Transient radiative transfer in the grey case: Well-balanced and asymptotic-preserving schemes built on Case's elementary solutions |
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Authors: | Laurent Gosse |
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Institution: | IAC-CNR “Mauro Picone” (sezione di Bari), Via Amendola 122/I, 70126 Bari, Italy |
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Abstract: | An original well-balanced (WB) Godunov scheme relying on an exact Riemann solver involving a non-conservative (NC) product is developed. It is meant to solve accurately the time-dependent one-dimensional radiative transfer equation in the discrete ordinates approximation with an arbitrary even number of velocities. The collision term is thus concentrated onto a discrete lattice by means of Dirac masses; this induces steady contact discontinuities which are integral curves of the stationary problem. One solves it by taking advantage of the method of elementary solutions mainly developed by Case, Zweifel and Cercignani. This approach produces a rather simple scheme that compares advantageously to standard existing upwind schemes, especially for the decay in time toward a Maxwellian distribution. It is possible to reformulate this scheme in order to handle properly the parabolic scaling in order to generate a so-called asymptotic-preserving (AP) discretization. Consistency with the diffusive approximation holds independently of the computational grid. Several numerical results are displayed to show the realizability and the efficiency of the method. |
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Keywords: | Radiative transfer Diffusive approximation Discrete ordinate method Slab geometry Case's elementary solutions Well-balanced schemes Asymptotic-preserving schemes Non-conservative products |
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