A reconstructed discontinuous Galerkin method for the compressible Euler equations on arbitrary grids

19th AIAA Computational Fluid Dynamics Conference

Volumn , Issue , 2009, Pages

  Luo, Hong ^a   Luo, Luqing ^a   Nourgaliev, Robert ^b   Mousseau, Vincent A ^b  

^a North Carolina State University   (United States)

^b IDAHO NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARBITRARY GRIDS; COMPUTING COST; DISCONTINUOUS GALERKIN; DISCONTINUOUS GALERKIN METHODS; FLOW PROBLEMS; LEAST SQUARES METHODS; NUMERICAL RESULTS; POLYNOMIAL SOLUTION; SECOND ORDERS; STORAGE REQUIREMENTS; THIRD-ORDER; VON NEUMANN NEIGHBORHOOD;

COMPUTATIONAL FLUID DYNAMICS; EULER EQUATIONS; FLUID DYNAMICS; POLYNOMIALS;

GALERKIN METHODS;

EID: 77958495852     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (32)

1. Reed, W.H. Reed and T.R. Hill, "Triangular Mesh Methods for the Neutron Transport Equation," Los Alamos Scientific Laboratory Report, LA-UR-73-479, 1973.
2. B. Cockburn, S. Hou, and C. W. Shu, "TVD Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for conservation laws IV: the Multidimensional Case, '' Mathematics of Computation, Vol. 55, pp. 545-581, 1990.eorge, P. L., Automatic Mesh Generation, J. Wiley & Sons, 1991.
3. B. Cockburn, and C. W. Shu, "The Runge-Kutta Discontinuous Galerkin Method for conservation laws V: Multidimensional System," Journal of Computational Physics, Vol. 141, pp. 199-224, 1998.
4. B. Cockburn, G. Karniadakis, and C. W. Shu, "The Development of Discontinuous Galerkin Method'', in Discontinuous Galerkin Methods, Theory, Computation, and Applications, edited by B. Cockburn, G.E. Karniadakis, and C. W. Shu, Lecture Notes in Computational Science and Engineering, Springer-Verlag, New York, 2000, Vol. 11 pp. 5-50, 2000.
5. F. Bassi and S. Rebay, "High-Order Accurate Discontinuous Finite Element Solution of the 2D Euler Equations," Journal of Computational Physics, Vol. 138, pp. 251-285, 1997.
6. H. L. Atkins and C. W. Shu, "Quadrature Free Implementation of Discontinuous Galerkin Method for Hyperbolic Equations," AIAA Journal, Vol. 36, No. 5, 1998.
7. F. Bassi and S. Rebay, "GMRES discontinuous Galerkin solution of the Compressible Navier-Stokes Equations, '' Discontinuous Galerkin Methods, Theory, Computation, and Applications, edited by B. Cockburn, G.E. Karniadakis, and C. W. Shu, Lecture Notes in Computational Science and Engineering, Springer-Verlag, New York, 2000, Vol. 11 pp. 197-208, 2000.
8. T. C. Warburton, and G. E. Karniadakis, "A Discontinuous Galerkin Method for the Viscous MHD Equations," Journal of Computational Physics, Vol. 152, pp. 608-641, 1999.
9. J. S. Hesthaven and T. Warburton, "Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications, '' Texts in Applied Mathematics, Vol. 56, 2008.
10. P. Rasetarinera and M. Y. Hussaini, "An Efficient Implicit Discontinuous Spectral Galerkin Method," Journal of Computational Physics, Vol. 172, pp. 718-738, 2001.
11. B. T. Helenbrook, D. Mavriplis, and H. L. Atkins, "Analysis of p-Multigrid for Continuous and Discontinuous Finite Element Discretizations, " AIAA Paper 2003-3989, 2003.
12. K. J. Fidkowski, T. A. Oliver, J. Lu, and D. L. Darmofal, "p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations," Journal of Computational Physics, Vol. 207, No. 1, pp. 92-113, 2005.
13. H. Luo, J. D. Baum, and R. Löhner, "A Discontinuous Galerkin Method Using Taylor Basis for Compressible Flows on Arbitrary Grids," Journal of Computational Physics, DOI: 210.1016/j.jcp.2008.06.035, Vol. 227, No 20, pp. 8875-8893, October 2008.
14. H. Luo, J.D. Baum, and R. Löhner, "On the Computation of Steady-State Compressible Flows Using a Discontinuous Galerkin Method", International Journal for Numerical Methods in Engineering, Vol. 73, No. 5, pp. 597-623, 2008. (Pubitemid 351308447)
15. H. Luo, J. D. Baum, and R. Löhner, "A Hermite WENO-based Limiter for Discontinuous Galerkin Method on Unstructured Grids," Journal of Computational Physics, Vol. 225, No. 1, pp. 686-713, 2007.
16. H. Luo, J.D. Baum, and R. Löhner, "A p-Multigrid Discontinuous Galerkin Method for the Euler Equations on Unstructured Grids", Journal of Computational Physics, Vol. 211, No. 2, pp. 767-783, 2006. (Pubitemid 41472450)
17. H. Luo, J.D. Baum, and R. Löhner, "A Fast, p-Multigrid Discontinuous Galerkin Method for Compressible Flows at All Speeds", AIAA Journal, Vol. 46, No. 3, pp.635-652, 2008.
18. F. Bassi and S. Rebay, "A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations, '' Journal of Computational Physics, Vol. 131, pp. 267-279, 1997.
19. B. Cockburn and C.W. Shu, "The Local Discontinuous Galerkin Method for Time-dependent Convection-Diffusion System, SIAM, Journal of Numerical Analysis, Vo. 16, 2001.
20. C. E. Baumann and J. T. Oden, "A Discontinuous hp Finite Element Method for the Euler and Navier-Stokes Equations," International Journal for Numerical Methods in Fluids, Vol. 31, 1999.
21. D. N. Arnold, F. Brezzi, B. Cockburn, and L. D. Marini, "Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems", SIAM Journal on Numerical Analysis. Vol. 39, No. 5., pp. 1749-1779, 2002.
22. H. Luo and K. Xu - A BGK-based Discontinuous Galerkin Method for the Navier-Stokes Equations on Arbitrary Grids, AIAA-2008-0748, 2008.
23. B. van Leer and S. Nomura, "Discontinuous Galerkin Method for Diffusion," AIAA Paper 2005-5108, 2005.
24. B. van Leer and M. Lo, "A Discontinuous Galerkin Method for Diffusion Based on Recovery," AIAA Paper 2007-4083, 2007.
25. M. Raalte and B. van Leer, "Bilinear Forms for the Recovery-Based Discontinuous Galerkin Method for Diffusion," Communication of Computational Physics, Vol. 5, No. 2-4, pp. 683-693, 2009.
26. M. Aftosmis, D. Gaitonde, and T. S. Tavares, "On the Accuracy, Stability, and Monotonicity of Various Reconstruction Algorithms for Unstructured Meshes," AIAA Paper 94-0415, 1994.
27. A. Haselbacher, J. J. McGuirk, and G. J. Page, "Finite-Volume Discretization Aspects for Viscous Flows for Mixed Unstructured Meshes," AIAA Journal, 37(2), pp. 177-184, 1999.
28. H. Luo, J. D. Baum, and R. Löhner, "A Fast, Matrix-free Implicit Method for Compressible Flows on Unstructured Grids," Journal of Computational Physics, Vol. 146, No. 2, pp. 664-690, 1998.
29. H. Luo, D. Sharov, J. D. Baum, and R. Löhner, "On the Computation of Compressible Turbulent Flows Flows on Unstructured Grids", International Journal of Computational Fluid Dynamics, Vol. 14, pp. 253-270, 2001.
30. R. Nourgaliev, T.G. Theofanous, H. Park, V. Mousseau, and D. Knoll, "Direct Numerical Simulation of Interfacial Flows: Implicit Sharp-Interface Method," AIAA-2008-1453, 2008.
31. R. Nourgaliev, H. Park, and V. Mousseau, "Recovery Discontinuous Galerkin Jacobian-Free Newton-Krylov Method for Multiphysics Problems," To be appeared in Computational Fluid Dynamics Review 2009, 2009.
32. P. Colella and P. R. Woodward, "The Piecewise Parabolic Method (PPM) for Gas-Dynamical Simulations," Journal of Computational Physics, Vol. 54, No. 1, pp. 115-173, 1984.