Abstract
The paper deals with a discussion of different adaptation concepts presently applied to simulations of reactive flows. The governing equations of inviscid, reactive flows are solved by Finite-Volume methods in combination with upwind schemes. Adaptive grid redistribution and hierarchical grid refinement methods are employed on structured grids. Hierarchical grid refinement concepts, like adaptive mesh refinement (AMR) and directional mesh refinement (DMR) have shown to be more flexible and efficient for multidimensiona flows than grid redistribution. Unstructured, triangulated meshes offer good properties for grid adaptation due the fact that grid cells can be added, removed or deformed. Adaptation of unsteady features on unstructured grids are performed with a combinations of static and dynamic meshes. The different methods are demonstrated by results for detonations and other wave problems
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M.S. Liou, On a new Class of Flux Splitting Schemes. Lecture Notes in Physics, Springer Verlag Berlin, 414 (1992), 115–119.
R. Schwane and D. Hänel, An Implicit Flux-Vector Splitting Scheme for the Computation of Viscous Hypersonic Flow, AIAA-paper No. 89–0274, 1989.
R. Vilsmeier and D. Hänel, Adaptive Solutions for Unsteady Laminar Flows on Unstructured Grids, Int. J. for Numerical Methods in Fluids, 22 (1995), 85–101.
R. Vilsmeier and D. Hänel,A Field Method for 3-D Tetrahedral Mesh Generation and Adaption, Proc. of 14th Int. Conf. on Num. Meth. in Fluid Dynamics, Bangalore (India), 1994.
B. van Leer, Towards the Ultimate Conservative Difference Scheme, A second-order sequel to Godunov’s method. J. Comp. Phys., 32 (1979), 101–136.
R. Vilsmeier and D. Hänel, Solutions of the Conservation Equations and Adaptivity on 3-D Unstructured Meshes, Proc. of 9th International Conference on Numerical Methods in Laminar and Turbulent Flow, 1995.
P.L. Roe, Approximate Riemann Solvers, Parameter Vectors and Difference Schemes, J. Comp. Phys., 22 (1981), 357.
H.C. Yee, A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods, in VKI Lecture Series 1989–04, Rhode-Saint-Genese, 1989; also in H.C. Yee, Upwind and Symmetric Shock-Capturing Schemes, NASA TM-89464, 1987.
A. Harten, High Resolution Schemes for Hyperbolic Conservation Laws, J. Comp. Phys, 49 (1983), 357–393.
M. Berger and P. Colella, Local Adaptive Mesh Refinement for Shock Hydrodynamics, J. Comp. Phys, 82 (1989), 67–84.
J.J. Quirk, An Adaptive Grid Algorithm for Computational Shock Hydrodynamics, Ph.D. Thesis, Cranfield Inst. of. Technology, U.K., 1991.
C. Thill, U. Uphoff and D. Hänel, Structured Mesh-Refinement Techniques for Reactive and Multi-Phase Flow, Proc. of ECCOMACS 96, Paris, Sept, 1996.
P.R. Eiseman, Adaptive Grid Generation, Computer Meth. in Appl. Mech. and Eng., 64 (1987), 321–376.
K. Nakahashi and G.S. Deiwert, Self-Adaptive Grid Method with Application to Airfoil Flow, AIAA-J., 25 (1987), 513–520.
U. Uphoff, D. Hänel and P. Roth, Influence of Reactive Particles on the Formation of a One-Dimensional Detonation Wave, Combustion Science and Technology, 110–111 (1995), 419-441.
U. Uphoff, Numerische Simulation von Verbrennungswellen in Gas-Partikel Gemischen Thesis at Univ. of Duisburg, Germany, 1997.
R. Le Veque and M. Berger, CLAWPACK with Marsha Berger’s Adaptive Mesh Refinement codes, Web address: http://www.amath.washington.edu/rjl/clawpack, 1997.
J. Bell, M.J. Berger, J. Saltzman and M. Welcome, Three dimensional adaptive mesh refinement for hyperbolic conservation laws, J. Sci. Comput., 15 (1994), 127–138.
W. Speares and E.F. Toro, A High Resolution Algorithm for Time-Dependent Shock Dominated Meshes with Adaptive Mesh Refinement, Z. Flugwiss. Weltraumforschung, 19 (1995), 267–281.
U. Uphoff, D. Hänel and P. Roth, A Grid Refinement Study for Detonation Simulation with Detailed Chemistry, Proc. of 6th Int. Conf. on Num. Combustion, New Orleans, March 4–6, 1996.
T. Plewa and M. Rozyczka, Modern numerical hydrodynamics and the evolution of dense medium, Rev. Mex. Astr. Astrofls., (1996). Proc. Starburst Activity in Galaxies, Eds. J. Franco, R. Terlevich, and G. Tenorio-Tagle, 1996.
J. Fischer and E.H. Hirschel, Adaptive Navier-Stokes Calculations using a Combination of an Implicit Finite-Volume Method with a Hierarchically Ordered Grid Structure, in Notes on Num. Fluid. Mech., Vieweg-Verlag Braunschweig, 38 (1993), 279–294.
W. J. Coirier, An Adaptively-refined Cartesian Cell-Based Scheme for the Eueler and Navier-Stokes Equations, Ph.D. Thesis, The Univ. of Michigan, 1994, and NASA TM 106754, 1994
H. Deconinck, T.J. Barth (ed.), Special course on unstructured grid methods for advection dominated flows, AGARD Rep. 787, AGARD, Paris, 1992.
V. Venkatakrishnan: A Perspective on Unstructured Grid Flow Solvers, NASA CR-195025 ICASE Report No. 95–3, Institute for Computer Applications in Science and Engineering, ICASE, 1995.
R. Vilsmeier and D. Hänel, Computational Aspects of Flow Simulation on 3-D, Unstructured, Adaptive Grids, in E.H. Hirschel (Ed.): Flow Simulation with High Performance Computers, Notes on Numerical Fluid Mechanics, Vieweg Verlag, Wiesbaden, 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Basel AG
About this paper
Cite this paper
Hänel, D., Roth, P., Rose, M., Thill, C., Uphoff, U., Vilsmeier, R. (1999). Adaptive Grid Methods for Reactive Flows. In: Fey, M., Jeltsch, R. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 129. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8720-5_48
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8720-5_48
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9742-6
Online ISBN: 978-3-0348-8720-5
eBook Packages: Springer Book Archive