solver for the Two-Dimensional Euler Equations, Computers Math. Applic., Vol. 35, 8 (1998), 63-77.
  • [10] P. Glaister, Riemann Solvers with Primitive Parameter Vectors for Two-Dimensional Cornpressible Flows of a Real Gas, An International Journal Computers and Mathematics with Applications, 37 (1999), 75-92.
  • [11] S. K. Godunov, Chislennoe reshenie mnogomernykh zadach gazovojj dinamiki, Nauka, Moskva, 1976.
  • [12] J. J. Gottlieb, C. P. T. Groth, Assessment of Riemann Solvers for Unstedy One-Dimensional Invascid Flows of Perfect Gases, Journal of Computational Physics, 78 (1988), 437-458.
  • [13] A. Harten, High Resolution Schemes for Hyperbolic Conservation Laws, Journal Computational Physics, 135 (1997), 260-278.
  • [14] A. Harten, P. D. Lax, B. Van Leer, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Review, 61, (1983).
  • [15] P. Jenny, B. Muller, Rankine-Hugoniot-Riemann Solver Considering Source Terms and Multidimensional Effects, Journal of Computational Physics, 145 (1998), 575-611
  • [16] B. Van Leer, Flux- Vector Splitting for the Euler Equations, Proceedings of Eight International Conference on Numerical Methods in Fluid Dynamics, June 28-July Aachen, 1982, in: Lecture Notes in Physics, 170 (1982), 507-512.
  • [17] S. Osher, Riemann Solvers, the Entropy Condition, and Difference Approximation SIAM J. Numer. Anal., Vol. 21 (2) (1984), 217-235.
  • [18] W. J. Rider, A Review of Approximate Riemann Solvers with Godunov's Method in Lagrangian Coordinates, Computers & Fluids, Vol. 23 (1994), 397-413.
  • [19] W. J. Rider, An adaptive Riemann solver using a two-shock approximation, Computers & Fluids, Vol. 28 (1999), 741-777.
  • [20] P. L. Roe, Approximate Riemann Solvers, Parameters Vectors and Difference Schemes, Journal of Computational Physics, 43 (1981), 357-372.
  • [21] J. E. Romate, An Approximate Riemann Solver For a Two-Phase Flow Model with Numerically Given Slip Relation, Computers & Fluids, Vol. 27, 4 (1998) 455-477.
  • [22] J. L. Steger, R. F. Warming, Flux Vector Splitting of the inviscid Gasdynamic Equations with Application to Finite-Difference Methods, Journal of Computational Physics, 40 (1981), 263-293.
  • [23] E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics: a practical introduction, Springer-Verlag Berlin Heidelberg New York, ISBN 3-540-61676-4, 1997.
  • [24] R. J. Leveque, Finite Difference Methods for Differential Equations, Draft version for use in the courses AMath 585-6, University of Washington, 1998.
  • [25] R. J. Leveque, Simplified Multi-Dimensional Flux Limiter Methods, Proceedings of the ICFD Conference on Numerical Methods for Fluid Dynamics, Reading, U.K., April, 1992, Published as: Numerical Methods for Fluid Dynamics 4, M. J. Baines, K. W. Morton, Oxford University Press, 1993.
  • [26] B. Wendroff, A Two-dimensional HLLE Riemann Solver and Associated Godunov-Type Difference Scheme for Gas Dynamics, Los Alamos National Laboratory Report, LAUR 98-5490, An International Journal Computers and Mathematics with Applications, 38 (1999), 175-185.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BWA2-0005-0284
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