Comparison of reconstruction techniques for unstructured mesh vertex centered finite volume schemes

Collection of Technical Papers - 18th AIAA Computational Fluid Dynamics Conference

Volumn 1, Issue , 2007, Pages 543-564

  Smith, Thomas M ^a,b,c   Barone, Matthew F ^a,c,d   Bond, Ryan B ^a,c,d   Lorber, Alfred A ^a,e   Baur, David G ^a,d  

^a SANDIA NATIONAL LABORATORIES   (United States)

^b Exploratory Simulation Technologies   (United States)

^c AIAA   (United States)

^d Advanced Computational Mechanics Architectures

^e Thermal Fluids Computational Engineering Sciences

Author keywords

[No Author keywords available]

Indexed keywords

ASPECT RATIO; DATA STRUCTURES; FINITE VOLUME METHOD; INTERPOLATION; MESH GENERATION; TOPOLOGY;

COLLINEAR EDGE; ELEMENT INTERPOLATION; MESH FINITE VOLUME; MESH VERTEX;

VISCOUS FLOW;

EID: 35648946260     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.2007-3958     Document Type: Conference Paper

References (38)

1. Roe, P. L., "Approximate Riemann Solvers, Parameters Vectors and Difference Schemes," Journal of Computational Physics, Vol. 43, 1981, pp. 357-372.
2. Yee, H. C., "Construction of Explicit and Implicit Symmetric TVD Schemes and Their Applications," Journal of Computational Physics, Vol. 68, 1987, pp. 151-179.
3. Löhner, R., Applied CFD Techniques An Introduction based on Finite Element Methods, Wiley, Chichester England, 2001.
4. Kuzmin, D. and Moller, M., "Algebraic Flux Correction I. Scalar Conservation Laws," Flux-Corrected Transport Principles, Algorithms and Applications, edited by D. Kuzmin, R. Löhner, and S. Turek, Springer, Berlin, Heidelberg, New York, 2005, pp. 155-206.
5. Lyra, P., Morgan, K., Peraire, J., and Peiro, J., "TVD Algorithms for the Solution of the Compressible Euler Equations on Unstructured Meshes," International Journal for Numerical Methods in Fluids, Vol. 19, 1994, pp. 827-847.
6. Barth, T., "A 3-D upwind Euler solver for unstructured meshes," AIAA Paper 91-1548-CP, 1991.
7. Haselbacher, A. and Blazek, J., "Accurate and Efficient discretization of Navier-Stokes Equations on Mixed Grids," AIAA Journal, Vol. 38, No. 11, November 2000, pp. 2094-2102.
8. Schneider, G. E. and Raw, M. J., "Control Volume Finite-Element Method for Heat Transfer and Fluid Flow Using Colocated Variables - 1. Computational Procedure," Numerical Heat Transfer, Vol. 11, 1987, pp. 363-390.
9. Schneider, G. E. and Raw, M. J., "Control Volume Finite-Element Method for Heat Transfer and Fluid Flow Using Colocated Variables - 1. Application and Validation," Numerical Heat Transfer, Vol. 11, 1987, pp. 391-400.
10. Luo, H., Baum, J., and Löhner, R., "An improved finite volume scheme for compressible flows on unstructured grids," AIAA Paper 1995-0348, January 1995.
11. Weatherill, N., Hassan, O., and Marcum, D., "Calculations of Steady Compressible Flowfields with the Finite Element Method," Paper AIAA-1993-0341, January 1993.
12. Weatherill, N., Hassan, O., and Marcum, D., "Compressible Flowfield Solutions with Unstructured Grids by Delaunay Triangulation," AIAA Journal, Vol. 33, No. 7, July 1995, pp. 1196-1204.
13. Lyra, P., Manzari, M., Morgan, K., Hassan, O., and Peraire, J., "Upwind Side-Based Unstructured Grid Algorithms for Compressible Viscous Flow Computations," International Journal for Engineering Analysis and Design, Vol. 2, 1995, pp. 197-211.
14. Lyra, P. and Morgan, K., "A Review and Comparative Study of Upwind Biased Schemes for Compressible Flow Computation. Part III: Multidimentional Extension on Unstructured Grids," Archives of Computational Methods in Engineering, Vol. 9, No. 3, 2002, pp. 207-256.
15. Gnoffo, P. and White, J., "Computational Aerothermodynamic Simulation Issues on Unstructured Grids," AIAA Paper 2004-2371, 2004.
16. Spalart, P. R. and Allmaras, S. R., "A One-Equation Turbulence Model for Aerodynamic Flows," AIAA Paper 92-0439, 1992.
17. Haselbacher, A. C., A Grid-Transparent Numerical Method for Compressible Viscous Flows on Mixed Unstructured Grids, Ph.D. thesis, Dept. of Aeronautical Engineering, Loughborough University, Loughborough University, September 1999.
18. van Leer, B., "Towards the Ultimate Conservation Difference Scheme. V. A Second-Order Sequel to Godunov's Method," Journal of Computational Physics, Vol. 32, 1979, pp. 101-136.
19. Hirsch, C., Numerical Computation of Internal and External Flows, Volume II, John Wiley & Sons, New York, 1990.
20. Fromm, J., "A Method for Reducing Dispersion in Convective Difference Schemes," Journal of Computational Physics, Vol. 3, 1968, pp. 176-189.
21. Leonard, B., "A Stable and Accurate Convective Modelling Procedure Based on Quadratic Upstream Interpolation," Computer Methods in Applied Mechanics adn Engineering, Vol. 19, 1979, pp. 59-98.
22. Luo, H., Baum, J. D., and Löhner, R., "Edge-Based Finite Element scheme for the Euler Equations," AIAA Journal, Vol. 32, No. 6, June 1994, pp. 1180-1190.
23. 23Aftosmis, M., Gaitonde, D., and Tavares, T. S., "Behavior of Linear Reconstruction Techniques on Unstructured Meshes," AIAA Journal, Vol. 33, No. 11, 1995, pp. 2038-2049.
24. Barth, T., "The Design and Application of Upwind Schemes on Unstructured Meshes," AIAA Paper 89-0366, January 1989.
25. Venkatakrishnan, V., "Convergence to steady state solutions of the Euler Equations on unstructured grids with limiters," Journal of Computational Physics, Vol. 118, 1995, pp. 120-130.
26. Barth, T., "Special Course on Unstructured Grid Methods for Advection Dominated Flows," Tech. Rep. AGARD-R-787, AGARD Advisory Group Report, 1992.
27. Fezoui, L. and Stoufflet, B., "A Class of Implicit Upwind Schemes for Euler Simulations with Unstructured Meshes," Journal of Computational Physics, Vol. 84, 1989, pp. 174-206.
28. Whitaker, D. L., "Three-Dimensional Unstructured Grid Euler Computations Using a Fully-Implicit, Upwind Method," AIAA Paper 93-3337, January 1993.
29. Liou, M.-S. and van Leer, B., "Choice of Implicit and Explicit operators for the upwind differencing method," AIAA Paper 1988-0624, January 1988.
30. McNeil, F. and Gnoffo, P. A., "User's Manual for the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA)," NASA TM-4674, NASA Langley Research Center, April 1996.
31. Chen, R. and Wang, Z., "Fast, Block Lower-Upper Symmetric Gauss-Seidel Scheme for Arbitrary Grids," AIAA Journal, Vol. 38, No. 12, 2000, pp. 2238-2244.
32. Sharov, D., Luo, H., and Baum, J. D., "Implementation of Unstructured Grid GMRES+LU-SGS Method on Shared-Memory, Cache-Based Parallel Computers," AIAA Paper 2000-0927, January 2000.
33. Jameson, A. and Yoon, S., "Lower-Upper Implicit Schemes with Multiple Grids for the Euler Equations," AIAA Journal, Vol. 25, No. 7, July 1987, pp. 929-935.
34. Smith, T. M., Hooper, R. W., Ober, C. C., and Lorber, A. A., "Intelligent Nonlinear Solvers for Computational Fluid Dynamics," AIAA Paper 2006-1483, January 2006.
35. Bond, R., Ober, C., and Knupp, P., "A Manufactured Solution for Verifying CFD Boundary Conditions, Part III," Paper AIAA-2006-3722, June 2006.
36. Mavriplis, D. J., "Revisiting the Least-Squares Procedure for Gradient Reconstruction on Unstructured Meshes," Paper AIAA-2003-3986, June 2003.
37. Peterson, C. W., Henfling, J. F., Erven, R. J., and McWherter-Payne, M. A., "Experimental characterization of supersonic spin motor nozzle flow," AIAA Paper 2004-1295, January 2004.
38. th ICFD Conference on Numerical Methods for Fluid Dynamics, Institute for Computational Fluid Dynamics, Oxford University, Oxford, 1998, pp. 425-432.