In this paper, we investigate accurate and efficient time advancing methods for computational acoustics, where nondissipative and
In this paper, we investigate accurate and efficient timenondispersive properties are of critical importance. Our analysis advancing schemes for computational acoustics. In particupertains to the application of Runge-Kutta methods to high-order lar, the family of Runge-Kutta methods is considered. The finite difference discretization. In many CFD applications, multistage present analysis pertains to the application of Runge-Runge-Kutta schemes have often been favored for their low storage Kutta methods to high-order finite difference schemes.
requirements and relatively large stability limits. For computing acoustic waves, however, the stability consideration alone is not In many CFD applications, popular time-advancing sufficient, since the Runge-Kutta schemes entail both dissipation schemes are the classical third-and fourth-order Rungeand dispersion errors. The time step is now limited by the tolerable Kutta schemes because they provide relatively large stabildissipation and dispersion errors in the computation. In the present ity limits [10]. For acoustic calculations, however, the paper, it is shown that if the traditional Runge-Kutta schemes are stability consideration alone is not sufficient, since the used for time advancing in acoustic problems, time steps greatly smaller than those allowed by the stability limit are necessary. Low-Runge-Kutta schemes retain both dissipation and disperdissipation and low-dispersion Runge-Kutta (LDDRK) schemes are sion errors. The numerical solutions need to be time accuproposed, based on an optimization that minimizes the dissipation rate to resolve the wave propagation. In this paper, we and dispersion errors for wave propagation. Optimizations of both show that when the classical Runge-Kutta schemes are single-step and two-step alternating schemes are considered. The used in wave propagation problems using high-order spaproposed LDDRK schemes are remarkably more efficient than the classical Runge-Kutta schemes for acoustic computations. More-tial finite difference, time steps much smaller than those over, low storage implementations of the optimized schemes are allowed by the stability limit are necessary in the longdiscussed. Special issues of implementing numerical boundary contime integrations. This certainly undermines the efficiency ditions in the LDDRK schemes are also addressed. ᮊ 1996 Academic of the classical Runge-Kutta schemes.