Exact Jacobians of Roe-type flux difference splitting of the equations of radiation hydrodynamics (and Euler equations) for use in time-implicit higher-order Godunov schemes.

Details Exact Jacobians of Roe-type flux difference splitting of the equations of radiation hydrodynamics (and Euler equations) for use in time-implicit higher-order Godunov schemes. Exact Jacobians of Roe-type flux difference splitting of the equations of radiation hydrodynamics (and Euler equations) for use in time-implicit higher-order Godunov schemes.

Jun 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999jqsrt..62..255b&link_type=abstract

Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 62, issue 3, pp. 255-278

Statistics

Computation

1

Numerical Methods: Magnetohydrodynamics, Numerical Methods: Radiative Transfer

Scientific paper

In this paper the author analyzes some of the numerical issues that are involved in making time-implicit higher-order Godunov schemes for the equations of radiation hydrodynamics (and the Euler or Navier-Stokes equations). This is done primarily with the intent of incorporating such methods in the author's RIEMANN code. After examining the issues it is shown that the construction of a time-implicit higher-order Godunov scheme for radiation hydrodynamics would be benefited by the author's ability to evaluate exact Jacobians of the numerical flux that is based on Roe-type flux difference splitting. In this paper the author shows that this can be done analytically in a form that is suitable for efficient computational implementation. It is also shown that when multiple fluid species are used or when multiple radiation frequencies are used the computational cost in the evaluation of the exact Jacobians scales linearly with the number of fluid species or the number of radiation frequencies. Connections are made to other types of numerical fluxes, especially those based on flux difference splittings. It is shown that the evaluation of the exact Jacobian for such numerical fluxes is also benefited by the present strategy and the results given here. It is, however, pointed out that time-implicit schemes that are based on the evaluation of the exact Jacobians for flux difference splittings using the methods developed here are both computationally more efficient and numerically more stable than corresponding time-implicit schemes that are based on the evaluation of the exact or approximate Jacobians for flux vector splittings.

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