An adaptive numerical scheme for high-speed reactive flow on overlapping grids

Journal of Computational Physics

Volumn 191, Issue 2, 2003, Pages 420-447

  Henshaw, William D ^a   Schwendeman, Donald W ^b  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

^b RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF STATE; MESH GENERATION; NUMERICAL METHODS; RUNGE KUTTA METHODS;

ADAPTIVE NUMERICAL SCHEME; BLOCK STRUCTURED; COMPLEX GEOMETRIES; EULER'S EQUATION; HIGH SPEED; NUMERICAL SOLUTION; OVERLAPPING GRIDS; REACTION MODELLING; REACTIVE FLOW; STRUCTURED ADAPTIVE MESH REFINEMENT;

DETONATION;

EID: 0242299310     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9991(03)00323-1     Document Type: Article

References (37)

1. M.J. Berger, J. Oliger, Adaptive mesh refinement for hyperbolic partial differential equations, J. Comp. Phys. 53 (1984) 484-512.
2. S.K. Godunov, Difference methods for the numerical calculation of the equations of fluid dynamics, Mat. Sb. 47 (1959) 271-306.
3. G. Chesshire, W. Henshaw, Composite overlapping meshes for the solution of partial differential equations, J. Comp. Phys. 90 (1) (1990) 1-64.
4. J.L. Steger, J.A. Benek, On the use of composite grid schemes in computational aerodynamics, Comput. Methods Appl. Mech. Eng. 64 (1987) 301-320.
5. W. Henshaw, G. Chesshire, Multigrid on composite meshes, SIAM J. Sci. Stat. Comput. 8 (6) (1987) 914-923.
6. M. Hinatsu, J. Ferziger, Numerical computation of unsteady incompressible flow in complex geometry using a composite multigrid technique, Int. J. Numer. Methods Fluids 13 (1991) 971-997.
7. F. Olsson, J. Yström, Some properties of the upper convected Maxwell model for viscoelastic fluid flow, J. Non-Newtonian Fluid Mech. 48 (1993) 125-145.
8. R. Meakin, Moving body overset grid methods for complete aircraft tiltrotor simulations, paper 93-3350, AIAA, 1993.
9. D. Pearce, S. Stanley, F. Martin, R. Gomez, G.L. Beau, P. Buning, W. Chan, T. Chui, A. Wulf, V. Akdag, Development of a large scale chimera grid system for the space shuttle launch vehicle, paper 93-0533, AIAA, 1993.
10. R. Maple, D. Belk, A new approach to domain decomposition, the beggar code, in: N. Weatherill (Ed.), Numerical Grid Genertation in Computational Fluid Dynamics and Related Fields, Pineridge Press Limited, 1994, pp. 305-314.
11. J.Y. Tu, L. Fuchs, Calculation of flows using three-dimensional overlapping grids and multigrid methods, Int. J. Numer. Methods Eng. 38 (1995) 259-282.
12. N.A. Petersson, Hole-cutting for three-dimensional overlapping grids, SIAM J. Sci. Comp. 21 (1999) 646-665.
13. R.L. Meakin, Composite overset structured grids, in: J.F. Thompson, B.K. Soni, N.P. Weatherill (Eds.), Handbook of Grid Generation, CRC Press, Boca Raton, 1999, pp. 1-20 (Chapter 11).
14. K. Brislawn, D.L. Brown, G. Chesshire, J. Saltzman, Adaptively-refined overlapping grids for the numerical solution of hyperbolic systems of conservation laws, Report LA-UR-95-257, Los Alamos National Laboratory, 1995.
15. E.P. Boden, E.F. Toro, A combined chimera-amr technique for computing hyperbolic pdes, in: Djilali (Ed.), Proceedings of the Fifth Annual Conference of the CFD Society of Canada, 1997, pp. 5.13-5.18.
16. D.L. Brown, W.D. Henshaw, D.J. Quinlan, Overture: an object oriented framework for solving partial differential equations, in: Scientific Computing in Object-Oriented Parallel Environments, Springer Lecture Notes in Computer Science, vol. 1343, 1997, pp. 177-194.
17. D.L. Brown, G.S. Chesshire, W.D. Henshaw, D.J. Quinlan, Overture: an object oriented software system for solving partial differential equations in serial and parallel environments, in: Proceedings of the Eighth SIAM Conference on Parallel Processing for Scientific Computing, 1997.
18. C. Helzel, R.J. LeVeque, G. Warnecke, A modified fractoinal step method for the accurate approximation of detonation waves, SIAM J. Sci. Comp. 22 (2000) 1489-1510.
19. P. Colella, A. Majda, V. Roytburd, Theoretical and numerical structure for reacting shock waves, SIAM J. Sci. Comp. 7 (1986) 1059-1080.
20. R.J. LeVeque, H.C. Yee, A study of numerical methods for hyperbolic conservation laws with stiff source terms, J. Comp. Phys. 86 (1990) 187-210.
21. A.K. Kapila, Homogeneous branched-chain explosion: initiation to completion, J. Eng. Math. 12 (1978) 221-235.
22. M. Short, A.K. Kapila, J.J. Quirk, The chemical-gas dynamic mechanisms of pulsating detonation wave instability, Philos. Trans. R. Soc. Lond. A 357 (1999) 3621-3637.
23. N. Nikiforakis, J.F. Clarke, Quasi-steady structures in the two-dimensional initiation of detonations, Proc. R. Soc. Lond. A 452 (1996) 2023-2042.
24. N. Nikiforakis, J.F. Clarke, Numerical studies of the evolution of detonations, Math. Comput. Model. 24 (8) (1996) 149-164.
25. A.K. Kapila, D.W. Schwendeman, J.J. Quirk, T. Hawa, Mechanisms of detonation formation due to a temperature gradient, Combust. Theory Model. 6 (2002) 553-594.
26. W. Henshaw, Ogen: an overlapping grid generator for Overture, Research Report UCRL-MA-132237, Lawrence Livermore National Laboratory, 1998.
27. D.L. Brown, W.D. Henshaw, D.J. Quinlan, Overture: an object-oriented framework for solving partial differential equations on overlapping grids, in: Object Oriented Methods for Interoperable Scientific and Engineering Computing, SIAM, Philadelphia, PA, 1999, pp. 245-255.
28. M.J. Berger, Adaptive mesh refinement for hyperbolic partial differential equations, Ph.D. Thesis, Stanford University, Stanford, CA, 1982.
29. M. Berger, I. Rigoutsos, An algorithm for point clustering and grid generation, IEEE Trans. Syst. Man Cybernet 21 (1991) 1278-1286.
30. P. Collela, Multidimensional upwind methods for hyperbolic conservation laws, J. Comp. Phys. 87 (1990) 171-200.
31. D.L. Brown, An unsplit Godunov method for systems of conservation laws on curvilinear overlapping grids, Math. Comput. Model. 20 (1994) 29-48.
32. E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer, New York, 1997.
33. P.L. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comp. Phys. 43 (1981) 357-372.
34. R.J. LeVeque, Numerical Methods for Conservation Laws, Birkhäuser, Basel, 1992.
35. P. Colella, P. Woodward, The piecewise parabolic method (ppm) for gas dynamical simulations, J. Comp. Phys. 54 (1984) 174-201.
36. W. Fickett, W.C. Davis, Detonation, University of California Press, Berkeley, 1979.
37. G.B. Whitham, Linear and Nonlinear Waves, Wiley/Interscience, New York, 1974.