Numerical algorithms for the Hall effect in MHD codes: a note of caution

Summary form only given. The Hall effect may play an important role in the opening behavior of plasma opening switches. Inclusion of this effect in MHD codes introduces a nonlinear term into the equation for the time evolution of magnetic field which leads to shock-like solutions. A number of different algorithms designed to implement the Hall effect have been examined. Several of these were implemented into the MACH2 code and gave results which appeared to be reasonable, but failed to give consistent propagation velocities. Various algorithms were tested against the analytical solution for the transient one-dimensional Burgers equation. Algorithms which passed this test were further tested on a series of one-dimensional and two-dimensional axisymmetric test problems designed to uncover other weaknesses in the algorithms. A modified version of the Roscoe-Roach algorithm for two-dimensional axisymmetric problems has been implemented and appears to give satisfactory results for a variety of test problems.