2.3 Exact solution of the 2 Special Relativistic Hydrodynamics2.1 Equations

2.2 SRHD as a hyperbolic system of conservation laws 

An important property of system (5Popup Equation) is that it is hyperbolic for causal EOS [6]. For hyperbolic systems of conservation laws, the Jacobians tex2html_wrap_inline5743 have real eigenvalues and a complete set of eigenvectors (see Section  9.2). Information about the solution propagates at finite velocities given by the eigenvalues of the Jacobians. Hence, if the solution is known (in some spatial domain) at some given time, this fact can be used to advance the solution to some later time (initial value problem). However, in general, it is not possible to derive the exact solution for this problem. Instead one has to rely on numerical methods which provide an approximation to the solution. Moreover, these numerical methods must be able to handle discontinuous solutions, which are inherent to non-linear hyperbolic systems.

The simplest initial value problem with discontinuous data is called a Riemann problem, where the one dimensional initial state consists of two constant states separated by a discontinuity. The majority of modern numerical methods, the so-called Godunov-type methods, are based on exact or approximate solutions of Riemann problems. Because of its theoretical and numerical importance, we discuss the solution of the special relativistic Riemann problem in the next subsection.



2.3 Exact solution of the 2 Special Relativistic Hydrodynamics2.1 Equations

image Numerical Hydrodynamics in Special Relativity
Jose Maria Martí and Ewald Müller
http://www.livingreviews.org/lrr-1999-3
© Max-Planck-Gesellschaft. ISSN 1433-8351
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