An effective low dissipation method for compressible flows

An effective low-dissipation method for simulating compressible flows is proposed in this paper. The method adapts between the high order WENO-type schemes and the TVD reconstruction procedures with an indicator based upon the local fluid properties, such as the discontinuity sensor and the local Mach number. The method is capable of capturing shock waves without oscillations and resolving small scales without introducing excessive numerical dissipation. By choosing an appropriate method for different circumstances, the method is robust, low dissipative and high effective. The detailed construction of the method is presented and the numerical performances are validated with several numerical experiments. Finally, the dissipation's property of the method is investigated and quantified by conducting analyses on the Taylor Green vortex problem and the compressible isotropic turbulence problems. These results show that the proposed scheme is a promising candidate for the DNS (Direct Numerical Simulation) and the LES (Large Eddy Simulation) for compressible flows.