Characteristic-based treatment of source terms in Euler equations for Roe scheme

AIAA journal

Volumn 37, Issue 4, 1999, Pages 417-424

  Mohanraj, Rajendran ^a   Neumeier, Yedidia ^a   Zinn, Ben T ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; FLOW OF FLUIDS; FRICTION; LINEARIZATION; MASS TRANSFER; MATHEMATICAL OPERATORS; STEADY FLOW; THERMODYNAMICS; UNSTEADY FLOW;

ENERGY ADDITION; EULER EQUATIONS; RIEMANN SOLVER; ROE SCHEME; SECONDARY MASS ADDITION;

DIFFERENTIAL EQUATIONS;

EID: 0033115905     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/2.749     Document Type: Article

References (24)

1. Roe, P. L., "Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes," Journal of Computational Physics, Vol. 43, No. 2, 1981, pp. 357-372.
2. Heiser, W. H., McClure, W. B., and Wood, C. W., "Simulating Heat Addition via Mass Addition in Variable Area Compressible Flows," AIAA Journal, Vol. 34, No. 5, 1996, pp. 1076-1078.
3. Fey, M., Jeltsch, R., and Muller, S., "The Influence of a Source Term, an Example: Chemically Reacting Hypersonic Flow," Proceedings of the Fourth International Conference on Hyperbolic Problems, edited by A. Donato and F. Oliveri, Vieweg, Brunswick, Germany, 1992, pp. 235-245.
4. Bermudez, A., and Vazquez, M. E., "Upwind Methods for Hyperbolic Conservation Laws with Source Terms," Computers and Fluids, Vol. 23, No. 8, 1994, pp. 1049-1071.
5. Ali, F., and Kassar, M. A., "Hyperbolic Conservation Laws Having Source Terms and Donor Cell Differencing," International Journal of Modern Physics C, Vol. 5, No. 3, 1994, pp. 519-536.
6. Chalabi, A., "Stable Upwind Schemes for Hyperbolic Conservation Laws with Source Terms," IMA Journal of Numerical Analysis, Vol. 12, No. 2, 1992, pp. 217-241.
7. Godlewski, E., and Raviart, P. A., "Numerical Approximation of Hyperbolic Systems of Conservation Laws," Applied Mathematical Sciences, Vol. 118, Springer-Verlag, Berlin, 1996.
8. Toro, E. F., Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer-Verlag, New York, 1997, Chap. 15.
9. Roe, P. L., "Characteristic-Based Schemes for the Euler Equations," Annual Review of Fluid Mechanics, Vol. 18, 1986, pp. 337-365.
10. Glaister, P., "Flux Difference Splitting for the Euler Equations in One Spatial Coordinate with Area Variation," International Journal for Numerical Methods in Fluids, Vol. 8, No. 1, 1988, pp. 97-119.
11. Roe, P. L., "Upwind Differencing for Hyperbolic Conservation Laws with Source Terms," Proceedings of International Conference on Non-linear Hyperbolic Problems, edited by C. Carasso, P. A. Raviart, and D. Serre, Springer-Verlag, Berlin, 1986, pp. 41-51.
12. Zucrow, M. J., and Hoffman, J. D., Gas Dynamics, Wiley, New York, 1976, Vol. 1, Chap. 9, and Vol. 2, Chap. 19.
13. Shapiro, A. H., The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol. 1, Ronald, New York, 1953, Chap. 8.
14. Strehlow, R. A., Combustion Fundamentals, McGraw-Hill, New York, 1984, Chap. 5.
15. l5 Van Leer, B., "Towards the Ultimate Conservative Difference Scheme. V. A Second Order Sequel to Godunov's Method," Journal of Computational Physics, Vol. 32, No. 1, 1979, pp. 101-136.
16. Glaister, P., "Second Order Accurate Upwind Difference Schemes for Scalar Conservation Laws with Source Terms," Computers and Mathematics with Applications, Vol. 25, No. 4, 1993, pp. 65-73.
17. Grossman, B., and Cinella, P., "The Development of Flux-Split Algorithms for Flows with Non-Equilibrium Thermodynamics and Chemical Reactions," Proceedings of the AIAA 9th Computational Fluid Dynamics Conference, AIAA, Washington, DC, 1988, pp. 1443-1454 (AIAA Paper 88-3595).
18. Grossman, B., and Walters, R. W., "Analysis of Flux-Split Algorithms for Euler's Equations with Real Gases," AIAA Journal, Vol. 27, No. 5, 1989, pp. 524-531.
19. Glaister, P., "An Approximate Linearised Riemann Solver for the Euler Equations for Real Gases," Journal of Computational Physics, Vol. 74, No. 2, 1988, pp. 382-408.
20. Vinokur, M., and Montagne, J. L., "Generalized Flux Vector Splitting and Roe Average for an Equilibrium Real Gas," Journal of Computational Physics, Vol. 89, No. 2, 1990, pp. 276-300.
21. Poinsot, T. J., and Lele, S. K., "Boundary Conditions for Direct Simulations of Compressible Viscous Flows," Journal of Computational Physics, Vol. 101, No. 1, 1992, pp. 104-129.
22. Tannehill, J. C., Anderson, D. A., and Pletcher, R. H., Computational Fluid Mechanics and Heat Transfer, 2nd ed., Taylor and Francis, Washington, DC, 1997, p. 397.
23. Hirsch, C., Numerical Computation of Internal and External Flows, Vol. 2, Wiley, New York, 1988, Chap. 21.
24. Clarke, J. F., and Toro, E. F., "Flows Generated by Solid Propellant Burning," Lecture Notes in Physics, Vol. 241, Springer-Verlag, Berlin, 1985, pp. 192-205.