Numerical Scheme

The numerical splitting scheme we chose is:

where:

The constants $\alpha_q, \beta_q$ and $\gamma_0$ are integration weights and are defined in [55] for the stiffly stable splitting schemes of first-, second- or third-order depending on the set of coefficients chosen. The convective terms are treated explicitly and the viscous terms are treated implicitly. The boundary conditions for the magnetic streamfunction can be set to $\phi = U_\infty y$ for uniform magnetic field at a boundary or $\phi = 0$ for an infinitely conducting wall.