Third-Order Energy Stable WENO Scheme

[1]  Chi-Wang Shu,et al.  Monotonicity Preserving Weighted Essentially Non-oscillatory Schemes with Increasingly High Order of Accuracy , 2000 .

[2]  Harold L. Atkins,et al.  A Finite-Volume High-Order ENO Scheme for Two-Dimensional Hyperbolic Systems , 1993 .

[3]  Jianxian Qiu,et al.  On the construction, comparison, and local characteristic decomposition for high-Order central WENO schemes , 2002 .

[4]  H. Kreiss,et al.  Finite Element and Finite Difference Methods for Hyperbolic Partial Differential Equations , 1974 .

[5]  Chi-Wang Shu.  Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws , 1998 .

[6]  S. Osher,et al.  Uniformly high order accurate essentially non-oscillatory schemes, 111 , 1987 .

[7]  V. Gregory Weirs,et al.  A bandwidth-optimized WENO scheme for the effective direct numerical simulation of compressible turbulence , 2006, J. Comput. Phys..

[8]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

[9]  Zhi J. Wang,et al.  Optimized weighted essentially nonoscillatory schemes for linear waves with discontinuity: 381 , 2001 .

[10]  Gabriella Puppo,et al.  Compact Central WENO Schemes for Multidimensional Conservation Laws , 1999, SIAM J. Sci. Comput..

[11]  S. Osher,et al.  On the convergence of difference approximations to scalar conservation laws , 1988 .

[12]  D. Gottlieb,et al.  A Stable and Conservative Interface Treatment of Arbitrary Spatial Accuracy , 1999 .

[13]  P. Lax,et al.  Systems of conservation laws , 1960 .

[14]  Shih-Hsien Yu,et al.  Discrete Shocks for Finite Difference Approximations to Scalar Conservation Laws , 1998 .

[15]  S. Osher,et al.  Weighted essentially non-oscillatory schemes , 1994 .

[16]  Magnus Svärd,et al.  Stable and Accurate Artificial Dissipation , 2004, J. Sci. Comput..

[17]  D. Gottlieb,et al.  Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes , 1994 .

[18]  Jan S. Hesthaven,et al.  A Stable Penalty Method for the Compressible Navier-Stokes Equations: I. Open Boundary Conditions , 1996, SIAM J. Sci. Comput..

[19]  David Gottlieb,et al.  Spectral Methods on Arbitrary Grids , 1995 .

[20]  O. Friedrich,et al.  Weighted Essentially Non-Oscillatory Schemes for the Interpolation of Mean Values on Unstructured Grids , 1998 .

[21]  M. Carpenter,et al.  Accuracy of Shock Capturing in Two Spatial Dimensions , 1999 .

[22]  B. Strand.  Summation by parts for finite difference approximations for d/dx , 1994 .

[23]  Chi-Wang Shu.  Total-variation-diminishing time discretizations , 1988 .

[24]  J. Hesthaven,et al.  Nodal high-order methods on unstructured grids , 2002 .

[25]  Roberto Ferretti,et al.  Convergence of Semi-Lagrangian Approximations to Convex Hamilton-Jacobi Equations under (Very) Large Courant Numbers , 2002, SIAM J. Numer. Anal..

[26]  Huanan Yang,et al.  On Wavewise Entropy Inequality for High Resolution Schemes II: Fully Discrete MUSCL Schemes with Exact Evolution in Small Time , 1998 .