Discontinuous galerkin for stiff hyperbolic systems

14th Computational Fluid Dynamics Conference

Volumn , Issue , 1999, Pages 516-525

  Lowrie, Robert B ^a   Morel, Jim E ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; DIFFUSION IN LIQUIDS; FINITE VOLUME METHOD;

BROADWELL MODEL; DIFFUSION LIMITS; DISCONTINUOUS GALERKIN; DISCONTINUOUS GALERKIN METHODS; HYPERBOLIC HEAT EQUATION; HYPERBOLIC SYSTEM; RADIATION-HYDRODYNAMICS; TIME INTEGRATION METHODS;

GALERKIN METHODS;

EID: 84983146546     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.1999-3307     Document Type: Conference Paper

References (27)

1. Chen, G.-Q., Levermore, C. D., and Liu, T.-P., “Hyperbolic Conservation Laws with Stiff Relaxation Terms and Entropy,” CommunicationS on Pure and Applied Mathematics, Vol. 47, 1994, pp. 787-830.
2. Liu, T.-P., “Hyperbolic Conservation Laws with Relaxation,” Communications in Mathematical Physics, Vol. 108, 1987, pp. 153-175.
3. Whitham, G. B., Linear and Nonlinear Waves, Wiley, 1974.
4. Arora, M. and Roe, P. L., “Issues and Strategies for Hyperbolic Problems with Stiff Source Terms,” Barriers and Challenges in Computational Fluid Dynamics, Vol. 6 of ICASE/LaRC Interdisciplinary Series in Science and Engineering, Kluwer, 1998, pp. 139-154.
5. Hittinger, J., “Model Problem for Hyperbolic Systems with Relaxation,” preprint, 1999.
6. Pember, R. B., “Numerical Methods for Hyperbolic Conservation Laws with Stiff Relaxation I. Spurious Solutions.” SIAM Journal on Applied Matlrematics, Vol. 53, No. 5, 1993, pp. 1293-1330.
7. Pember, R. B., “Numerical Methods for Hyperbolic Conservation Laws with Stiff Relaxation II. Higher-Order Godunov Methods.’ SIAM Journal on Scientific Computing, Vol. 14, No. 4, 1993, pp. 824-859.
8. Bereux, F. and Sainsaulieu, L., “A Roe-Type Riemann Solver for Hyperbolic Systems with Relaxation Based on Time-Dependent Wave’ Decomposition,” Numerische Mathematik, Vol. 77, 1997, pp. 143-185.
9. Jin, S. and Levermore, C. D., “Numerical Schemes for Hyperbolic Conservation Laws with Stiff Relaxation Terms,” Journal of Computational Physics, Vol. 126, 1996, pp. 449-467.
10. Jin, S.,, “Runge-Kutta Methods for Hyperbolic Conservation Laws with Stiff Relaxation,” Journal of Computational Physics, Vol. 122, 1995, pp. 51-67.
11. Harsen, E., Morel, J., and Miller, W., “Asymptotic Solutions of Numerical Transport Problems in Optically Thick, Diifusive Regimes,“, Journal of Computational Physics, Vol. 69, No. 2, 1987, pp. 283-324.
12. Morel, J. E., Wareing, T. A., and Smith, K., “A Linear- Discontinuous Spatial Differencing Scheme for S, Radiative Transfer Calculations,” Journal of Computational Physics, Vol. 128, 1996, pp. 445-462.
13. Cockburn, B. and Shu, C., “TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework,” Mathematics of Computation, Vol. 52, 1989, pp. 411-435.
14. Cockburn, B., Lin, S., and Shu, C., “TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws III: One-Dimensional Systems,” Journal of Computational Physics, Vol. 84, 1989, pp. 90-113.
15. Cockburn, B., Hou, S., and Shu, C., “TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws IV: The Multi-dimensional Case,” Mathematics of Computation, Vol. 54, 1990, pp. 545-581
16. Cockburn, B.’ and Shu, C. W., “The Runge-Kutta Discontinuous’ Galerkin Method for Conservation-Laws V: Multidimensional Systems,” Journal of Computational Physics, Vol. 141, No. 2, 1998, pp. 199-224.
17. Abramowita, M. and Stegun, I. A., Handbook of Mathematical Functions, Dover, 1972.
18. Atkins, H. and Shu, C. W., “Quadrature-Free Implementation of Discontinuous Galerkin Method for Hyperbolic- Equations,” AIAA Journal, Vol. 36, No. 5, 1998, pp. 775-782.
19. Shu, C. W. and Osher, S., ‘Efficient Implementation of Essentially Non-Oscillatory Shock Capturing Schemes,” Journal of Computational Physics, Vol. 77, 1988, pp. 439-471.
20. van Leer, B., “Towards the Ultimate Conservative Difference Scheme. IV. A New Approach to Numerical Convection,” Journal of Computational Physics, Vol. 23, 1977.
21. Arora, M., Explicit Characteristic-Based High-Resolution Algorithms for Hyperbolic Conservation Laws with StiflSource Terms, Ph.D. thesis, University of Michigan, 1996.
22. Mihalas, D. and Mihalas, B. W., Foundations of Radiation Hydrodynamics, Oxford University Press, 1984.
23. Lowrie, R., Morel, J., and Hittinger, J., “Coupling Radiation and Hydrodynamics,” Astrophysical Journal, Vol. 521, No. 1, 1999.
24. Roe, P. L., L‘Approximate Riemann Solvers, Parameter Vectors and Difference Schemes,” Journal of Computational Physics, Vol. 43, 1981.
25. Shuen, J.-S., Liou, M.-S., and van Leer, B., “Inviscid Flux-Splitting Algorithms for Real Gases with Nonequilibrium Chemistry,” Journal of Computational Physics, Vol. 90, 1990, pp. 371-395.
26. Mottura, L., Vigevano, L., and Zaccanti, M., “An Evaluation of Roe’s Scheme Generalizations for Equilibrium Real Gas Flows,” Journal of Computational Physics, Vol. 138, 1997, pp. 354-399.
27. Lowrie, R. and Morel, J., Linear Transport,” “High-Resolution Methods for in preparation, 1999.