Isogeometric analysis of the time-dependent incompressible MHD equations

Abstract

This paper presents an isogeometric (IGA) solver for time-dependent, incompressible magnetohydrodynamics (MHD). In this paper, a combination of inf-sup stable mixed discretisations is considered to discretise the hydrodynamic pair (i.e. velocity and pressure) and magnetic pair (i.e. magnetic field and magnetic pressure). The one step θmethod is used for the temporal discretisation. Manufactured and analytical solutions are considered to assess convergence, accuracy and performance of the IGA solver. Moreover, benchmark problems involving a MHD flow over an obstacle and MHD flow under nonuniform magnetic field are considered to examine the effect of the magnetic field on the flow behaviour.