We study semi-discrete central-upwind schemes and develop a new technique that allows one to decrease the amount of numerical dissipation present in these schemes without compromising their robustness. The goal is achieved by obtaining more accurate estimates for the one-sided local speeds of propagation using the discrete Rankine-Hugoniot conditions. In the two-dimensional case, these estimates are further enhanced with the help of the numerical dissipation switch mechanism, which is automatically activated near contact discontinuities and shear layers. The resulting central-upwind Rankine-Hugoniot schemes are tested on a number of numerical examples for both the one- and two-dimensional Euler equations of gas dynamics. The obtained results clearly demonstrate the superiority of the proposed method over the existing semi-discrete central-upwind schemes.

我们研究了半离散中央迎风方案，并开发了一种新技术，该技术可以减少这些方案中存在的数值耗散量，而不会损害其鲁棒性。该目标是通过使用离散的Rankine-Hugoniot条件获得更精确的单侧传播速度估计来实现的。在二维情况下，借助数字耗散开关机制进一步增强了这些估计，该机制在接触间断点和剪切层附近自动激活。对于一维和二维气体动力学欧拉方程，在许多数值示例上测试了所得的中心迎风朗肯-休格尼奥特方案。