Optimized Low Dispersion and Low Dissipation Runge-Kutta Algorithms in Computational Aeroacoustics

Abstract

A new explicit fourth-order six-stage Runge-Kutta scheme with low dispersion and low dissipation properties is developed. This new Runge-Kutta scheme is shown to be more efficient in terms of disp ersion and dissipation properties than existing algorithms such as Runge-Kutta temporal schemes developed by Hu et al. (1996), Mead and Renaut (1999), Tselios and Simos (2005). We perform a spectral analysis of the dispersion and dissipation errors. Numerical experiments dealing with wave propagation are performed with these four temporal Runge-Kutta schemes, all coupled with a nine-point centred difference scheme of eight order. The variation of two types of error: the error rate with respect to the L1 norm and the Total Mean Square Error, both with respect to the CFL are obtained for all the four different schemes and it is seen that low CFL numbers are in general more effective than larger CFL numbers.