Numerical investigation of decomposed magnetofluid dynamics equations

In addition to the two commonly used formulations for magnetofluid dynamics, a third formulation based on the decomposition of the magnetic field for solving full magnetofluid dynamics equations is explored. The governing equations are transformed to a generalized computational domain and discretized using a finite difference technique. A time-explicit multistage Runge--Kutta scheme augmented with total variation diminishing limiters for time integration is implemented. The developed codes have been validated with the existing closed-form solution of the magnetic Rayleigh problem. Results obtained from the decomposed magnetofluid dynamics equations compare well with results obtained by solving the classical full magnetofluid dynamics equations for a wide range of magnetic Reynolds numbers. It is shown that the decomposed magnetofluid dynamics technique requires substantially less computation time compared with classical full magnetofluid dynamics equations for the solution involving flowfields with high imposed magnetic fields. DOI: 10.2514/1.42626