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Astron. Astrophys. 348, 233-248 (1999)

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Computing radiative heating on unstructured spatial grids

J.H.M.J. Bruls, P. Vollmöller and M. Schüssler

Kiepenheuer-Institut für Sonnenphysik, Schöneckstrasse 6, D-79104 Freiburg, Germany (bruls, voll, msch@kis.uni-freiburg.de)

Received 26 January 1999 / Accepted 16 April 1999

Abstract

We discuss the basic problems and methods involved in the design of a radiative transfer module for a 2D/3D (magneto-)hydrodynamics simulation code aimed at applications in cool-star atmospheres. Attention is focused on the difficulties arising from the unstructured triangular/tetrahedral grid and the need to minimize the communication overhead, so that the code runs efficiently on parallel computers. In a first step, we use the gray approximation and ignore scattering effects, but even then the computation of the radiative heating rate, required as a source term in the energy equation, involves several integration steps that are discussed in detail. In particular, the details of the short-characteristics solver for the radiative transfer equation, the influence of the cell size, and the accuracy of the angular integrations of the specific intensity are considered. Theoretical estimates of possible errors are in general cumbersome to obtain; instead we use simple model problems for the accuracy estimates. A plane-parallel model for the quiet Sun serves as a testground for the basics while a schematic model of a magnetic flux sheet provides an acid test for the behavior of the computational methods under typical circumstances arising during simulations. Two alternative methods to compute the radiative heating rate are compared and their weaknesses are identified. The errors are minimized by a hybrid scheme that selects a method depending on the optical path length within a grid cell.

Key words: radiative transfer – methods: numerical – Sun: atmosphere

Send offprint requests to: J. Bruls; paper available online at http://www.kis.uni-freiburg.de/~bruls/papers/ (with Figs. 10, 11 and 12 in color)

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© European Southern Observatory (ESO) 1999

Online publication: July 16, 1999
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