Variational multiscale stabilized finite element analysis of transient MHD Stokes equations with application to multiply driven cavity flow (Q6546882)

The transient Stokes magnetohydrodynamic (MHD) equations are thoroughly investigated in this paper using the variational subgrid multiscale stabilized finite element method. In order to get the optimal order of convergence, appropriate expressions for stabilization parameter have been derived using Fourier analysis. The theoretical convergence analysis of the subgrid algebraic stabilized numerical scheme is also presented in this study. The numerical studies on multiply-driven cavity flow establish the credibility of the variational algebraic subgrid multiscale stabilized finite element approach. Further, the theoretically determined convergence rate is validated numerically. For different Hartmann number, Reynolds number, and magnetic force inclination angles, the flow fields are traced.