High order weighted essentially nonoscillatory schemes for convection dominated problems

SIAM Review

Volumn 51, Issue 1, 2009, Pages 82-126

  Shu, Chi Wang ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

Computational astronomy and astrophysics; Computational biology; Computational fluid dynamics; Convection dominated problems; Hyperbolic partial differential equations; Semiconductor device simulation; Traffic flow models; Weighted essentially nonoscillatory (WENO) scheme

Indexed keywords

COMPUTATIONAL ASTRONOMY AND ASTROPHYSICS; COMPUTATIONAL BIOLOGY; CONVECTION DOMINATED PROBLEMS; HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS; SEMICONDUCTOR DEVICE SIMULATION; TRAFFIC FLOW MODELS; WEIGHTED ESSENTIALLY NONOSCILLATORY (WENO) SCHEME;

AIRCRAFT ENGINES; APPLICATIONS; ASTRONOMY; ASTROPHYSICS; BIOINFORMATICS; BIOLOGY; COMPUTATIONAL FLUID DYNAMICS; DYNAMICS; ELECTRIC CONDUCTIVITY; FLOW SIMULATION; FLUID DYNAMICS; IMAGE SEGMENTATION; SEMICONDUCTING INDIUM; SEMICONDUCTOR DEVICE MANUFACTURE; SEMICONDUCTOR DEVICE MODELS; SEMICONDUCTOR MATERIALS; SEMICONDUCTOR SWITCHES; SUPERSONIC FLOW; TRAFFIC SURVEYS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 59749100711     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/070679065     Document Type: Review

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148. C.-W. SHU, Total-variation-diminishing time discretizations, SIAM J. Sci. Statist. Comput., 9 (1988), pp. 1073-1084.
149. C.-W. SHU, Essentially nofi-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, in Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, B. Cockburn, C. Johnson, C.-W. Shu, E. Tadmor, and A. Quarteroni, eds., Lecture Notes in Math. 1697, Springer-Verlag, Berlin, 1998, pp. 325-432.
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151. C.-W. SHU, High order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD, Internat. J. Comput. Fluid Dynam., 17 (2003), pp. 107-118.
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156. K. SIDDIQI, B.B. KIMIA, AND C.-W. SHU, Geometric shock-capturing ENO schemes for subpixel interpolation, computation and curve evolution, Graphical Models Image Processing (CVGIP:GMIP), 59 (1997), pp. 278-301.
157. B.A. STEVE AND D. LEVY, High-order semi-discrete central-upwind schemes for multi-dimensional Hamilton-Jacobi equations, J. Comput. Phys., 189 (2003), pp. 63-87.
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169. Z.J. WANG AND R.F. CHEN, Optimized weighted essentially nonoscillatory schemes for linear waves with discontinuity, J. Comput. Phys., 174 (2001), pp. 381-404.
170. C.C. WU AND T. CHANG, Dynamical evolution of coherent structures in intermittent two-dimensional MHD turbulence, IEEE Trans. Plasma Sci., 28 (2000), pp. 1938-1943.
171. Y. XING AND C.-W. SHU, High order finite difference WENO schemes with the exact conservation property for the shallow water equations, J. Comput. Phys., 208 (2005), pp. 206-227.
172. Y. XING AND C.-W. SHU, High order well-balanced finite difference WENO schemes for a class of hyperbolic systems with source terms, J. Sci. Comput., 27 (2006), pp. 477-494.
173. Y. XING AND C.-W. SHU, High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms, J. Comput. Phys., 214 (2006), pp. 567-598.
174. Y. XING AND C.-W. SHU, A new approach of high order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms, Commun. Comput. Phys., 1 (2006), pp. 101-135.
175. Z. XU AND C.-W. SHU, Anti-diffusive flux corrections for high order finite difference WENO schemes, J. Comput. Phys., 205 (2005), pp. 458-485.
176. Z. XU AND C.-W. SHU, Anti-diffusive high order WENO schemes for Hamilton-Jacobi equations, Methods Appl. Anal., 12 (2005), pp. 169-190.
177. Z. XU AND C.-W. SHU, Anti-diffusive finite difference WENO methods for shallow water with transport of pollutant, J. Comput. Math., 24 (2006), pp. 239-251.
178. R. WANG AND R.J. SPITERI, Linear instability of the fifth-order WENO method, SIAM J. Numer. Anal., 45 (2007), pp. 1871-1901.
179. C. YANG AND Z.S. MAO, Numerical simulation of interphase mass transfer with the level set approach, Chem. Engrg. Sci., 60 (2005), pp. 2643-2660.
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181. J.Y. YANG, Y.C. PERNG, AND R.H. YEN, Implicit weighted essentially nonoscillatory schemes for the compressible Navier-Stokes equations, AIAA J., 39 (2001), pp. 2082-2090.
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183. J.Y. YANG, R.H. YEN, AND Y.C. PERNG, Three-dimensional wing flow computations using implicit WENO Euler solvers, J. Aircraft, 39 (2002), pp. 181-184.
184. L. YUAN AND C.-W. SHU, Discontinuous Galerkin method based on non-polynomial approximation spaces, J. Comput. Phys., 218 (2006), pp. 295-323.
185. N.J. ZABUSKY, S. GUPTA, AND Y. GULAK, Localization and spreading of contact discontinuity layers in simulations of compressible dissipationless flows, J. Comput. Phys., 188 (2003), pp. 348-364.
186. M. ZHANG, C.-W. SHU, G.C.K. WONG, AND S.C WONG, A weighted essentially non-oscillatory numerical scheme for a multi-class Lighthill-Whitham-Richards traffic flow model, J. Comput. Phys., 191 (2003), pp. 639-659.
187. P. ZHANG, S.C. WONG, AND C.-W. SHU, A weighted essentially non-oscillatory numerical scheme for a multi-class traffic flow model on an inhomogeneous highway, J. Comput. Phys., 212 (2006), pp. 739-756.
188. Q. ZHANG, M. ZHANG, G. JIN, D. LIU, AND C.-W. SHU, Modeling, numerical methods and simulation for particle-fluid two phase flow problems, Comput. Math. Appl., 47 (2004), pp. 1437-1462.
189. S. ZHANG AND C.-W. SHU, A new smoothness indicator for the WENO schemes and its effect on the convergence to steady state solutions, J. Sci. Comput., 31 (2007), pp. 273-305.
190. S. ZHANG, Y.-T. ZHANG, AND C.-W. SHU, Multi-stage interaction of a shock wave and a strong vortex, Phys. Fluids, 17 (2005), article 116101.
191. S. ZHANG, Y.-T. ZHANG, AND C.-W. SHU, Interaction of a shock uraue with an oblique vortex pair: Shock dynamics and mechanism of sound generation, Phys. Fluids, 18 (2006), article 126101.
192. W. ZHANG AND A. MACFADYEN, RAM: A relativistic adaptive mesh refinement hydrodynamics code, Astrophys. J. Suppl. Ser., 164 (2006), pp. 255-279.
193. Y.-T. ZHANG, J. SHI, C.-W. SHU, AND Y. ZHOU, Numerical viscosity and resolution of high-order weighted essentially nonoscillatory schemes for compressible flows with high Reynolds numbers, Phys. Rev. E, 68 (2003), article 046709.
194. Y.-T. ZHANG AND C.-W. SHU, High-order WENO schemes for Hamilton-Jacobi equations on triangular meshes, SIAM J. Sci. Comput., 24 (2003), pp. 1005-1030.
195. Y.-T. ZHANG AND C.-W. SHU, Third order WENO scheme on three dimensional tetrahedral meshes, Commun. Comput. Phys., 5 (2009), pp. 836-848.
196. Y.-T. ZHANG, C-W. SHU, AND Y. ZHOU, Effects of shock waves on Rayleigh-Taylor instability, Phys. Plasmas, 13 (2006), article 062705.
197. Y.-T. ZHANG, H.-K. ZHAO, AND J. QIAN, High order fast sweeping methods for static Hamilton-Jacobi equations, J. Sci. Comput., 29 (2006), pp. 25-56.
198. T. ZHOU, Y. LI, AND C.-W. SHU, Numerical comparison of WENO finite volume and RungeKutta discontinuous Galerkin methods, J. Sci. Comput., 16 (2001), pp. 145-171.