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.

提出了一种模拟可压缩流动的有效低耗散方法。该方法在高阶WENO型方案和TVD重建程序之间进行调整，并具有基于局部流体属性（例如间断传感器和局部马赫数）的指示器。该方法能够捕获冲击波而不会产生振荡，并且能够解决小尺度问题而不会引入过多的数值耗散。通过针对不同情况选择合适的方法，该方法是健壮，低耗散且高效的。给出了该方法的详细构造，并通过几个数值实验验证了数值性能。最后，耗散' 通过对泰勒格林涡旋问题和可压缩各向同性湍流问题进行分析，研究和量化了该方法的性质。这些结果表明，该方案是可压缩流的DNS（直接数值模拟）和LES（大涡模拟）的有希望的候选者。