Spectral/hp Methods for Viscous Compressible Flows on Unstructured 2D Meshes

Journal of Computational Physics

Volumn 144, Issue 2, 1998, Pages 325-357

  Lomtev, I ^a   Quillen, C B ^a   Karniadakis, G E ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPRESSIBLE FLOW; GALERKIN METHODS; POLYNOMIALS; TENSORS;

2D MESHES; DISCONTINUOUS GALERKIN FORMULATION; GALERKIN FORMULATION; HIGH-ORDER; HIGHER ORDER ACCURACY; HIGHER-ORDER; JACOBI POLYNOMIALS; SPECTRAL/HP; UNSTRUCTURED MESHES; VISCOUS COMPRESSIBLE FLOWS;

NAVIER STOKES EQUATIONS;

EID: 0001234668     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1997.5831     Document Type: Article

References (41)

1. T. J. Barth, Recent developmets in high order k-exact reconstruction on unstructured meshes, 1993.
2. R. A. Shapiro, E. M. Murman, Higher-order and 3-d finite element methods for the Euler equations.
3. Morgan K., Hassan O., Peraire J. An unstructured grid algorithm for the solution of the Maxwell's equations in the time domain. Int. J. Numer. Methods Fluids. 19:1994;849.
4. Kreiss H. O., Olinger J. Methods for the Approximate Solution of Time-Dependent Problems. 10:1973.
5. Kopriva D. A. Multidomain spectral solution of the Euler gas-dynamics equations. J. Comput. Phys. 96:1991;428.
6. Kopriva D. A. Spectral solutions of inviscid supersonic flows over wedges and axisymmetric cones. Comput. & Fluids. 21:1992;247.
7. Cai W., Gottlieb D., Shu C. W. Non-oscillatory spectral Fourier methods for shock wave calculations. Math. Comput. 52:1989;389.
8. Sidilkover D., Karniadakis G. E. Non-oscillatory spectral element Chebyshev method for shock wave calculations. J. Comput. Phys. 107:1993.
9. Giannakouros J., Karniadakis G. E. A spectral element-FCT method for the compressible Euler equations. J. Comput. Phys. 115:1994;65.
10. Kopriva D. A., Kolias J. H. A conservative staggered-grid Chebyshev multidomain method for compressible flows. J. Comput. Phys. 125:1996;244.
11. Hesthaven J. S. A stable penalty method for the compressible Navier-Stokes equations. II. One dimensional domain decomposition schemes. SIAM J. Sci. Comput. 18:1997.
12. J. S. Hesthaven, A stable penalty method for the compressible Navier-Stokes equations. III. Multi-dimensional domain decomposition schemes, SIAM J. Sci. Comput.
13. Hesthaven J. S., Gottlieb D. A stable penalty method for the compressible Navier-Stokes equations. I. Open boundary conditions. SIAM J. Sci. Comput. 17:1996;579.
14. Karniadakis G. E., Orszag S. A. Nodes, modes and flow codes. Phys. Today. 46:1993;34.
15. Lele S. K. Compact finite difference schemes with spectral like resolution. J. Comput. Phys. 103:1992;16.
16. Patera A. T. A spectral method for fluid dynamics: Laminar flow in a channel expansion. J. Comput. Phys. 54:1984;468.
17. Karniadakis G. E., Bullister E. T., Patera A. T. A spectral element method for solution of two- and three-dimensional time dependent Navier-Stokes equations. Finite Element Methods for Nonlinear Problems. 1985;803.
18. Weatherill N. P., Hassan O. Efficient three-dimensional Delaurnay triangularisation with automatic point creation and imposed boundary constaints. Int. J. Numer. Methods Eng. 37:1994;2005.
19. D. J. Mavriplis, V. Venkatakrishnan, A unified multigrid solver for the Navier-Stokes equations on mixed element meshes, AIAA-95-1666, San Diego, CA, 1995.
20. V. Parthasarathy, Y. Kallindereris, K. Nakajima, Hybrid adaption method and directional viscous multigrid with presmatic-tetrahedral meshes, AIAA-95-0670, Reno, NV, 1995.
21. Sherwin S. J., Karniadakis G. E. A triangular spectral element method; applications to the incompressible Navier-Stokes equations. Comput. Meth. Appl. Mech. Eng. 23:1995;83.
22. Sherwin S. J., Karniadakis G. E. Tetrahedralhp. J. Comput. Phys. 122:1995;191.
23. Wingate B. A., Boyd J. P. Triangular spectral element methods for geophysical fluid dynamics applications. Houston J. Math. 1996;305.
24. Dubiner M. Spectral methods on triangles and other domains. J. Sci. Comput. 6:1991;345.
25. Cockburn B., Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: General framework. Math. Comput. 52:1989;411.
26. Cockburn B., Lin S.-Y., Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One-dimensional systems. J. Comput. Phys. 84:1989;90.
27. Cockburn B., Hou S., Shu C.-W. The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: The multi-dimensional case. J. Comput. Phys. 54:1990;545.
28. 1RKDG, Proc. Fourth Int. Symp. on CFD, UC Davis, 1991.
29. Biswas R., Devine K., Flaherty J. Parallel, adaptive finite element methods for conservation laws. Appl. Numer. Math. 14:1994;255.
30. Peiro J., Peraire J., Morgan K. 2D Felisa System - Reference Manual. 1994.
31. Johnson C. Numerical Solution of Partial Differential Equations by the Finite Element Method. 1994.
32. Sherwin S. J., Karniadakis G. E. A new triangular and tetrahedral basis for high-order finite element methods. Int. J. Numer. Meth. Eng. 38:1995;3775.
33. Canuto C., Hussaini M. Y., Quarteroni A., Zang T. A. Spectra Methods in Fluid Mechanics. 1987.
34. Roe P. L. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43:1981;357.
35. Y. Maday, A. T. Patera, Spectral element methods for the Navier-Stokes equations, Proc. State of the Art Surveys in Computational Mechanics, ASME, 1987.
36. I. Lomtev, G. E. Karniadakis, Simulations of viscous supersonic flows on unstructured meshes, 1997.
37. Hammache M., Gharib M. An experimental study of the parallel and oblique vortex shedding from circular cylinders. J. Fluid Mech. 232:1991;567.
38. Henderson R. D. Details of the drag curve near the onset of vortex shedding. Phys. Fluids. 7:1995;1.
39. Williamson C. H. K., Roshko A. Measurements of base pressure in the wake of a cylinder at low Reynolds number. Z. Flugwiss. Weltraumforsch. 14:1990;38.
40. A. Beskok, G. E. Karniadakis, A collocation spectral element method for compressible viscous flows.
41. T. C. E. Warburton, Spectral/hp Methods on Polymorphic Domains, Brown University, Division of Applied Mathematics.