A characteristic-based shock-capturing scheme for hyperbolic problems

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 flux vector splittings. The upwind schemes are projected along characteristic directions in a different way, and their amplitudes are carefully controlled by a special limiter in order to meet entropy condition and to prevent 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 some benchmark problems in one, two and three space dimensions. Numerical results show that it is high-order accurate with high resolution and oscillation-free.