tailieunhanh - Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws

In these lecture notes we describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton-Jacobi equations. ENO and WENO schemes are high order accurate nite di erence schemes designed for problems with piecewise smooth solutions containing discontinuities. | NASA CR-97-206253 ICASE Report No. 97-65 Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws Chi-Wang Shu Brown University Institute for Computer Applications in Science and Engineering NASA Langley Research Center Hampton VA Operated by Universities Space Research Association National Aeronautics and Space Administration Langley Research Center Hampton Virginia 23681-2199 Prepared for Langley Research Center under Contract NAS1-19480 November 1997 ESSENTIALLY NON-OSCILLATORY AND WEIGHTED ESSENTIALLY NON-OSCILLATORY SCHEMES FOR HYPERBOLIC CONSERVATION LAWS CHI-WANG SHU Abstract. In these lecture notes we describe the construction analysis and application of ENO Essentially Non-Oscillatory and WENO Weighted Essentially Non-Oscillatory schemes for hyperbolic conservation laws and related Hamilton-Jacobi equations. ENO and WENO schemes are high order accurate finite difference schemes designed for problems with piecewise smooth solutions containing discontinuities. The key idea lies at the approximation level where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil hence avoiding crossing discontinuities in the interpolation procedure as much as possible. ENO and WENO schemes have been quite successful in applications especially for problems containing both shocks and complicated smooth solution structures such as compressible turbulence simulations and aeroacoustics. These lecture notes are basically self-contained. It is our hope that with these notes and with the help of the quoted references the reader can understand the algorithms and code them up for applications. Sample codes are also available from the author. Key words. essentially non-oscillatory conservation laws high order accuracy Subject classification. Applied and Numerical Mathematics 1. Introduction. ENO Essentially Non-Oscillatory schemes started with the classic paper of Harten Engquist Osher and .