MHD in Divergence Form: a Computational Method for Astrophysical Flow.

The equations of MHD in curved space-time are presented in divergence form for the purpose of numerical implementation. This result follows from a covariant divergence form of the single fluid theory of electro-magneto-hydrodynamics in curved space-time with general constitutive relations. Some one- and two-dimensional shock computations are given. A pseudo-spectral method with weak smoothing is used in all of our computations. The pseudo-spectral method is constructed by consideration of Riemann problems in one dimension. The power of MHD in divergence form is brought about by using uniform grid-spacing and explicit time-stepping. The problems considered are shock-tube problems in transverse MHD with analytical comparison solution and a coplanar Riemann problem as discussed for nonrelativistic MHD in Brio and Wu (37). In a limit of nonrelativistic velocities comparison is made of the results of the latter with those in (37). In two dimensions cylindrically symmetric problems are considered for test of isotropy, independence of coordinate system and convergence (using comparison results in polar coordinates). We conclude with a computation of a shock induced vortex in jet flow with Gamma ~ 2.35, a relativistic jet computation with Gamma~ 3.25 and, finally, computations on magnetic pressure dominated stagnation points in a 2D shock problem in nontransverse MHD. This work is proposed for numerical study of astrophysical flows, and in particular as a "vehicle" towards the origin of jets.