A Finite Volume - Spectral Approach for the Fully Compressible MHD Simulation in the Torus Geometry
TAKAHIRO MIYOSHI, YASUAKI KISHIMOTO, NEXT GROUP
Plasma Theory Laboratory, Naka Fusion Research Establishment, JAERI
Abstract.
New numerical schemes for the fully compressible nonlinear MHD simulation in the torus geometry are constructed based on the finite volume-spectral method. One is the extension of the conventional finite difference-spectral scheme on a flux coordinate system. In our method, though the time development of the magnetic field is explicitly described by the contravariant components, the equation of motion is indicated both by the contravariant and the cartesian components in a flux coordinate system. Then, the radial derivatives are estimated based on the finite volume method, while the derivatives to the poloidal and the toroidal directions are calculated by the conventional psuedo-spectral method. The other numerical scheme is constructed by the finite volume method on triangular meshes in the poloidal plane and by the pseudo-spectral method in the toroidal direction. In this approach, due to the adoption of the unstructured grid system in the poloidal plane, the real machine geometry will be easily realized without any singularities at the magnetic null points. Moreover, the high accuracy of the toroidal modes is also achieved by the benefit of the spectral method. By comparing with the results of those schemes, we will discuss advantages and disadvantages of each scheme.