Application of MFS–MPS to the current-hole simulation in a Tokamak

A meshless method based on fundamental and particular solutions (MFS–MPS) has been implemented for the current-hole simulation in cylindrical tokamaks. We first benchmark the method by solving the Grad–Shafranov (GS) equation for zero as well as nonzero inverse aspect ratios and noncircular cross-sections. Thereafter, the method is implemented to solve the time-dependent reduced resistive MHD equations for the current-hole simulation. The initial current density profile with a negative current density near the center is chosen and the corresponding equilibrium magnetic flux profile is first computed using the GS equation. These profiles are then used to solve the coupled nonlinear system of MHD equations using MFS–MPS and a semi-implicit time differencing scheme. After an initial linear phase extending up to a few thousand Alfvén times, the nonlinear oscillations are observed which continue for several Alfvén times. This oscillating behavior is in agreement with the previous simulations using other numerical methods. It is also found that these oscillations are damped out at higher resistivity.