Low dissipative high-order numerical simulations of supersonic reactive flows

We report the performance of a newly developed low dissipative sixth-order spatial and fourth-order temporal scheme (J. Comput. Phys. 1999; 150: 199; RIACS Report 01.01, NASA Ames Research Centre, October 2000) for multiscale supersonic reactive flows that contain shock waves. The accuracy and efficiency of the scheme are compared with a lowdissipative fifth-order weighted ENO (WENO) scheme (ICASE Report No. 95-73, 1995). This paper confirms and complements the grid convergence study of Sj?green and Yee where a complex shock/shear/boundary-layer interactions model was also included. A 2D viscous flow consisting of a planar Mach 2 in air interacting with a circular zone of hydrogen bubbles in two different initial configurations is considered. The two initial configurations are a single bubble and two non-aligned bubbles. The gradient in pressure across the shock in conjunction with the gradient in fluid density between the air and hydrogen produce a large increase in vorticity as the shock passes through the hydrogen fuel. As can be seen in the study of Don and Quillen (J. Comput. Phys. 1995; 122: 244), Don and Gottlieb (SIAM J. Numer. Anal. 1998; 35: 2370) and the present grid convergence tudy, the size, spacing and velocity of the fine-scale vortical structures are very difficult to accurately simulate numerically. The difficulty in obtaining well-resolved multiscale combustion flows by all methods considered will be illustrated.