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  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].
|Numerical Hydrodynamics in Special Relativity
Jose Maria Martí and Ewald Müller
© Max-Planck-Gesellschaft. ISSN 1433-8351
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