Quadratic reconstruction finite volume schemes on 3D arbitrary unstrtictured polyhedral grids

14th Computational Fluid Dynamics Conference

Volumn , Issue , 1999, Pages 80-90

  Delanaye, Michel ^a,b   Liu, Yen ^a,b  

^a NASA AMES RESEARCH CENTER   (United States)

^b Computational Physics and Simulation Branch ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FLUID DYNAMICS;

CRITICAL EVALUATION; FINITE VOLUME SCHEMES; GAUSS QUADRATURE RULES; HIGHER-ORDER METHODS; IMPLEMENTATION STRATEGIES; MEMORY REQUIREMENTS; SECOND-ORDER METHODS; UNSTRUCTURED GRID;

COMPUTATIONAL FLUID DYNAMICS;

EID: 84982318083     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (25)

1. Barth, T. and Prederickson, P., “Higher Order Solution of the Euler Equations on Unstructured Grids Using Quadratic Reconstruction,” AIAA paper 93-0668, 1990.
2. Mitchell, C. and Walters, R., “K-Exact Reconstruction for the Navier-Stokes Equations on Arbitrary Grids,” AIAA paper 93- 0536, 1993.
3. Abgrall, R., “An Essentially Non-Oscillatory Reconstruction Procedure on Finite-Element Type Meshes: Application to Compressible Flows,” Comp. Meth. Appl. Mech. Eng., No. 116, 1994, pp. 95-101.
4. Berger, M. and Melton, J., “An Accuracy Test of a Cartesian Grid Method for Steady Flow in Complex Geometries,” Tech. Rep. 95.02, RIACS, 1995.
5. Mitchell, C, “Improved Reconstruction Schemes for the Navier-Stokes Equations on Unstructured Meshes,” AIAA paper 94-0642, 1994.
6. Okong'o, N. and D., K., “Accurate Three-Dimensional Unsteady Flow Simulation Using Unstructured Grids,” AIAA paper 98-0787, 1999.
7. Delanaye, M. and Essers, J., “Quadratic Reconstruction Finite Volume Scheme for Compressible Flows on Unstructured Adaptive Grids,” AIAA Journal, Vol. 35, No. 3, March 1997.
8. Delanaye, M., Geuzaine, P., and Essers, J., “Development and Applications of Quadratic Reconstruction Schemes for Compressible Flows on Unstructured Adaptive Grids,” AIAA Paper 97-2120, June 1997.
9. Aftosmis, M., “Solution Adaptive Cartesian Grid Methods for Aerodynamic Flows with Complex Geometries,” CFD VKI Lectures Series 1997-05, 1997.
10. Schwab, C, “hp-FEM for fluid flow simulation,” NATO Special Course on High Order Discretization Methods in Computational Fluid Dynamics, 1998.
11. Aftosmis, M., Melton, J., and Berger, M., “Adaptation and Surface Modeling for Cartesian Mesh Methods,” AIAA paper 95-1725-CP, Jun. 1995.
12. Berger, M. and Aftosmis, M., “Aspects (and Aspect Ratios) of Cartesian Mesh Methods,” 16th International Conf. on Numerical Methods in Fluid Dynamics (Arcachon, France), to appear in Lecture Notes in Physics, Springer Verlag, July 1998.
13. Roe, P., “Approximate Riemann Solvers, Parameter Vectors and Difference Schemes,” Journal of Computational Physics, Vol. 43, 1981, pp. 357-372.
14. Barth, T. and Jespersen, D., “The Design and Application of Upwind Schemes on Unstructured Meshes,” AIAA paper 890366, January 1989.
15. Fezoui, L. and Stoufflet, B., “A Class of Implicit Upwind Schemes for Euler Simulations with Unstructured Meshes,” Journal of Computational Physics, Vol. 84, No. 1, 1989, pp. 174-206.
16. Barth, T., “Aspect of Unstructured Grids and Finite Volume Solvers for the Euler and Navier-Stokes Equations,” Tech. Rep. AR-787, Unstructured Grid Methods for Advection Dominated Flows, AGARD, 1992.
17. Liu, Y. and Vinokur, M., “Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids,” Journal of Computational Physics, Vol. 140, 1998, pp. 122-147.
18. Sonar, T., “Optimal Recovery Using Thin Plates Splines in Finite Volume Methods for the Numerical Solution of Hyperbolic Conservation Laws,” IMA J. Num. Anal, (to appear), 1996.
19. Golub, G. and Van Loan, C., Matrix Computations, The Johns Hopkins University Press, 1985.
20. Abgrall, R., “On Essentially Non-Oscillatory Schemes on Unstructured Meshes: Analysis and Implementation,” Journal of Computational Physics, No. 114, 1994, pp. 45-58.
21. Johan, Z., Hughes, T., and Shakib, F., “A Globally Convergent Matrix-free Algorithm for Implicit Time-marching Schemes Arising in Finite Element Analysis in Fluids,” Comp. Meth. in App. Mec. and Eng., Vol. 87, 1991.
22. Delanaye, M., Geuzaine, P., Essers, J., and Rogiest, P., “A Second-Order Finite-Volume Scheme for Solving Euler and Navier-Stokes Equations on Unstructured Adaptive Grids with an Implicit Acceleration Procedure,” 77th AGARD FDP Symposium on Progress and Challenges in CFD Methods and Algorithms, Seville, October 1995.
23. Barth, T. and Linton, S., “An Unstructured Mesh Newton Solver for Compressible Fluid Flow and its Parallel Implementation,” AIAA paper 95-0221, 1995.
24. Brown, P. and Saad, Y., “Hybrid Krylov Methods for Nonlinear Systems of Equations,” SIAM Journal of Scientific and Statistical Computing, Vol. 11, No. 3, May 1990, pp. 450-481.
25. Balay, S., Gropp, W., Mclnnes, L. C, and Smith, D., “PETSc 2.0 Users Manual,” Tech. Rep. ANL 95/11, Argonne National Laboratory, http://www.mcs.anl.gov/petsc/petsc.html, 1997.