High-order maximum-principle-preserving and positivity-preserving weighted compact nonlinear schemes for hyperbolic conservation laws
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In this paper, the maximum-principle-preserving (MPP) and positivity-preserving (PP) flux limiting technique will be generalized to a class of high-order weighted compact nonlinear schemes (WCNSs) for scalar conservation laws and the compressible Euler systems in both one and two dimensions. The main idea of the present method is to rewrite the scheme in a conservative form, and then define the local limiting parameters via case-by-case discussion. Smooth test problems are presented to demonstrate that the proposed MPP/PP WCNSs incorporating a third-order Runge-Kutta method can attain the desired order of accuracy. Other test problems with strong shocks and high pressure and density ratios are also conducted to testify the performance of the schemes.
Key wordshyperbolic conservation law maximum-principle-preserving (MPP) positivity-preserving (PP) weighted compact nonlinear scheme (WCNS) finite difference scheme
Chinese Library ClassificationO241
2010 Mathematics Subject Classification65N12 76M20
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- DENG, X. G., LIU, X., MAO, M. L., and ZHANG, H. X. Advances in high-order accurate weighted compact nonlinear schemes. Advances in Mechanics, 37(3), 417–427 (2007)Google Scholar
- NONOMURA, T., GOTO, Y., and FUJII, K. Improvements of efficiency in seventh-order weighted compact nonlinear scheme. 6th Asia Workshop on Computational Fluid Dynamics, Tokyo, Japan, AW6-16 (2010)Google Scholar