The RMHD (for relativistic MHD) equations then become a system
of evolution equations for the integrated variational parts
, which reads
together with the conservation condition
The quantities
are defined as
They are continuous, and standard methods can be used to
integrate the system (44). Van Putten uses a leapfrog method.
The new state vector
is then obtained from
by numerical differentiation. This process can lead to
oscillations in the case of strong shocks and a smoothing
algorithm should be applied. Details of this smoothing algorithm
and of the numerical method in one and two spatial dimensions can
be found in [180
] together with results on a large variety of tests.
Van Putten has applied his method to simulate relativistic
hydrodynamic and magneto hydrodynamic jets with moderate flow
Lorentz factors (< 4.25) [182,
184
].
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Numerical Hydrodynamics in Special Relativity
Jose Maria Martí and Ewald Müller http://www.livingreviews.org/lrr-1999-3 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |