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A Systematic Methodology for Constructing High-Order Energy-Stable WENO SchemesA third-order Energy Stable Weighted Essentially Non-Oscillatory (ESWENO) finite difference scheme developed by Yamaleev and Carpenter (AIAA 2008-2876, 2008) was proven to be stable in the energy norm for both continuous and discontinuous solutions of systems of linear hyperbolic equations. Herein, a systematic approach is presented that enables \energy stable" modifications for existing WENO schemes of any order. The technique is demonstrated by developing a one-parameter family of fifth-order upwind-biased ESWENO schemes; ESWENO schemes up to eighth order are presented in the appendix. New weight functions are also developed that provide (1) formal consistency, (2) much faster convergence for smooth solutions with an arbitrary number of vanishing derivatives, and (3) improved resolution near strong discontinuities.
Document ID
20080043618
Acquisition Source
Langley Research Center
Document Type
Technical Memorandum (TM)
Authors
Yamaleev, Nail K. (North Carolina Agricultural and Technical State Univ. Greensboro, NC, United States)
Carpenter, Mark H. (NASA Langley Research Center Hampton, VA, United States)
Date Acquired
August 24, 2013
Publication Date
October 1, 2008
Subject Category
Numerical Analysis
Report/Patent Number
L-19503
NASA/TM-2008-215532
Funding Number(s)
WBS: WBS 599489.02.07.07.04.03.01
Distribution Limits
Public
Copyright
Public Use Permitted.

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