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MHD in divergence form : a computational method for astrophysical flow


van Putten, Maurice H. P. M. (1992) MHD in divergence form : a computational method for astrophysical flow. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/263j-a556.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Applied and Computational Mathematics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied And Computational Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Phinney, E. Sterl
Group:TAPIR, Astronomy Department
Thesis Committee:
  • Unknown, Unknown
Defense Date:18 May 1992
Record Number:CaltechETD:etd-08152007-144037
Persistent URL:
van Putten, Maurice H. P. M.0000-0002-9212-411X
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3139
Deposited By: Imported from ETD-db
Deposited On:23 Aug 2007
Last Modified:12 Jul 2023 21:17

Thesis Files

PDF (vanPutten_mhpm_1992.pdf) - Final Version
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