A new solver for magnetohydrodynamic flow simulations

Numerical schemes for magnetized rotating flows often attempt to solve the induction equation directly. Due to numerical difficulties, this approach is limited to magnetic Prandtl numbers larger than 0.01, i.e., four orders of magnitude above the values typical for liquid metals. This makes a direct comparison of numerical results with liquid metal experiments difficult. Here we present an alternative approach based on a finite volume scheme for the Navier-Stokes and the Poisson equation describing the electric potential combined with a magnetic field calculation via Biot-Savart’s law. Using this integro-differential formulation, it is possible to circumvent the magnetic Prandtl number limitation mentioned above. First, we will discuss the implementation of this method in the framework of the open source library OpenFOAM. Second, calculations of the Tayler instability (TI), a kink-type current-driven instability, will be presented and compared to the data from a recent liquid metal TI experiment (Seilmayer et al., 2012). The computations faithfully reproduce the experimentally findings. Then, we will elaborate on further details of the TI in liquid metals, as the influence of the aspect ratio on the critical current, transient helical states, and possible implications for large-scale liquid metal batteries.