An integral equation approach to two-dimensional incompressible resistive magnetohydrodynamics

In the present work, an integral equation approach is developed to solve two-dimensional incompressible resistive magnetohydrodynamic equations. This approach is examined by simulating the magnetic reconnection driven by the Orszag–Tang vortex and the doubly periodic coalescence instability. The results show that when the viscosity and magnetic resistivity of the plasma are reduced, the current sheet forming in the magnetic reconnection driven by the Orszag–Tang vortex becomes thinner. In comparison with the spectral method, the integral equation approach has much better accuracy and convergence.