SIMULATING WAVES IN FLOWS BY RUNGE-KUTTA AND COMPACT DIFFERENCE-SCHEMES

The solution procedure of the unsteady Euler equations by various comb inations of Runge-Kutta (RK) methods and compact difference (CD) schem es is investigated. Fourier analysis is performed on the fully discret ized equation to assess the numerical accuracy and stability. The resu lts clearly show a significant improvement of numerical characteristic s by using the fourth-order CD scheme compared to the second-order one . Further increase of the order of the spatial differencing, however, results in little improvement. For time marching, the fourth-order RK scheme enlarges the time step for stable calculation as compared to a third-order one. Four numerical examples are included: acoustic waves in a converging nozzle, shocked sound waves in a straight tube, a sing le vortex in a uniform flow, and a vortex pairing. The fourth-order RK method combined with fourth- and sixth-order CD schemes shows crisp r esolution of unsteady now structures.