where the state vector
and the flux vector
are defined in (6
) and (7
), respectively. In the following we explicitly give both the
eigenvalues and the right and left eigenvectors of the Jacobi
matrix
only (the cases
i
=
y,
z
are easily obtained by symmetry considerations).
The eigenvalues of matrix
are
and
A complete set of right-eigenvectors is
where
The corresponding complete set of left-eigenvectors is
where
is the determinant of the matrix of right-eigenvectors,
i.e.,
For an ideal gas equation of state
, i.e.,
, and hence
for
.
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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 |