ZARM rho-Central MHD Foam

Charles Chelem

For the numerical simulation of the Magnetoplasmadynamics (MPD) Thrusters, a numerical compressible Magnetohydrodynamics (MHD) solvers was recently developed. The numerical proposed method uses the semi-discrete, non-staggered central scheme of Greenshields (Greenschields, 2010) for flux calculation, which is a density based method. The contribution of this work is essentially the consideration of the magnetic effects in the algorithm proposed by Greenshields. For that purpose, we make use of the OpenFOAM package as a developer tool for our new code. The standard rhoCentralFoam makes use of the KT (Kurganov and Tadmor) and KNP (Kurganov, Noelle and Petrova) methods in their original form for multi-dimensional systems using the so-called ‘dimension-by-dimension’ reconstruction. The interpolation procedure is split in two directions corresponding to flow outward and inward of the face owner cell. The volumetric fluxes associated with the local speeds of propagation have to taking into account the fast and low magnetosonic speed through the Alfvén speed. The transport properties are evaluated as a scalar field given by the Spitzer-Harm formulation for electrical conductivity and the Sutherland thermophysical model for thermal conductivity. We also make use of the hyperbolic divergence cleaning method for the magnetic field divergence constraint. The robustness of the new MHD density-based numerical algorithm was tested on a cloud-shock interaction benchmark experiment and some preliminary results on a 3D MPD thruster are available.