COMPACT FINITE DIFFERENCE SCHEMES WITH HIGH ORDER OF ACCURACY FOR CAPTURING DISCONTINUITY

摘要

In order to suppress numerical oscillations of linear compact schemes around discontinuities, a characteristic-based flux splitting limited method is introduced instead of ENO/WENO or other shock-capturing algorithms. This method begins with upwind schemes and Lax-Friedrich type fluxvector splitting, and variables (fluxes or conservative variables,etc.) are projected along characteristic directions in a difference form, and their amplitudes are carefully controlled by a special limiter in order to meeting entropy criterions and to preventing non-physical oscillations. A fifth-order linear compact upwind scheme is modified by this method for solving problems involving discontinuities. The properties of the numerical algorithm are checked on several classical one-dimensional and multidimensional test cases. Numerical results show it is highorder accurate with high resolution and oscillation-free.