References
- Adams , N. A. and Shariff , K. 1996 . A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems . J. Comput. Phys. , 127 : 27 – 51 . (doi:10.1006/jcph.1996.0156)
- Anderson , J. D. 1995 . Computational Fluid Dynamics , New York : Mc Graw Hill .
- Bassi , F. and Rebay , S. 1997 . A high-order accurate discontinuous finite element menthod for the numerical solution of the compressible Navier–Stokes equations . J. Comput. Phys. , 131 : 267 – 279 . (doi:10.1006/jcph.1996.5572)
- Bhagatwala , A. and Lele , S. K. 2009 . A modified artificial viscosity approach for compressible turbulence simulations . J. Comput. Phys. , 228 : 4965 – 4969 . (doi:10.1016/j.jcp.2009.04.009)
- Cockburn , B. 2003 . Discontinuous Galerkin methods . J. Appl. Math. Mech. , 83 : 731 – 754 .
- Cockburn , B. and Shu , C. W. 1998 . The local discontinuous Galerkin method for time-dependent convection–diffusion systems . SIAM J. Numer. Anal. , 35 : 2440 – 2463 . (doi:10.1137/S0036142997316712)
- Cockburn , B. , Lin , S. Y. and Shu , C. W. 1989 . TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One-dimensional systems . J. Comput. Phys. , 84 : 90 – 113 . (doi:10.1016/0021-9991(89)90183-6)
- Cook , A. W. and Cabot , W. H. 2004 . A high-wave number viscosity for high-resolution numerical methods . J. Comput. Phys. , 195 : 594 – 601 . (doi:10.1016/j.jcp.2003.10.012)
- Costa , B. and Don , W. S. 2007 . High order hybrid central-WENO finite difference scheme for conservation laws . J. Comput. Appl. Math. , 204 : 209 – 218 . (doi:10.1016/j.cam.2006.01.039)
- Eddy , W. F. 1990 . The DECstation 3100 – UNIX for power users . Chance , 3 : 42 – 47 .
- Godunov , S. K. 1959 . A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics . Mat. Sb. (N.S.) , 47 : 271 – 306 .
- Harten , A. 1978 . The artificial compression method for computation of shocks and contact discontinuities: III. Self-adjusting hybrid schemes . Math. Comp. , 32 : 363 – 389 .
- Harten , A. 1983 . High resolution schemes for hyperbolic conservation laws . J. Comput. Phys. , 49 : 357 – 393 . (doi:10.1016/0021-9991(83)90136-5)
- Harten , A. , Engquist , B. , Osher , S. and Chakravarthy , S. R. 1997 . Uniformly high order accurate essentially non-oscillatory schemes, III . J. Comput. Phys. , 131 : 3 – 47 . (doi:10.1006/jcph.1996.5632)
- Jiang , G. S. and Shu , C. W. 1996 . Efficient implementation of weighted ENO scheme . J. Comput. Phys. , 126 : 202 – 228 . (doi:10.1006/jcph.1996.0130)
- Jiang , L. , Shan , H. and Liu , C. 2001 . Weighted compact scheme for shock capturing . Int. J. Comput. Fluid Dyn. , 15 : 147 – 155 . (doi:10.1080/10618560108970024)
- Kim , D. and Kwon , J. 2005 . A high-order accurate hybrid scheme using a central flux scheme and a WENO scheme for compressible flowfield analysis . J. Comput. Phys. , 210 : 554 – 583 . (doi:10.1016/j.jcp.2005.04.023)
- van Leer , B. 1979 . Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method . J. Comput. Phys. , 32 : 101 – 136 . (doi:10.1016/0021-9991(79)90145-1)
- Lele , S. K. 1992 . Compact finite difference schemes with spectral-like resolution . J. Comput. Phys. , 103 : 16 – 42 . (doi:10.1016/0021-9991(92)90324-R)
- Liu , D. , Osher , S. and Chan , T. 1994 . Weighted essentially non-oscillatory schemes . J. Comput. Phys. , 115 : 200 – 212 . (doi:10.1006/jcph.1994.1187)
- Liu , Y. , Vinokur , M. and Wang , Z. J. 2006 . Spectral (finite) volume method for conservation laws on unstructured grids. V: Extension to three-dimensional systems . J. Comput. Phys. , 212 : 454 – 472 . (doi:10.1016/j.jcp.2005.06.024)
- Liu , Y. , Vinokur , M. and Wang , Z. J. 2006 . Spectral difference method for unstructured grids I: Basic formulation . J. Comput. Phys. , 216 : 780 – 801 . (doi:10.1016/j.jcp.2006.01.024)
- Ma , Y. and Fu , D. 2001 . Forth order accurate compact scheme with group velocity control (GVC) . Sci. China , 44 : 1197 – 1204 . (doi:10.1007/BF02877439)
- M.L. Oliveira, High-order numerical schemes for high-speed flows, PhD diss., Mathematics Dept., University of Texas at Arlington, Arlington, TX, 2009.
- Patera , A. 1984 . A spectral element method for fluid dynamics: Laminar flow in a channel expansion . J. Comput. Phys. , 54 : 468 – 488 . (doi:10.1016/0021-9991(84)90128-1)
- Ren , Y. , Liu , M. and Zhang , H. 2003 . A characteristic-wise hybrid compact-WENO scheme for solving hyperbolic conservation laws . J. Comput. Phys. , 192 : 365 – 386 . (doi:10.1016/j.jcp.2003.07.006)
- Roe , P. L. 1981 . Approximate Riemann solvers, parameter vectors, and difference schemes . J. Comput. Phys. , 43 : 357 – 372 . (doi:10.1016/0021-9991(81)90128-5)
- Shu , C. W. 1998 . Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws . Lecture Notes in Mathematics , 1697 : 325 – 432 . (doi:10.1007/BFb0096355)
- Shu , C. W. 2009 . High order weighted essentially non-oscillatory schemes for convection dominated problems . SIAM Rev. , 51 : 82 – 126 . (doi:10.1137/070679065)
- Shu , C. W. and Osher , S. 1988 . Efficient implementation of essentially non-oscillatory shock-capturing scheme . J. Comput. Phys. , 77 : 439 – 471 . (doi:10.1016/0021-9991(88)90177-5)
- Shu , C. W. and Osher , S. 1989 . Efficient implementation of essentially non-oscillatory shock-capturing schemes II . J. Comput. Phys. , 83 : 32 – 78 . (doi:10.1016/0021-9991(89)90222-2)
- Sod , G. A. 1978 . A survey of several finite difference methods for systems on non-linear hyperbolic conservation laws . J. Comput. Phys. , 27 : 1 – 31 . (doi:10.1016/0021-9991(78)90023-2)
- Steger , J. and Warming , R. 1981 . Flux vector splitting of the inviscid gasdynamic equations with applications to finite-difference methods . J. Comput. Phys. , 40 : 263 – 293 . (doi:10.1016/0021-9991(81)90210-2)
- Sun , Y. , Wang , Z. J. and Liu , Y. 2007 . High-order multi-domain spectral difference method for the Navier–Stokes equations on unstructured hexahedral grids . Comm. Comput. Phys. , 2 : 310 – 333 .
- Vichevenetsky , R. V. and Bowles , J. B. 1982 . Fourier Analysis of Numerical Approximations of Hyperbolic Equations . SIAM, Philadelphia ,
- Visbal , M. and Gaitonde , D. 2002 . On the use of higher-order finite-difference schemes on curvilinear and deforming meshes . J. Comput. Phys. , 181 : 155 – 158 . (doi:10.1006/jcph.2002.7117)
- Wang , Z. J. 2002 . Spectral (finite) volume method for conservation laws on unstructured grids: Basic formulation . J. Comput. Phys. , 178 : 210 – 251 . (doi:10.1006/jcph.2002.7041)
- Wang , Z. and Huang , G. P. 2002 . An essentially non-oscillatory high-order Padé-type (ENO-Padé) scheme . J. Comput. Phys. , 177 : 37 – 58 . (doi:10.1006/jcph.2002.6998)
- Yee , H. C. 1997 . Explicit and implicit multidimensional compact high-resolution shock-capturing methods: Formulation . J. Comput. Phys. , 131 : 216 – 232 . (doi:10.1006/jcph.1996.5608)
- Yee , H. C. , Sjogreen , B. , Sandham , N. D. and Hadjadj , A. Progress in the development of a class of efficient low dissipative high order shock-capturing methods . Proceeding of the Symposium in Computational Fluid Dynamics for the 21st Century . Kyoto