The three-point fifth-order accurate generalized compact scheme and its applications

A three-point fifth-order accurate generalized compact scheme (GC scheme) w ith a spectral-like resolution is constructed in a general way. The scheme satisfies the principle of stability and the principle about suppression of the oscillations, therefore numerical errors can decay automatically and n o spurious oscillations are generated around shocks. The third-order TVD ty pe Runge-Kutta method is employed for the time integration, thus making the GC scheme best suited for unsteady problems. Numerical results show that t he GC scheme is shock-capturing. The time-dependent boundary conditions pro posed by Thompson are well employed when the algorithm is applied to the Eu ler equations of gas dynamics.