THE EARLY INFLUENCE OF PETER LAX ON COMPUTATIONAL HYDRODYNAMICS AND AN APPLICATION OF LAX-FRIEDRICHS AND#br#
LAX-WENDROFF ON TRIANGULAR GRIDS IN LAGRANGIAN COORDINATES

doi:10.1016/S0252-9602(11)60393-7

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (6): 2195-2202.doi: 10.1016/S0252-9602(11)60393-7

THE EARLY INFLUENCE OF PETER LAX ON COMPUTATIONAL HYDRODYNAMICS AND AN APPLICATION OF LAX-FRIEDRICHS AND#br# LAX-WENDROFF ON TRIANGULAR GRIDS IN LAGRANGIAN COORDINATES

Richard Liska¹, Mikhail Shashkov², Burton Wendroff³

1.Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Bˇrehová|7, 115 19 Prague 1, Czech Republic|2.Group XCP-4, MS-F644, Los Alamos National Laboratry, Los Alamos, New Mexico 87545, USA|3.Group T-5, MS-B284, Los Alamos National Laboratry, Los Alamos, New Mexico 87545, USA

收稿日期:2011-07-27 出版日期:2011-11-20 发布日期:2011-11-20
基金资助:
This work was performed under the auspices of the National Nuclear Secu-rity Administration of the US Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396. The first author has been supported in part by the Czech Science Foundation Grant P205/10/0814 and by the Czech Ministry of Education grants MSM 6840770022 and LC528.

THE EARLY INFLUENCE OF PETER LAX ON COMPUTATIONAL HYDRODYNAMICS AND AN APPLICATION OF LAX-FRIEDRICHS AND#br# LAX-WENDROFF ON TRIANGULAR GRIDS IN LAGRANGIAN COORDINATES

Richard Liska¹, Mikhail Shashkov², Burton Wendroff³

1.Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Bˇrehová|7, 115 19 Prague 1, Czech Republic|2.Group XCP-4, MS-F644, Los Alamos National Laboratry, Los Alamos, New Mexico 87545, USA|3.Group T-5, MS-B284, Los Alamos National Laboratry, Los Alamos, New Mexico 87545, USA

Received:2011-07-27 Online:2011-11-20 Published:2011-11-20
Supported by:
This work was performed under the auspices of the National Nuclear Secu-rity Administration of the US Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396. The first author has been supported in part by the Czech Science Foundation Grant P205/10/0814 and by the Czech Ministry of Education grants MSM 6840770022 and LC528.

摘要/Abstract

摘要：

We give a brief discussion of some of the contributions of Peter Lax to Com-putational Fluid Dynamics. These include the Lax-Friedrichs and Lax-Wendroff numerical schemes. We also mention his collaboration in the 1983 HLL Riemann solver. We de-velop two-dimensional Lax-Friedrichs and Lax-Wendroff schemes for the Lagrangian form of the Euler equations on triangular grids. We apply a composite scheme that uses a Lax-Friedrichs time step as a dissipative filter after several Lax-Wendroff time steps. Numerical results for Noh’s infinite strength shock problem, the Sedov blast wave problem, and the Saltzman piston problem are presented.

关键词: Lax-Friedrichs, Lax-Wendroff, conservation laws, Lagrangian coordinates, triangular grid

Abstract:

Key words: Lax-Friedrichs, Lax-Wendroff, conservation laws, Lagrangian coordinates, triangular grid

中图分类号:

35L65

Richard Liska, Mikhail Shashkov, Burton Wendroff. THE EARLY INFLUENCE OF PETER LAX ON COMPUTATIONAL HYDRODYNAMICS AND AN APPLICATION OF LAX-FRIEDRICHS AND#br# LAX-WENDROFF ON TRIANGULAR GRIDS IN LAGRANGIAN COORDINATES[J]. 数学物理学报(英文版), 2011, 31(6): 2195-2202.

Richard Liska, Mikhail Shashkov, Burton Wendroff. THE EARLY INFLUENCE OF PETER LAX ON COMPUTATIONAL HYDRODYNAMICS AND AN APPLICATION OF LAX-FRIEDRICHS AND#br# LAX-WENDROFF ON TRIANGULAR GRIDS IN LAGRANGIAN COORDINATES[J]. Acta mathematica scientia,Series B, 2011, 31(6): 2195-2202.

参考文献

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[2] Lax P D, Wendroff B. Systems of conservation laws. Comm Pure Appl Math, 1960, 13: 217–237

[3] Lax P D, Wendroff B. Difference schemes for hyperbolic equations with high order of accuracy. Comm Pure Appl Math, 1964, 17: 381–398

[4] Richtmyer R D. A survey of difference methods for non-steady fluid dynamics. Tech Report NCAR Technical Notes 63-2, National Center for Atmospheric Research, 1962

[5] Harten A, Lax P D, van Leer B. On upstream differencing and Godunov-type schemes for hyperbolic conaervation laws. SIAM Review, 1983, 25(1): 35–61

[6] Loubere R, Shashkov M. A subcell remapping method on staggered polygonal grids for arbitrary lagrangian eulerian methods. J Comp Phys, 2005, 209: 105–138

[7] Maire P H. A high-order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes. J Comp Phys, 2009, 228(7): 2391–2425

[8] Farhat C, Geuzaine P, Grandmont C. The discrete geometric conservation law and the nonlinear stability of ALE schemes for the solution of the flow problems on the moving grids. J Comp Phys, 2001, 174: 669–694

[9] Noh W F. Errors for calculations of strong shocks using an artificial viscosity and artificial heat flux. J Comp Phys, 1987, 72: 78–120

[10] Sedov L I. Similarity and Dimensional Methods in Mechanics. New York: Academic Press, 1959

[11] Kamm J R, Timmes F X. On efficient generation of numerically robust Sedov solutions. Tech Report LA-UR-07-2849, Los Alamos National Laboratory, 2007

[12] Caramana E J, Burton D E, Shashkov M J, Whalen P P. The construction of compatible hydrodynamics algorithms utilizing conservation of total energy. J Comp Phys, 1998, 146(1): 227–262

[13] Laney C B. Computational Gas Dynamics. Cambridge University Press, 1998

[14] Shashkov M, Wendroff B. A composite scheme for gas dynamics in Lagrangian coordinates. J Comp Phys, 1999, 150: 502–517

[15] Liska R, Shashkov M, Wendroff B. Lagrangian composite schemes on triangular unstructured grids//Kocandrlova M, Kelar V, eds. Mathematical and Computer Modelling in Science and Engineering, Inter-national Conference in honour of the 80th birthday of K. Rektorys. Prague 2003

[16] Toro E F. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. 2nd ed. Springer-Verlag, 1999

[17] Liska R, Wendroff B. Composite schemes for conservation laws. SIAM J Numer Anal, 1998, 35(6): 2250–2271

THE EARLY INFLUENCE OF PETER LAX ON COMPUTATIONAL HYDRODYNAMICS AND AN APPLICATION OF LAX-FRIEDRICHS AND#br# LAX-WENDROFF ON TRIANGULAR GRIDS IN LAGRANGIAN COORDINATES

THE EARLY INFLUENCE OF PETER LAX ON COMPUTATIONAL HYDRODYNAMICS AND AN APPLICATION OF LAX-FRIEDRICHS AND#br# LAX-WENDROFF ON TRIANGULAR GRIDS IN LAGRANGIAN COORDINATES

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