Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics (Q1913748)

We show that if the traditional Runge-Kutta schemes are used for time advancing in acoustic problems, time steps greatly smaller than those allowed by the stability limit are necessary. Low-dissipation and low-dispersion Runge-Kutta (LDDRK) schemes are proposed, based on an optimization that minimizes the dissipation and dispersion errors for wave propagation. Optimizations of both single-step and two-step alternating schemes are considered. The proposed LDDRK schemes are remarkably more efficient than the classical Runge-Kutta schemes for acoustic computations.