Physics
Scientific paper
Mar 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999jqsrt..61..629b&link_type=abstract
Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 61, issue 5, pp. 629-635
Physics
11
Radiative Transfer: Hydrodynamics
Scientific paper
The solution of the Riemann problem is one of the fundamental ingredients in the process of building higher-order Godunov schemes for the numerical solution of hyperbolic problems. In Balsara (1999) the author was able to show that the equations of radiation hydrodynamics can be viewed as a hyperbolic system of equations. As suggested by Roe (1981), much of the information generated in the process of solving the Riemann problem for hyperbolic systems is actually never used in the construction of upwinded fluxes. This fact prompts the development of linearized formulations of the Riemann problem. In this paper the author formulates such a linearized Riemann solver for the equations of radiation hydrodynamics. It is shown that a consistent state exists. The consistent state that he has found also satisfies Roe's Property U. As a result, isolated strong shocks of arbitrary strength are exactly modeled by the Riemann solver. It is also shown that this consistent state can be used to advantage in evaluating the eigenvalues and eigenvectors that result from the linearization of the Riemann problem for radiation hydrodynamics.
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