Arbitrary high order PNPM schemes on unstructured meshes for the compressible Navier-Stokes equations

Computers and Fluids

Volumn 39, Issue 1, 2010, Pages 60-76

  Dumbser, Michael ^a,b  

^a UNIVERSITY OF TRENTO   (Italy)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CFD APPLICATIONS; COMPRESSIBLE MIXING LAYER; COMPRESSIBLE NAVIER-STOKES EQUATIONS; DISCONTINUOUS GALERKIN; DISCONTINUOUS GALERKIN METHODS; FINITE VOLUME; FINITE VOLUME SCHEMES; FLAT PLATE; HIGH ORDER; HIGH REYNOLDS NUMBER; HYPERBOLIC SYSTEM; LAMINAR BOUNDARY LAYER FLOW; NUMERICAL CONVERGENCE; POLYNOMIAL DEGREE; TEST FUNCTIONS; TETRAHEDRAL MESHES; TWO SPACE DIMENSIONS; UNSTRUCTURED MESHES;

AERODYNAMICS; AIRFOILS; CIRCULAR CYLINDERS; COMPUTATIONAL FLUID DYNAMICS; CONVERGENCE OF NUMERICAL METHODS; FLUID DYNAMICS; GALERKIN METHODS; MACH NUMBER; MESH GENERATION; REYNOLDS NUMBER; UNSTEADY FLOW; VISCOUS FLOW;

NAVIER STOKES EQUATIONS;

EID: 70350223969     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compfluid.2009.07.003     Document Type: Article

References (46)

1. Abgrall R. On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation. J Comput Phys 144 (1994) 45-58
2. Arnold D.N., Brezzi F., Cockburn B., and Marini L.D. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J Numer Anal 39 (2002) 1749-1779
3. Babucke A., Kloker M., and Rist U. DNS of a plane mixing layer for the investigation of sound generation mechanisms. Comput Fluids 37 (2008) 360-368
4. Barth TJ, Frederickson PO. Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction. In: AIAA paper no. 90-0013, 28th Aerospace Sciences Meeting; January 1990.
5. Barth TJ, Jespersen DC. The design and application of upwind schemes on unstructured meshes, AIAA paper 89-0366; 1989. p. 1-12.
6. Bassi F., and Rebay S. A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. J Comput Phys 131 (1997) 267-279
7. Bassi F., and Rebay S. High-order accurate discontinuous finite element solution of the 2D Euler equations. J Comput Phys 138 (1997) 251-285
8. Becker R. Stosswelle und detonation. Physik 8 (1923) 321
9. Blasius H. Grenzschichten in Flüssigkeiten mit kleiner Reibung. Z Math Phys 56 (1908) 1-37
10. Bonnet A, Luneau J. Aérodynamique, Théories de la dynamique des fluides, Cepadues Editions, Toulouse; 1989. ISBN: 2.85428.218.3.
11. Cockburn B., Hou S., and Shu C.W. The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws: IV. The multidimensional case. Math Comput 54 (1990) 545-581
12. Cockburn B., and Shu C.W. The local discontinuous Galerkin method for time-dependent convection diffusion systems. SIAM J Numer Anal 35 (1998) 2440-2463
13. Cockburn B., and Shu C.W. The Runge-Kutta discontinuous Galerkin method for conservation laws: V. Multidimensional systems. J Comput Phys 141 (1998) 199-224
14. Cockburn B., and Shu C.W. Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. J Sci Comput 16 (2001) 173-261
15. Colonius T., Lele S.K., and Moin P. Sound generation in a mixing layer. J Fluid Mech 330 (1997) 375-409
16. Dumbser M., Balsara D., Toro E.F., and Munz C.D. A unified framework for the construction of one-step finite-volume and discontinuous Galerkin schemes. J Comput Phys 227 (2008) 8209-8253
17. Dumbser M., Castro M., Parés C., and Toro E.F. ADER schemes on unstructured meshes for nonconservative hyperbolic systems: applications to geophysical flows. Comput Fluids 38 (2009) 1731-1748
18. Dumbser M., Enaux C., and Toro E.F. Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws. J Comput Phys 227 (2008) 3971-4001
19. Dumbser M., and Käser M. Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems. J Comput Phys 221 (2007) 693-723
20. Dumbser M., Käser M., A Titarev V., and Toro E.F. Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems. J Comput Phys 226 (2007) 204-243
21. Dumbser M., and Munz C.D. Building blocks for arbitrary high order discontinuous Galerkin schemes. J Sci Comput 27 (2006) 215-230
22. Dumbser M., and Munz C.D. On source terms and boundary conditions using arbitrary high order discontinuous Galerkin schemes. Int J Appl Math Sci Comput 17 (2007) 297-310
23. Gassner G., Lörcher F., and Munz C.D. A discontinuous Galerkin scheme based on a space-time expansion: II. Viscous flow equations in multi-dimensions. J Sci Comput 34 (2008) 260-286
24. Gassner G., Lörcher F., and Munz C.D. A contribution to the construction of diffusion fluxes for finite volume and discontinuous Galerkin schemes. J Comput Phys 224 (2007) 1049-1063
25. Harten A., Engquist B., Osher S., and Chakravarthy S. Uniformly high order essentially non-oscillatory schemes: III. J Comput Phys 71 (1987) 231-303
26. Hartmann R., and Houston P. Symmetric interior penalty DG methods for the compressible Navier-Stokes equations: I. Method formulation. Int J Numer Anal Model 3 (2006) 1-20
27. Hartmann R., and Houston P. An optimal order interior penalty discontinuous galerkin discretization of the compressible navier stokes equations. J Comput Phys 227 (2008) 9670-9685
28. Hu C., and Shu C.W. Weighted essentially non-oscillatory schemes on triangular meshes. J Comput Phys 150 (1999) 97-127
29. Johnson T., and Patel V. Flow past a sphere up to a Reynolds number of 300. J Fluid Mech 378 (1999) 19-70
30. Klaij C., van der Vegt J.J.W., and van der Ven H. Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations. J Comput Phys 217 (2006) 589-611
31. Lele S.K. Compact finite difference schemes with spectral like resolution. J Comput Phys 103 (1992) 16-42
32. Levy D., Shu C.W., and Yan J. Local discontinuous Galerkin methods for nonlinear dispersive equations. J Comput Phys 196 (2004) 751-772
33. Müller B. High order numerical simulation of aeolian tones. Comput Fluids 37 (2008) 450-462
34. Ollivier-Gooch C., and Van Altena M. A high-order-accurate unstructured mesh finite-volume scheme for the advection-diffusion equation. J Comput Phys 181 (2002) 729-752
35. Prandtl L. Über Flüssigkeitsbewegung bei sehr kleiner Reibung. Verhandlg III: Int Math Kongr Heidelberg (1904) 484-491
36. Schlichting H., and Gersten K. Grenzschichttheorie (2005), Springer, Berlin
37. Stroud A.H. Approximate calculation of multiple integrals (1971), Prentice-Hall, Englewood Cliffs (NJ)
38. Titarev V.A., and Toro E.F. ADER schemes for three-dimensional nonlinear hyperbolic systems. J Comput Phys 204 (2005) 715-736
39. Toro E.F. Riemann solvers and numerical methods for fluid dynamics. 2nd ed. (1999), Springer, Berlin
40. Toro E.F., and Hidalgo A. ADER finite volume schemes for nonlinear reaction-diffusion equations. Appl Numer Math 59 (2009) 73-100
41. Toro E.F., and Titarev V.A. Solution of the generalized Riemann problem for advection-reaction equations. Proc Roy Soc Lond (2002) 271-281
42. van der Vegt J.J.W., and van der Ven H. Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows: I. General formulation. J Comput Phys 182 (2002) 546-585
43. van Leer B. Towards the ultimate conservative difference scheme: V. A second order sequel to Godunov's method. J Comput Phys 32 (1979) 101-136
44. van Leer B, Nomura S. Discontinuous Galerkin for diffusion. In: Proceedings of 17th AIAA computational fluid dynamics conference, AIAA-2005-5108; June 6-9 2005.
45. Woodward P., and Colella P. The numerical simulation of two-dimensional fluid flow with strong shocks. J Comput Phys 54 (1984) 115-173
46. Yan J., and Shu C.W. A local discontinuous Galerkin method for KdV-type equations. SIAM J Numer Anal 40 (2002) 769-791