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A parallel adaptive grid algorithm for computational shock hydrodynamics. (English) Zbl 0856.65108
The author presents an overview of a block-structured adaptive mesh refinement (AMR) algorithm: the grid structure, procedures to apply boundary conditions at the internal boundaries introduced by the method, description of the grid adaption process. Finally, an application is presented: the Mach reflection of a detonation wave from a ramp.
Reviewer: L.Vazquez (Madrid)

65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65Y05 Parallel numerical computation
76L05 Shock waves and blast waves in fluid mechanics
35L67 Shocks and singularities for hyperbolic equations
Full Text: DOI
[1] Akbar, R.; Quirk, J.J.; Shepherd, J.E., A numerical study of the Mach reflection of detonation waves, (), a follow-up manuscript is in preparation
[2] Arney, D.C.; Flaherty, J.E., An adaptive mesh moving and local refinement method for time-dependent partial differential equations, ACM trans. math. software, 16, 48-71, (1990) · Zbl 0900.65284
[3] Bell, J.B.; Colella, P.; Trangenstein, J.A.; Welcome, M., Adaptive methods for high Mach number reacting flow, AIAA paper 87-1168, (1987)
[4] Berger, M.J.; Colella, P., Local adaptive mesh refinement for shock hydrodynamics, J. comput. phys., 82, 67-84, (1989) · Zbl 0665.76070
[5] Berger, M.J.; Oliger, J., Local adaptive mesh refinement for hyperbolic partial differential equations, J. comput. phys., 53, 482-512, (1984) · Zbl 0536.65071
[6] Berger, M.J.; Saltzman, J.S., AMR on the CM-2, Appl. numer. math., 14, 239-253, (1994) · Zbl 0803.76062
[7] Biswas, R.; Strawn, R., A new procedure for dynamic adaptation of three-dimensional unstructured grids, AIAA paper 93-0672, (1993)
[8] Bourlioux, A.; Majda, A.J., Theoretical and numerical structure for unstable two-dimensional detonations, Combustion and flame, 90, 211-229, (1992)
[9] Brackbill, J.U.; Saltzman, J.S., Adaptive zoning for singular problems in two dimensions, J. comput. phys., 46, 342-368, (1982) · Zbl 0489.76007
[10] Butler, R.; Lusk, E., User’s guide to the p4 parallel programming system, Argonne national laboratory report ANL-92/17, (1992)
[11] Chiang, Y.-L.; van Leer, B.; Powell, K.G., Simulation of unsteady inviscid flow on an adaptively refined Cartesian grid, AIAA paper 92-0443, (1992)
[12] Clarke, J.F.; Karni, S.; Quirk, J.J.; Roe, P.L.; Simmonds, L.G.; Toro, E.F., Numerical computation of two-dimensional unsteady detonation waves in high energy solids, J. comput. phys., 106, 215-233, (1993) · Zbl 0770.76040
[13] Crutchfield, W.Y., Load balancing irregular algorithms, (), Preprint
[14] Crutchfield, W.Y., Parallel adaptive mesh refinement: an example of data encapsulation, (), Preprint
[15] DeZeeuw, D.; Powell, K.G., An adaptively refined Cartesian mesh solver for the Euler equations, J. comput. phys., 104, 56-68, (1993) · Zbl 0766.76066
[16] Fickett, W.; Davis, W., Detonation, (1979), University of California Press Berkeley
[17] Fischer, J., Selbstadaptive, lokale netzverfeinerungen für die numerische simulation kompressibler, reibungsbehafteter strömungen, ()
[18] Graham, R.L., Bounds on certain multiprocessing anomalies, SIAM J. appl. math., 17, 416-429, (1969) · Zbl 0188.23101
[19] Kallinderis, Y.; Vidwans, A., Generic parallel adaptive-grid Navier-Stokes algorithm, Aiaa j., 32, 54-61, (1994) · Zbl 0792.76065
[20] Karni, S., Multi-component flow calculations by a consistent primitive algorithm, J. comput. phys., 112, 31-43, (1994) · Zbl 0811.76044
[21] Löhner, R., Some useful data-structures for the generation of unstructured grids, Comm. appl. numer. methods, 4, 123-135, (1988) · Zbl 0643.65075
[22] Löhner, R.; Baum, J.D., Adaptive h-refinement on 3D unstructured grids for transient problems, Internat. J. numer. methods fluids, 14, 1407-1419, (1992) · Zbl 0753.76099
[23] Meltzer, J.; Shepherd, J.E.; Akbar, R.; Sabet, A., Mach reflection of detonation waves, Progress in aeronautics and astronautics, 153, 78-94, (1993)
[24] Powell, K.G.; Roe, P.L.; Quirk, J.J., Adaptive-mesh algorithms for computational fluid dynamics, (), 303-337
[25] Quirk, J.J., An adaptive grid algorithm for computational shock hydrodynamics, () · Zbl 0856.65108
[26] Quirk, J.J., A contribution to the great Riemann solver debate, Internat. J. numer. methods fluids, 18, 555-574, (1994) · Zbl 0794.76061
[27] Quirk, J.J., An alternative to unstructured grids for computing gas dynamics flows around arbitrarily complex two-dimensional bodies, Comput. & fluids, 23, 125-142, (1994) · Zbl 0788.76067
[28] Quirk, J.J., Godunov-type schemes applied to detonation flows, (), 575-596
[29] Quirk, J.J., Numerical soot traces. “the Writing’s on the wall”, (), 331-337
[30] J.J. Quirk, Dynamic load balancing strategies for parallel adaptive mesh refinement, in preparation.
[31] J.J. Quirk and U.R. Hanebutte, A parallel adaptive mesh refinement algorithm, NASA CR-191530, ICASE Report No. 93-63, unpublished.
[32] J.J. Quirk and S. Karni, On the dynamics of a shock bubble interaction, NASA CR-194978, ICASE Report No. 94-75; also: J. Fluid Mech., to appear.
[33] Simon, H.D., Partitioning of unstructured problems for parallel processing, Comput. syst. engrg., 2, 135-148, (1991)
[34] Strehlow, R.A., The nature of transverse waves in detonations, Astronaut. acta, 14, 539-548, (1969)
[35] Thompson, J.F.; Weatherill, N.P., Aspects of numerical grid generation: current science and art, AIAA paper 93-3539, (1993)
[36] Webster, B.E.; Shephard, M.S.; Rusak, Z.; Flaherty, J.E., Automated adaptive time-discontinuous finite element method for unsteady compressible airfoil aerodynamics, Aiaa j., 32, 748-757, (1994)
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