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Xin-liang Li, Yan Leng and Zhi-wei He Optimized sixth-order monotonicity-preserving scheme by nonlinear spectral analysis International Journal for Numerical Methods in Fluids 73

Version of Record online: 3 JUN 2013 | DOI: 10.1002/fld.3812

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Sixth-order monotonicity-preserving optimized scheme (OMP6) for the numerical solution of conservation laws is developed on the basis of the dispersion and dissipation optimization and monotonicity-preserving technique. The nonlinear spectral analysis method is developed and is used for the purpose of minimizing the dispersion errors and controlling the dissipation errors. Test cases show that the new scheme has robust shock capturing capability and high resolution for the small-scale waves due to fewer numerical dispersion and dissipation errors. Moreover, the new scheme has higher computational efficiency than the well-used WENO schemes.

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