High-order mixed weighted compact and non-compact scheme for shock/discontinuity and small length scale interaction

It is critical for numerical scheme to obtain numerical results as accurate as possible with limited computational resources. Turbulent processes are very sensitive to numerical dissipation, which may dissipate the small length scales. On the other hand, dealing with shock waves, capturing and reproducing of the discontinuity may lead to non-physical oscillations for non-dissipative schemes. In the present work, a new high-order mixed weighted compact and non-compact (WCNC) difference scheme is proposed for accurate approximation of the derivatives in the governing Euler equations although the idea was given by Xie and Liu in 2007. The basic idea is to recover the non-dissipative highorder weighted compact scheme (WCS) where solution is smooth, while using a lower-ordered noncompact scheme for near-shock areas. Formulation and numerical tests are performed for the one dimensional case and results are compared with the well established weighted essentially nonoscillatory (WENO) scheme and WCS.