Modified Weighted Compact Scheme for Shock Capturing

It is critical for a 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 modified weighted compact (MWCS) is proposed for accurate approximation of the derivatives in the governing Euler equations. The basic idea is to add the weighted essentially non-oscillatory scheme (WENO) to weighted compact scheme to make sure the scheme is diagonally dominant, and then add some WENO in additional to make sure that there's some dissipation in the smooth area to avoid oscillations. Formulation and numerical tests are performed for the one-and two-dimensional case and results are compared with the well-established WENO scheme. Nomenclature b a, = start, and end point of the one-dimensional domain