Optimized Sixth-order Monotonicity-Preserving Scheme

In this paper, sixth-order monotonicity-preserving optimized scheme (OMP6) for the numerical solution of conservation laws is developed based on the dispersion and dissipation optimization and monotonicity-preserving technique. The nonlinear spectral analysis is used for the purpose of minimizing the dispersion errors and controlling the dissipation errors. The new scheme (OMP6) is simple in expression and is easy for use in CFD codes. The suitability and accuracy of this new scheme has been tested through a set of one-dimensional, two-dimensional and three-dimensional tests, including the one-dimensional Shu-Osher problem and the Riemann problems, the two-dimensional double Mach reflection and the Rayleigh-Taylor instability problem, and the three-dimensional direct numerical simulation of decaying compressible isotropic turbulence. All numerical tests 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..