Dynamical grid method for time-dependent simulations of axisymmetric instabilities in tokamaks

A natural nonorthogonal time-dependent coordinate transformation based on the magnetic field lines is utilized for the numerical integration of the two-dimensional axisymmetric time-dependent ideal MHD equations in tokamak geometry. The finite-difference grid is treated as a dynamical variable, and its equations of motion are integrated simultaneously with those for the fluid and magnetic field. The method is applicable to tokamak systems of arbitrary pressure and cross section. It is particularly useful for the nearly incompressible ideal MHD modes which are of interest in tokamak stability studies.