An assessment of unstructured grid finite volume schemes for cold gas hypersonic flow calculations

Azevedo, João Luiz F.; Korzenowski, Heidi

doi:10.5028/jatm.2009.0102135152

Abstract:

A comparison of five different spatial discretization schemes is performed considering a typical high speed flow application. Flowfields are simulated using the 2-D Euler equations, discretized in a cell-centered finite volume procedure on unstructured triangular meshes. The algorithms studied include a central difference-type scheme, and 1st- and 2nd-order van Leer and Liou flux-vector splitting schemes. These methods are implemented in an efficient, edge-based, unstructured grid procedure which allows for adaptive mesh refinement based on flow property gradients. Details of the unstructured grid implementation of the methods are presented together with a discussion of the data structure and of the adaptive refinement strategy. The application of interest is the cold gas flow through a typical hypersonic inlet. Results for different entrance Mach numbers and mesh topologies are discussed in order to assess the comparative performance of the various spatial discretization schemes.

Keywords:
Hypersonic flow; Cold gas flow; Finite volume method; Unstructured grids; Spatial discretization schemes

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REFERENCES

Anderson, W. K., Thomas, J. L., Van Leer, B., 1986, "A Comparison of Finite Volume Flux Vector Splittings for the Euler Equations", AIAA Journal, Vol. 24, Nº. 9, pp. 1453-1460.
Azevedo, J. L. F., 1992, "On the Development of Unstructured Grid Finite Volume Solvers for High Speed Flows", IAE, São José dos Campos, Brazil, (Report NT-075-ASE-N/92).
Azevedo, J. L. F., Figueira da Silva, L.F., 1997, "The Development of an Unstructured Grid Solver for Reactive Compressible Flow Applications", 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Seattle, WA (AIAA Paper 97-3239).
Azevedo, J. L. F., Oliveira, L. C., 1994, "Unsteady Airfoil Flow Simulations Using the Euler Equations", Proceedings of the 12th AIAA Applied Aerodynamics Conference, Part 2, Colorado Springs, CO, pp. 650-660, (AIAA Paper 94-1892-CP).
Hirsch, C., 1990, "Numerical Computation of Internal and External Flows", Vol. 2: Computational Methods for Inviscid and Viscous Flows, Wiley, New York, Chap. 20, pp. 408-443.
Jameson, A., Mavriplis, D., 1986, "Finite Volume Solution of the Two-Dimensional Euler Equations on a Regular Triangular Mesh", AIAA Journal, Vol. 24, Nº. 4, pp. 611-618.
Jameson, A., Schmidt, W., Turkel, E., 1981, "Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes", AIAA 14th Fluid and Plasma Dynamics Conference, Palo Alto, CA (AIAA Paper 81-1259).
Liou, M.S., 1994, "A Continuing Search for a Near-Perfect Numerical Flux Scheme. Part I:AUSM⁺", NASA Lewis Research Center, Cleveland, OH (NASA TM-106524).
Liou, M.S.,1996,"A Sequel to AUSM: AUSM⁺", Journal of Computational Physics, Vol. 129, pp. 364-382.
Lyra, P. R. M., 1994, "Unstructured Grid Adaptive Algorithms for Fluid Dynamics and Heat Conduction", Ph.D.Thesis, Department of Civil Engineering, University of Wales Swansea, Swansea, Wales, U.K.
Mavriplis, D.J., 1988, "Multigrid Solution of the Two-Dimensional Euler Equations on Unstructured Triangular Meshes", AIAA Journal, Vol. 26, Nº.7, pp. 824-831.
Mavriplis, D.J., 1990, "Accurate Multigrid Solution of the Euler Equations on Unstructured and Adaptive Meshes", AIAA Journal, Vol. 28, Nº. 2, pp. 213-221.
Pulliam, T. H., 1986, "Artificial Dissipation Models for the Euler Equations", AIAA Journal, Vol. 24, Nº. 12, pp.1931-1940.
Steger, J. L., Warming, R. F., 1981, "Flux Vector Splitting of the Inviscid Gasdynamic Equations with Application to Finite-Difference Methods", Journal of Computational Physics, Vol. 40, Nº. 2, pp. 263-293.
Van Leer, B., 1979, "Towards the Ultimate Conservative Difference Scheme. V. A Second-Order Sequel to Godunov's Method", Journal of Computational Physics, Vol. 32, Nº. 1, pp. 101-136.
Van Leer, B., 1982, "Flux-Vector Splitting for the Euler Equations," Proceedings of the 8th International Conference on Numerical Methods in Fluid Dynamics, E. Krause, editor, Lecture Notes in Physics, Springer-Verlag, Berlin, Vol. 170, pp. 507-512.

Publication Dates

Publication in this collection
Jul-Dec 2009

History

Received
03 Sept 2009
Accepted
06 Oct 2009

This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

[1] Anderson, W. K., Thomas, J. L., Van Leer, B., 1986, "A Comparison of Finite Volume Flux Vector Splittings for the Euler Equations", AIAA Journal, Vol. 24, Nº. 9, pp. 1453-1460.

[2] Azevedo, J. L. F., 1992, "On the Development of Unstructured Grid Finite Volume Solvers for High Speed Flows", IAE, São José dos Campos, Brazil, (Report NT-075-ASE-N/92).

[3] Azevedo, J. L. F., Figueira da Silva, L.F., 1997, "The Development of an Unstructured Grid Solver for Reactive Compressible Flow Applications", 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Seattle, WA (AIAA Paper 97-3239).

[4] Azevedo, J. L. F., Oliveira, L. C., 1994, "Unsteady Airfoil Flow Simulations Using the Euler Equations", Proceedings of the 12th AIAA Applied Aerodynamics Conference, Part 2, Colorado Springs, CO, pp. 650-660, (AIAA Paper 94-1892-CP).

[5] Hirsch, C., 1990, "Numerical Computation of Internal and External Flows", Vol. 2: Computational Methods for Inviscid and Viscous Flows, Wiley, New York, Chap. 20, pp. 408-443.

[6] Jameson, A., Mavriplis, D., 1986, "Finite Volume Solution of the Two-Dimensional Euler Equations on a Regular Triangular Mesh", AIAA Journal, Vol. 24, Nº. 4, pp. 611-618.

[7] Jameson, A., Schmidt, W., Turkel, E., 1981, "Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes", AIAA 14th Fluid and Plasma Dynamics Conference, Palo Alto, CA (AIAA Paper 81-1259).

[8] Liou, M.S., 1994, "A Continuing Search for a Near-Perfect Numerical Flux Scheme. Part I:AUSM⁺", NASA Lewis Research Center, Cleveland, OH (NASA TM-106524).

[9] Liou, M.S.,1996,"A Sequel to AUSM: AUSM⁺", Journal of Computational Physics, Vol. 129, pp. 364-382.

[10] Lyra, P. R. M., 1994, "Unstructured Grid Adaptive Algorithms for Fluid Dynamics and Heat Conduction", Ph.D.Thesis, Department of Civil Engineering, University of Wales Swansea, Swansea, Wales, U.K.

[11] Mavriplis, D.J., 1988, "Multigrid Solution of the Two-Dimensional Euler Equations on Unstructured Triangular Meshes", AIAA Journal, Vol. 26, Nº.7, pp. 824-831.

[12] Mavriplis, D.J., 1990, "Accurate Multigrid Solution of the Euler Equations on Unstructured and Adaptive Meshes", AIAA Journal, Vol. 28, Nº. 2, pp. 213-221.

[13] Pulliam, T. H., 1986, "Artificial Dissipation Models for the Euler Equations", AIAA Journal, Vol. 24, Nº. 12, pp.1931-1940.

[14] Steger, J. L., Warming, R. F., 1981, "Flux Vector Splitting of the Inviscid Gasdynamic Equations with Application to Finite-Difference Methods", Journal of Computational Physics, Vol. 40, Nº. 2, pp. 263-293.

[15] Van Leer, B., 1979, "Towards the Ultimate Conservative Difference Scheme. V. A Second-Order Sequel to Godunov's Method", Journal of Computational Physics, Vol. 32, Nº. 1, pp. 101-136.

[16] Van Leer, B., 1982, "Flux-Vector Splitting for the Euler Equations," Proceedings of the 8th International Conference on Numerical Methods in Fluid Dynamics, E. Krause, editor, Lecture Notes in Physics, Springer-Verlag, Berlin, Vol. 170, pp. 507-512.

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