EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 6 / No 3 (2011) Math. Model. Nat. Phenom., 6 3 (2011) 28-56 References
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. [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. [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. [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. [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. [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. [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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.