Free Access
Issue
Math. Model. Nat. Phenom.
Volume 6, Number 3, 2011
Computational aerodynamics
Page(s) 28 - 56
DOI https://doi.org/10.1051/mmnp/20116302
Published online 16 May 2011
  1. F. Bassi, S. Rebay. 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. [CrossRef] [MathSciNet] [Google Scholar]
  2. F. Bassi, S. Rebay. GMRES discontinuous Galerkin solution of the compressible Navier- Stokes equations. In B. Cockburn, G.E. Karniadakis, and C. W. Shu, editors, Discontinuous Galerkin Methods: Theory, Computations and Applications, volume 11 of Lecture Note in Computational Science and Engineering. Springer, 2000. [Google Scholar]
  3. Q. Chen and I. Babuska. Approximate optimal points for polynomial interpolation of real functions in an interval and in a triangle. Comput. Methods Appl. Mech. Eng., 128 (1995), 405-417. [CrossRef] [Google Scholar]
  4. B. Cockburn, S. Y. Lin, C. W. Shu. TVD Runge-Kutta local projection discontinuous Galerkin Finite element method for conservation laws III: one-dimensional systems. J. Comput. Phys., 84 (1989), 90-113. [CrossRef] [MathSciNet] [Google Scholar]
  5. B. Cockburn, C. W. Shu. TVD Runge-Kutta local projection discontinuous Galerkin Finite element method for conservation laws II: general framework. Math. Comput., 52 (1989), 411-435. [Google Scholar]
  6. B. Cockburn, C. W. Shu. The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal., 35 (1998), No. 6, 2440-2463. [CrossRef] [MathSciNet] [Google Scholar]
  7. B. Cockburn, C. W. Shu. The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems. J. Comput. Phys., 141 (1998), 199-224. [CrossRef] [MathSciNet] [Google Scholar]
  8. K. Fidkowski, T. A. Oliver, J. Lu, D. Darmofal. p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. J. Comput. Phys., 207 (2005), 92-113. [CrossRef] [Google Scholar]
  9. H. Gao, Z. J. Wang. A high-order lifting collocation penalty formulation for the Navier- Stokes equations on 2D mixed grids. AIAA Paper 2009-3784, 2009. [Google Scholar]
  10. G. J. Gassner, F. Lorcher, C-D. Munz, and J. S. Hesthaven. Polymorphic nodal elements and their application in discontinuous Galerkin methods. J. Comput. Phys., 228 (2009), 1573-1590. [CrossRef] [MathSciNet] [Google Scholar]
  11. S. K. Godunov. A difference scheme for numerical computation of discontinuous solutions of equations of fluid dynamics. Math. Sbornik, 47 (1959), 271-306, In Russian. [Google Scholar]
  12. T. Haga, M. Furudate, K. Sawada. RANS simulation using high-order spectral volume method on unstructured tetrahedral grids. AIAA Paper 2009–404, 2009. [Google Scholar]
  13. T. Haga, K. Sawada, Z. J. Wang. An implicit LU-SGS scheme for the spectral volume method on unstructured tetrahedral grids. Communications in Computational Physics, 6 (2009), No. 5, 978-996. [CrossRef] [MathSciNet] [Google Scholar]
  14. R. Harris, Z. J. Wang, Y. Liu. Efficient quadrature-free high-order spectral volume method on unstructured grids: Theory and 2D implementation. J. Comput. Phys., 227 (2008), 1620-1642. [CrossRef] [MathSciNet] [Google Scholar]
  15. J. S. Hesthaven. From electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex. SIAM J. Numer. Anal., 35 (1998), No. 2, 655-676. [CrossRef] [MathSciNet] [Google Scholar]
  16. H. T. Huynh. A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods. AIAA Paper 2007–4079, 2007. [Google Scholar]
  17. H. T. Huynh. A reconstruction approach to high-order schemes including discontinuous Galerkin for diffusion. AIAA Paper 2009–403, 2009. [Google Scholar]
  18. A. Jameson. Analysis and design of numerical schemes for gas dynamics. I. Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence. Int. J. Comput. Fluid Dyn., 4 (1994), 171–218. [CrossRef] [Google Scholar]
  19. T. A. Johnson and V. C. Patel. Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech., 378 (1999), 19-70. [CrossRef] [Google Scholar]
  20. D. A. Kopriva and J. H. Kolias. A conservative staggered-grid Chebyshev multidomain method for compressible flows. J. Comput. Phys., 125 (1996), 244–261. [CrossRef] [MathSciNet] [Google Scholar]
  21. M. S. Liou. A sequel to AUSM, Part II: AUSM+-up for all speeds. J. Comput. Phys., 214 (2006), 137-170. [CrossRef] [MathSciNet] [Google Scholar]
  22. Y. Liu, M. Vinokur, and Z. J. Wang. Discontinuous spectral difference method for conservation laws on unstructured grids. In Proceedings of the Third International Conference on Computational Fluid Dynamics, Toronto, Canada, July 2004. [Google Scholar]
  23. Y. Liu, M. Vinokur, and Z. J. Wang. Spectral difference method for unstructured grids I: Basic formulation. J. Comput. Phys., 216 (2006), 780-801. [CrossRef] [MathSciNet] [Google Scholar]
  24. Y. Liu, M. Vinokur, Z. J. Wang. Spectral (finite) volume method for conservation laws on unstructured grids V: Extension to three-dimensional systems. J. Comput. Phys., 212 (2006), 454-472. [CrossRef] [MathSciNet] [Google Scholar]
  25. H. Luo, J. D. Baum, and R. Lohner. A discontinuous Galerkin method based on a Taylor basis for the compressible flows on arbitrary grids. J. Comput. Phys., 227 (2008), 8875-8893. [CrossRef] [MathSciNet] [Google Scholar]
  26. D. J. Mavriplis. Multigrid strategies for viscous flow solvers on anisotropic unstructured meshes. J. Comput. Phys., 145 (1998), 141-165. [CrossRef] [MathSciNet] [Google Scholar]
  27. G. May, A. Jameson. A spectral difference method for the Euler and Navier-Stokes equations. AIAA Paper 2006–304, 2006. [Google Scholar]
  28. C. R. Nastase, D. J. Mavriplis. High-order discontinuous Galerkin methods using an hp-multigrid approach. J. Comput. Phys., 213 (2006), 330-357. [CrossRef] [Google Scholar]
  29. S. Osher. Riemann solvers, the entropy condition, and difference approximations. SIAM J. Numer. Anal., 21 (1984), 217-235. [CrossRef] [MathSciNet] [Google Scholar]
  30. W. H. Reed, T. R. Hill. Triangular mesh methods for the neutron transport equation. Los Alamos Scientific Laboratory Report LA-UR-73-479, 1973. [Google Scholar]
  31. P. L. Roe. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys., 43 (1981), 357-372. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  32. V. V. Rusanov. Calculation of interaction of non-steady shock waves with obstacles. J. Comput. Math. Phys., 1 (1961), 267-279. [Google Scholar]
  33. S. J. Sherwin, G. E. Karniadaks. A new triangular and tetrahedral basis for high-order (hp) finite element methods. Int. J. Num. Meth. Eng., 38 (1995), 3775–3802. [CrossRef] [Google Scholar]
  34. C. W. Shu. Total-variation-diminishing time discretizations. SIAM Journal on Scientific and Statistical Computing, 9 (1988), 1073-1084. [CrossRef] [Google Scholar]
  35. C. W. Shu. Essentially non-oscillatory and weighted and non-oscillatory schemes for hyperbolic conservation laws. In B. Cockburn, C. Johnson, C.-W. Shu, and E. Tadmor, editors, Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, volume 1697 of Lecture Note in Mathematics. Springer, 1998. [Google Scholar]
  36. Y. Sun, Z. J. Wang, and Y. Liu. High-order multidomain spectral difference method for the Navier-Stokes equations on unstructured hexahedral grids. Communications in Computational Physics, 2 (2007), 310-333. [MathSciNet] [Google Scholar]
  37. S. Taneda. Experimental investigations of the wake behind a sphere at low reynolds nombers. J. Phys. Soc. Japan, 11 (1956), 1104-1108. [NASA ADS] [CrossRef] [Google Scholar]
  38. A. G. Tomboulides, S. A. Orzag. Numerical investigation of transitional and weak turbulent flow past a sphere. J. Fluid Mech., 416 (2000), 45-73. [CrossRef] [MathSciNet] [Google Scholar]
  39. K. Van den Abeele and C. Lacor. An accuracy and stability study of the 2D spectral volume method. J. Comput. Phys., 226 (2007), 1007-1026. [CrossRef] [MathSciNet] [Google Scholar]
  40. K. Van den Abeele, C. Lacor, Z. J. Wang. On the stability and accuracy of the spectral difference method. J. Sci. Comput., 37 (2008), 162-188. [CrossRef] [MathSciNet] [Google Scholar]
  41. B. Van Leer. Towards the ultimate conservative difference scheme V. A second order sequel to GodunovŠs method. J. Comput. Phys., 32 (1979), 110-136. [Google Scholar]
  42. B. Van Leer, S. Nomura. Discontinuous Galerkin for diffusion. AIAA Paper 2005–5108, 2005. [Google Scholar]
  43. Z. J. Wang. Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation. J. Comput. Phys., 178 (2002), 210-251. [CrossRef] [MathSciNet] [Google Scholar]
  44. Z. J. Wang. High-order methods for the Euler and Navier-Stokes equations on unstructured grids. Progress in Aerospace Sciences, 43 (2007), 1-41. [CrossRef] [Google Scholar]
  45. Z. J. Wang, H. Gao. A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids. J. Comput. Phys., 228 (2009), 8161-8186. [CrossRef] [MathSciNet] [Google Scholar]
  46. Z. J. Wang, Y. Liu. Spectral (finite) volume method for conservation laws on unstructured grids II: Extension to two-dimensional scalar equation. J. Comput. Phys., 179 (2002), 665-697. [CrossRef] [MathSciNet] [Google Scholar]
  47. Z. J. Wang, Y. Liu. Spectral (finite) volume method for conservation laws on unstructured grids III: One-dimensional systems and partition optimization. Journal of Scientific Computing, 20 (2004), No. 1, 137-157. [CrossRef] [MathSciNet] [Google Scholar]
  48. Z. J. Wang, L. Zhang, Y. Liu. Spectral (finite) volume method for conservation laws on unstructured grids IV: Extension to two-dimensional systems. J. Comput. Phys., 194 (2004), 716-741. [CrossRef] [MathSciNet] [Google Scholar]
  49. T. Warburton. An explicit construction of interpolation nodes on the simplex. J. Eng. Math., 56 (2006), 247-262. [CrossRef] [Google Scholar]
  50. O. C. Zienkiewicz, R. L. Taylor. The Finite Element Method The Basics, vol. 1. Butterworth-Heinemann, Oxford, England, 2000. [Google Scholar]

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