63 / 2019-11-24 23:06:15

A Three-Wave Splitting Method for Plane Free Supersonic Mixing Layers

High-order accuracy, Characteristic decomposition, Mathematically strict, Parallel algorithm

Compared with subsonic mixing layers, the high-order accurate calculation of supersonic mixing layers becomes difficult and easy to diverge due to the interaction between wave systems and vortex structure. When high-order filter or WENO method is adopted, it is difficult to ensure uniformly high-order accuracy in the whole field. In this paper, on the basis of the characteristic decomposition of flow flux, it is found that the numerical flux can be decomposed into the sum of a streamwise travelling wave, a sound wave and a stationary wave. This scheme introduces numerical dissipation through the upwind treatment of the stationary wave term to maintain computational stability. Some numerical examples show that the scheme has the characteristics of small dissipation and high resolution, and has the ability to simulate weak shock-vortex interaction with the same order of high-order accuracy and to simulate the mixed region and shocklets in the viscous shear layer. Finally, this method is successfully used to achieve the full-field uniformly high-order accurate calculation of the convective Mach 2.0 mixing layer flow. Moreover, a mathematically strict parallel algorithm for the compact format and a mathematically strict chasing algorithm for generalized tri-diagonal matrix formed by periodicity boundary conditions are also presented.