Comments on the stability of the RSF three-dimensional MHD plasma simulation algorithm
RSF [see: (*) \textit{H. R. Hicks, B. Carreras, J. A. Holmes, D. K. Lee} and \textit{B. V. Waddell}, ibid. 44, 46-69 (1981; Zbl 0471.76128)] is a spectral code which follows the time evolution of the reduced MHD equations [\textit{B. V. Waddell, B. Carreras, H. R. Hicks} and \textit{J. A. Holmes}, Phys. Fluids 22, 896-910 (1979)]. The purpose of this note is to discuss the stability properties of the time integration scheme used in RSF. We show in this note for both the typographically incorrect published algorithm (*) and for the corrected algorithm [\textit{H. R. Hicks, B. Carreras, J. A. Holmes, D. K. Lee} and \textit{B. V. Waddell}, J. Comput. Phys. 53, 205 (1984)] that stability of the integration scheme relies on the coupling of the flux and vorticity equation: The vorticity advection scheme is of the centred space/forward time type which requires the addition of physical or numerical dissipation for stability.
stability properties of the time integration scheme
coupling of the flux and vorticity equation
scientific article; zbMATH DE number 3920132