Improvement of stability and accuracy for weighted essentially nonoscillatory scheme

Yiqing Shen, GeCheng Zha, Baoyuan Wang

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Abstract

This paper studies the weights stability and accuracy of the implicit fifth-order weighted essentially nonoscillatory finite difference scheme. It is observed that the weights of the Jiang-Shu weighted essentially nonoscillatory scheme oscillate even for smooth flows. An increased ε value of 10 -2 is suggested for the weighted essentially nonoscillatory smoothness factors, which removes the weights oscillation and significantly improves the accuracy of the weights and solution convergence. With the improved ε value, the weights achieve the optimum value with minimum numerical dissipation in smooth regions and maintain the sensitivity to capture nonoscillatory shock profiles for the transonic flows. The theoretical justification of this treatment is given in the paper. The wall surface boundary condition uses a half-point mesh so that the conservative differencing can be enforced. A third-order accurate finite difference scheme is given to treat wall boundary conditions. The implicit time-marching method with unfactored Gauss-Seidel line relaxation is used with the high-order schemes to achieve a high convergence rate. Several transonic cases are calculated to demonstrate the robustness, efficiency, and accuracy of the methodology.

Original languageEnglish
Pages (from-to)331-344
Number of pages14
JournalAIAA Journal
Volume47
Issue number2
DOIs
StatePublished - Feb 1 2009

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ASJC Scopus subject areas

  • Aerospace Engineering

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