Comments on the stability of the RSF three-dimensional MHD plasma simulation algorithm. (English) Zbl 0575.76113
RSF [see: (*) H. R. Hicks, B. Carreras, J. A. Holmes, D. K. Lee and 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 [B. V. Waddell, B. Carreras, H. R. Hicks and 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 [H. R. Hicks, B. Carreras, J. A. Holmes, D. K. Lee and 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.
Keywords:
RSF algorithm; spectral code; reduced MHD equations; stability properties of the time integration scheme; coupling of the flux and vorticity equationReferences:
| [1] | Hicks, H. R.; Carreras, B.; Holmes, J. A.; Lee, D. K.; Waddell, B. V., J. Comput. Phys., 44, 46-69 (1981) · Zbl 0471.76128 |
| [2] | Waddell, B. V.; Carreras, B.; Hicks, H. R.; Holmes, J. A., Phys. Fluids, 22, 896-910 (1979) · Zbl 0396.76091 |
| [3] | Carreras, B.; Hicks, H. R.; Holmes, J. A.; Waddell, B. V., Phys. Fluids, 23, 1811-1826 (1980) · Zbl 0438.76098 |
| [4] | Hockney, R. W.; Eastwood, J. W., Computer Simulation Using Particles (1981), McGraw-Hill: McGraw-Hill New York · Zbl 0662.76002 |
| [7] | Hicks, H. R.; Carreras, B.; Holmes, J. A.; Lee, D. K.; Waddell, B. V., J. Comput. Phys., 53, 205 (1984) · Zbl 0525.76128 |
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