MHD in divergence form : a computational method for astrophysical flow

Author: van Putten, Maurice H. P. M.

Year: 1992

Degree: Dissertation (Ph.D.)

Advisor: Phinney, E. Sterl

Committee Member: Unknown, Unknown

Option: Applied And Computational Mathematics

DOI: 10.7907/263j-a556

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.

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 pseudospectral 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 [...] 2.35, a relativistic jet computation with [...] 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.

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