No . 98-32 Weighted Essentially Non-Oscillatory Schemes on Triangular Meshes

In this paper we construct high-order weighted essentially non-oscillatory schemes on two-dimensional unstructured meshes (triangles) in the finite volume formulation. We present third-order schemes using a combination of linear polynomials and fourth-order schemes using a combination of quadratic polynomials. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations.

[1]  Fred H. Walsteijn Robust numerical methods for 2D turbulence , 1994 .

[2]  Chi-Wang Shu,et al.  Energy Models for One-Carrier Transport in Semiconductor Devices , 1994 .

[3]  G. Sod A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws , 1978 .

[4]  Kaleem Siddiqi,et al.  Geometric Shock-Capturing ENO Schemes for Subpixel Interpolation, Computation and Curve Evolution , 1997, CVGIP Graph. Model. Image Process..

[5]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[6]  Chi-Wang Shu,et al.  High-order essentially non-oscillatory scheme for viscoelasticity with fading memory , 1997 .

[7]  P. Woodward,et al.  The numerical simulation of two-dimensional fluid flow with strong shocks , 1984 .

[8]  Joseph W. Jerome,et al.  Solution of the hydrodynamic device model using high-order non-oscillatory shock capturing algorithms. Final report , 1989 .

[9]  G. Russo,et al.  Central WENO schemes for hyperbolic systems of conservation laws , 1999 .

[10]  Chi-Wang Shu,et al.  Transport effects and characteristic modes in the modeling and simulation of submicron devices , 1995, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

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

[12]  Chi-Wang Shu,et al.  The Runge-Kutta Discontinuous Galerkin Method for Conservation Laws V , 1998 .

[13]  Thomas Sonar,et al.  On the construction of essentially non-oscillatory finite volume approximations to hyperbolic conservation laws on general triangulations : polynomial recovery, accuracy and stencil selection , 1997 .

[14]  Jay Casper,et al.  Finite-volume implementation of high-order essentially nonoscillatory schemes in two dimensions , 1992 .

[15]  Ami Harten,et al.  Preliminary results on the extension of eno schemes to two-dimensional problems , 1987 .

[16]  P. Roe Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[17]  Gordon Erlebacher,et al.  Interaction of a shock with a longitudinal vortex , 1996, Journal of Fluid Mechanics.

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

[19]  P. Lax Weak solutions of nonlinear hyperbolic equations and their numerical computation , 1954 .

[20]  P. Frederickson,et al.  Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction , 1990 .

[21]  S. Osher,et al.  Algorithms Based on Hamilton-Jacobi Formulations , 1988 .

[22]  A. Harten,et al.  Multi-Dimensional ENO Schemes for General Geometries , 1991 .

[23]  Gordon Erlebacher,et al.  High-order ENO schemes applied to two- and three-dimensional compressible flow , 1992 .

[24]  Gabriella Puppo,et al.  High-Order Central Schemes for Hyperbolic Systems of Conservation Laws , 1999, SIAM J. Sci. Comput..

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

[26]  E Weinan,et al.  A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow , 1992 .

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

[28]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[29]  - Chi ICASE . . . . . . . . A NUMERICAL RESOLUTION S _ DY OF HIGH ORDER ESSENTIALLY NON-OSCILL _ ORY SCHEMES APPLIED TO INCOMPRESSIBLE FLOW , .

[30]  J. Sethian Level set methods : evolving interfaces in geometry, fluid mechanics, computer vision, and materials science , 1996 .

[31]  Stanley Osher,et al.  An Eulerian Approach for Vortex Motion Using a Level Set Regularization Procedure , 1996 .

[32]  Nikolaus A. Adams,et al.  A High-Resolution Hybrid Compact-ENO Scheme for Shock-Turbulence Interaction Problems , 1996 .

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

[34]  Xiaodan Cai,et al.  Advection by polytropic compressible turbulence , 1995 .

[35]  S.S.M. Wong,et al.  Relativistic Hydrodynamics and Essentially Non-oscillatory Shock Capturing Schemes , 1995 .

[36]  Rémi Abgrall,et al.  On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation , 1994 .

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