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

Abstract

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 dispersion 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 L 1 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.

Wstęp

“…These mixed forms are called the Γ-forms. For isolating the terms responsible for numerical dispersion and dissipation it is necessary to express all time derivatives as spatial ones (see: Appadu et al, 2008;Appadu and Dauhoo, 2011;Appadu et al, 2014;Winnicki et al, 2019;Shokin et al, 2020).…”

Advances in Geodesy and Geoinformation

“…The forms of the MDEs are very useful in the detailed analysis of the dispersive and dissipative features of the difference schemes (see: Appadu et al (2008), Appadu and Dauhoo (2011), Appadu (2014)). For the elliptic partial differential equations we always obtain their Π-forms.…”