Unstructured high-order accurate finite-volume solutions of the Navier-Stokes equations

47th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition

Volumn , Issue , 2009, Pages

  Michalak, Chris ^a   Ollivier Gooch, Carl ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

INVERSE PROBLEMS; JACOBIAN MATRICES; LAMINAR FLOW; VISCOUS FLOW;

CYLINDRICAL COUETTE FLOW; FINITE VOLUME SCHEMES; FINITE VOLUME SOLUTION; FOURTH-ORDER SCHEME; ORDER OF ACCURACY; RAPID CONVERGENCE; RECONSTRUCTION MATRIX; STEADY-STATE PROBLEMS;

NAVIER STOKES EQUATIONS;

EID: 78549266201     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.2009-954     Document Type: Conference Paper

References (19)

1. Barth, T. J. and Frederickson, P. O., "Higher Order Solution of the Euler Equations on Unstructured Grids Using Quadratic Reconstruction," AIAA paper 90-0013, Jan. 1990.
2. Ollivier-Gooch, C., Nejat, A., and Michalak, C., "On Obtaining High-Order Finite-Volume Solutions to the Euler Equations on Unstructured Meshes," Proc. 18th AIAA CFD Conf., 2007, AIAA-2007-4464.
3. Nejat, A. and Ollivier-Gooch, C., "Effect of Discretization Order on Preconditioning and Convergence of a High-Order Unstructured Newton-GMRES Solver for the Euler Equations," J. Comp. Phys., Vol. 227, No. 4, 2008, pp. 2366-2386.
4. Nejat, A. and Ollivier-Gooch, C., "A High-Order Accurate Unstructured Finite Volume Newton-Krylov Algorithm for Inviscid Compressible Flows," J. Comp. Phys., Vol. 227, No. 4, 2008, pp. 2592-2609.
5. Michalak, K. and Ollivier-Gooch, C., "Matrix-Explicit GMRES for a Higher-Order Accurate Inviscid Compressible Flow Solver," Proc. 18th AIAA CFD Conf., 2007.
6. Delanaye, M. and Essers, J. A., "Quadratic-reconstruction finite volume scheme for compressible flows on unstructured adaptive grids," AIAA J., Vol. 35, No. 4, April 1997, pp. 631-639.
7. Geuzaine, P., Delanaye, M., and Essers, J.-A., "Computation of High Reynolds Number Flows with an Implicit Quadratic Reconstruction Scheme on Unstructured Grids," Proc. 13th AIAA CFD Conf., Amer. Inst. Aero. Astro., 1997, pp. 610-619.
8. Ollivier-Gooch, C. F. and Van Altena, M., "A High-order Accurate Unstructured Mesh Finite-Volume Scheme for the Advection-Diffusion Equation," J. Comp. Phys., Vol. 181, No. 2, 2002, pp. 729-752.
9. Barth, T. J., "Recent Developments in High Order K-Exact Reconstruction on Unstructured Meshes," AIAA paper 93-0668, Jan. 1993.
10. Mavriplis, D. J., "Revisiting the least-squares procedure for gradient reconstruction on unstructured meshes," Proceedings of the 16th AIAA Computational Fluid Dynamics Conference, 2003.
11. Golub, G. H. and Loan, C. F. V., Matrix Commutations, The Johns Hopkins University Press, Baltimore, 1983.
12. Diskin, B. and Thomas, J., "Accuracy Analysis for Mixed-Element Finite-Volume Discretization Schemes," Tech. Rep. 2007-08, National Institute of Aerospace, 2007.
13. Roe, P. L., "Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes," J. Comp. Phys., Vol. 43, 1981, pp. 357-372.
14. Saad, Y. and Schultz, M. H., "GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems," SIAM J. Sci. Stat. Comp., Vol. 7, No. 3, July 1986, pp. 856-869.
15. Mulder, W. and van Leer, B., "Experiments with implicit upwind methods for the Euler equations," J. Comp. Phys., Vol. 59, June 1985, pp. 232-246.
16. Illingworth, C, "Some Solutions of the Equations of Flow of a Viscous Compressible Fluid," Proc. Cambridge Phil. Soc, Vol. 46, 1950, pp. 469-478.
17. Pagnutti, D. and Ollivier-Gooch, C, "A Generalized Framework for High Order Anisotropic Mesh Adaptation," Comp. Struct., Vol. Submitted, 2008.
18. Mavriplis, D. and Jameson, A., "Multigrid Solution of the Two-Dimensional Euler Equations on Unstructured Triangular Meshes," AIAA paper 87-0353, Jan. 1987.
19. Radespiel, R., "A Cell-vertex Multigrid Method for the Navier-Stokes Equations," NASA TM-101557, 1989.