A high-order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes

Journal of Computational Physics

Volumn 228, Issue 7, 2009, Pages 2391-2425

  Maire, Pierre Henri ^a  

^a CENTRE LASERS INTENSES ET APPLICATIONS   (France)

Author keywords

Cell centered scheme; Compressible flow; Generalized Riemann problem; High order finite volume methods; Lagrangian hydrodynamics; Unstructured mesh

Indexed keywords

COMPRESSIBLE FLOW; GAS DYNAMICS; LAGRANGE MULTIPLIERS; MESH GENERATION; PARTIAL DIFFERENTIAL EQUATIONS; PHYSICAL PROPERTIES;

CELL-CENTERED SCHEME; FINITE-VOLUME METHOD; GENERALIZED RIEMANN PROBLEM; HIGH-ORDER; HIGH-ORDER FINITE VOLUME METHOD; HIGHER-ORDER; LAGRANGIAN HYDRODYNAMICS; RIEMANN PROBLEM; TWO-DIMENSIONAL; UNSTRUCTURED MESHES;

FINITE VOLUME METHOD;

EID: 60149098489     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.12.007     Document Type: Article

References (45)

1. F.L. Adessio, D.E. Carroll, K.K. Dukowicz, J.N. Johnson, B.A. Kashiwa, M.E. Maltrud, H.M. Ruppel. Caveat: a computer code for fluid dynamics problems with large distortion and internal slip, Technical Report LA-10613-MS, Los Alamos National Laboratory, 1986.
2. T.J. Barth, Numerical methods for conservation laws on structured and unstructured meshes, Technical report, VKI Lecture Series, 2003.
3. T.J. Barth, D.C. Jespersen, The design and application of upwind schemes on unstructured meshes, in: AIAA paper 89-0366, 27th Aerospace Sciences Meeting, Reno, Nevada, 1989.
4. Ben-Artzi M., and Birman A. Application of the generalized Riemann problem method to 1-D compressible flows. J. Comput. Phys. 65 (1986) 170-178
5. Ben-Artzi M., and Falcovitz J. A second-order Godunov-type scheme for compressible fluid dynamics. J. Comput. Phys. 55 1 (1984) 1-32
6. Ben-Artzi M., and Falcovitz J. An upwind second-order scheme for compressible duct flows. SIAM J. Sci. Stat. Comput. 7 3 (1986) 744-768
7. Ben-Artzi M., and Falcovitz J. Generalized Riemann Problems in Computational Fluids Dynamics (2003), Cambridge University Press
8. Campbell J.C., and Shashkov M.J. A tensor artificial viscosity using a mimetic finite difference algorithm. J. Comput. Phys. 172 4 (2001) 739-765
9. Campbell J.C., and Shashkov M.J. A compatible Lagrangian hydrodynamics algorithm for unstructured grids. Seltuk J. Appl. Math. 4 2 (2003) 53-70
10. Caramana E.J., Shashkov M.J., and Whalen P.P. Formulations of artificial viscosity for multidimensional shock wave computations. J. Comput. Phys. 144 (1998) 70-97
11. Caramana E.J., Burton D.E., Shashkov M.J., and Whalen P.P. The construction of compatible hydrodynamics algorithms utilizing conservation of total energy. J. Comput. Phys. 146 (1998) 227-262
12. Caramana E.J., and Shashkov M.J. Elimination of artificial grid distortion and hourglass - type motions by means of Lagrangian subzonal masses and pressures. J. Comput. Phys. 142 (1998) 521-561
13. G. Carré, S. Delpino, B. Després, E. Labourasse, A cell-centered Lagrangian hydrodynamics scheme in arbitrary dimension, J. Comput. Phys., submitted for publication.
14. Chorin A., and Marsden J. A Mathematical Introduction to Fluid Mechanics (1992), Springer-Verlag
15. R.B. Christensen, Godunov methods on a staggered mesh-an improved artificial viscosity, Technical Report UCRL-JC-105269, Lawrence Livermore National Laboratory, 1991.
16. de Groot S.R., and Mazur P. Non-equilibrium Thermodynamics (1984), Dover
17. Després B., and Mazeran C. Lagrangian gas dynamics in two dimensions and Lagrangian systems. Arch. Rational Mech. Anal. 178 (2005) 327-372
18. Dukowicz J.K. A general non-iterative Riemann solver for Godunov's method. J. Comput. Phys. 61 (1984) 119-137
19. Dukowicz J.K., and Meltz B. Vorticity errors in multidimensional Lagrangian codes. J. Comput. Phys. 99 (1992) 115-134
20. Godlewski E., and Raviart P.A. Hyperbolic Systems of Conservation Laws (2000), Springer-Verlag
21. Godunov S.K., Zabrodine A., Ivanov M., Kraiko A., and Prokopov G. RTsolution numTrique des problFmes multidimensionnels de la dynamique des gaz (1979), Mir
22. J.R. Kamm, W.J. Rider, J.S. Brock, Consistent metrics for code verification, Technical Report LA-UR-02-3794, Los Alamos National Laboratory, 2002.
23. J.R. Kamm, F.X. Timmes, On efficient generation of numerically robust Sedov solutions, Technical Report LA-UR-07-2849, Los Alamos National Laboratory, 2007.
24. Kidder R.E. Laser-driven compression of hollow shells: power requirements ANS stability limitations. Nucl. Fus. 1 (1976) 3-14
25. Landau L., and Lifchitz E. MTcanique des Fluides (1989), Mir
26. Li J., and Sun Z. Remark on the generalized Riemann problem method for compressible fluid flows. J. Comput. Phys. 222 (2007) 796-808
27. LoubFre R., and Shashkov M.J. A subcell remapping method on staggered polygonal grids for Arbitrary-Lagrangian-Eulerian methods. J. Comput. Phys. 23 (2004) 155-160
28. S.M. Murman, M. Berger, M.J. Aftosmis, Analysis of slope limiters on irregular grids, Technical Report NAS-05-007, NAS Technical Report, 2005.
29. Maire P.H., Abgrall R., Breil J., and Ovadia J. A cell-centered Lagrangian scheme for compressible flow problems. SIAM J. Sci. Comput. 29 4 (2007) 1781-1824
30. Maire P.H., and Breil J. A second-order cell-centered lagrangian scheme for two-dimensional compressible flow problems. Int. J. Numer. Methods Fluids 56 (2008) 1417-1423
31. P.H. Maire, B. Nkonga, Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics, J. Comput. Phys., 2008, doi: 10.1016/j.jcp.2008.10012.
32. Noh W.F. Errors for calculations of strong shocks using artificial viscosity and an artificial heat flux. J. Comput. Phys. 72 (1987) 78-120
33. B. Rebourcet, Comments on the filtering of numerical instabilities in Lagrangian hydrocodes, in: Conference on Numerical methods for multi-material fluid flows; Czech Technical University in Prague on September 10-14, 2007. .
34. Richtmyer R.D. Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Math. 13 (1960) 297-319
35. Scovazzi G. Stabilized shock hydrodynamics: II. Design and physical interpretation of the SUPG operator for Lagrangian computations. Comput. Methods Appl. Mech. Eng. 196 (2007) 966-978
36. Scovazzi G., Christon M.A., R Hughes T.J., and Shadid J.N. Stabilized shock hydrodynamics: I. A Lagrangian method. Comput. Methods Appl. Mech. Eng. 196 (2007) 923-966
37. Scovazzi G., Love E., and Shashkov M.J. Multi-scale Lagrangian shock hydrodynamics on Q1/P0 finite elements: theoretical framework and two-dimensional computations. Comput. Methods Appl. Mech. Eng. 197 (2008) 1056-1079
38. Shashkov M. Conservative Finite Difference Methods on General Grids (1996), CRC Press
39. Sod G.A. A survey of several finite difference methods for systems of non-linear hyperbolic conservation laws. J. Comput. Phys. 27 (1978) 1-31
40. Swartz B. Good neighborhoods for multidimensional Van Leer limiting. J. Comput. Phys. 154 (1999) 237-241
41. van Leer B. Towards the ultimate conservative difference scheme. J. Comput. Phys. 32 (1979) 101-136
42. Venkatakrishnan V. Convergence to steady state solutions of the Euler equations on unstructured grids with limiters. J. Comput. Phys. 118 (1995) 120-130
43. von Neumann J., and Richtmyer R.D. A method for the numerical calculations of hydrodynamical shocks. J. Appl. Phys. 21 (1950) 232-238
44. Wilkins M.L. Calculation of elastic plastic flow. Methods Comput. Phys. 3 (1964)
45. Yang Y., Zhang Q., and Sharp D.H. Small amplitude theory of Richtmyer-Meshkov instability. Phys. Fluids 6 5 (1994) 1856-1873