Low-dissipative high-order shock-capturing methods using characteristic-based filters
An approach which closely maintains the non-dissipative nature of classical fourth- or higher-order spatial differencing away from shock waves and steep gradient regions while being capable of accurately capturing discontinuities, steep gradient, and fine scale turbulent structures in a stable and efficient manner is described. The approach is a generalization of the method of Gustafsson and Olsson and the artificial compression method (ACM) switch of Harten. Spatially non-dissipative fourth- or higher-order compact and non-compact spatial differencings are used as the base schemes, Instead of applying a scalar filter as in Gustafsson and Olsson, an ACM switch is used to signal the appropriate amount of second- or third-order total variation diminishing (TVD) or essentially non-oscillatory (ENO) types of characteristic based numerical dissipation. This term acts as a characteristic filter to minimize numerical dissipation for the overall scheme, For time-accurate computations, time discretizations with low dissipation apr used, Numerical experiments on 2-D vortical flows, vortex-shock interactions, and compressible spatially and temporally evolving mixing layers showed that the proposed schemes have the desired property with only a 10% increase in operations count over standard second-order TVD schemes. Aside from the ability to accurately capture shock-turbulence interaction flows, this approach is also capable of accurately preserving vortex convection. Higher accuracy is achieved with fewer grid points when compared to that of standard second-order TVD, positive, or ENO schemes. (C) 1999 Academic Press.
low dissipation tvd schemes shock-turbulence interaction eno schemes high order explicit and implicit finite difference methods compact schemes high-order central differencings shock-capturing methods conservative differencing positive schemes