A GODUNOV METHOD FOR MULTIDIMENSIONAL RADIATION MAGNETOHYDRODYNAMICS BASED ON A VARIABLE EDDINGTON TENSOR
A GODUNOV METHOD FOR MULTIDIMENSIONAL RADIATION MAGNETOHYDRODYNAMICS BASED ON A VARIABLE EDDINGTON TENSOR
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基于变爱丁顿张量的多维辐射磁流体动力学Godunov方法
DOI：
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发表时间：
2012
期刊：
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通讯作者：
S. Davis
中科院分区：
文献类型：
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作者：
Yan;J. Stone;S. Davis
我们描述了一种使用戈杜诺夫方法对多维辐射磁流体动力学方程进行积分的数值算法。该算法求解混合框架中的辐射矩方程，而不调用任何类似扩散的近似。使用变量爱丁顿张量来闭合力矩方程，其分量是使用短特征方法从大量角度处的传递方程的形式解计算出来的。我们使用全面的测试套件来验证该算法，包括辐射修正线性声波和磁声波的收敛测试、辐射修正激波的结构以及光子气泡不稳定性和强辐射场对稠密云层烧蚀的二维测试。这些测试涵盖了非常广泛的范围，包括光学厚流和薄流，以及至少 10−4–104 的辐射与气压之比。在大部分参数空间中，我们发现该方法是准确的。然而，测试还表明，在某些情况下，该方法需要改进，例如当辐射压和吸收不透明度都非常大时。我们建议修改算法以提高这种情况下的准确性。我们讨论了该方法相对于基于通量限制扩散的方法的优点。特别是，我们发现该方法不仅更准确，而且通常不比我们预期应用的扩散近似更昂贵。
We describe a numerical algorithm to integrate the equations of radiation magnetohydrodynamics in multidimensions using Godunov methods. This algorithm solves the radiation moment equations in the mixed frame, without invoking any diffusion-like approximations. The moment equations are closed using a variable Eddington tensor whose components are calculated from a formal solution of the transfer equation at a large number of angles using the method of short characteristics. We use a comprehensive test suite to verify the algorithm, including convergence tests of radiation-modified linear acoustic and magnetosonic waves, the structure of radiation-modified shocks, and two-dimensional tests of photon bubble instability and the ablation of dense clouds by an intense radiation field. These tests cover a very wide range of regimes, including both optically thick and thin flows, and ratios of the radiation to gas pressure of at least 10−4–104. Across most of the parameter space, we find that the method is accurate. However, the tests also reveal there are regimes where the method needs improvement, for example when both the radiation pressure and absorption opacity are very large. We suggest modifications to the algorithm that will improve the accuracy in this case. We discuss the advantages of this method over those based on flux-limited diffusion. In particular, we find that the method is not only substantially more accurate, but often no more expensive than the diffusion approximation for our intended applications.