A comparative study of limiting strategies in discontinuous Galerkin schemes for the M1 model of radiation transport
A comparative study of limiting strategies in discontinuous Galerkin schemes for the M1 model of radiation transport
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DOI：
10.1016/j.cam.2018.04.017
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发表时间：
2017-06
期刊：
影响因子：
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通讯作者：
Prince Chidyagwai;M. Frank;F. Schneider;Benjamin Seibold
中科院分区：
文献类型：
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作者：
Prince Chidyagwai;M. Frank;F. Schneider;Benjamin Seibold
M1最小熵矩系统是一个近似辐射输运方程的双曲平衡律系统，具有许多理想的性质。其中包括对称双曲性、熵衰减、矩可实现性以及扩散和自由流极限中的正确行为。然而，数值上的困难时，近似的解决方案的M1模型的高阶数值方案，即保持可实现的数值解和控制寄生振荡。在本文中，我们将以前构建的一维可实现性限制策略扩展到二维。此外，我们进行了各种组合的可实现性限制器和TVBM局部斜率限制器的三阶间断Galerkin（DG）计划的三角形和矩形网格上的数值研究。在几个测试案例中，我们证明，在一般情况下，实现限制器和TVBM限制器的组合是必要的，以获得一个强大的和准确的数值方案。我们的代码是公开的，以便读者可以复制所有结果。
The M 1 minimum entropy moment system is a system of hyperbolic balance laws that approximates the radiation transport equation, and has many desirable properties. Among them are symmetric hyperbolicity, entropy decay, moment realizability, and correct behavior in the diffusion and free-streaming limits. However, numerical difficulties arise when approximating the solution of the M 1 model by high order numerical schemes; namely maintaining the realizability of the numerical solution and controlling spurious oscillations. In this paper, we extend a previously constructed one-dimensional realizability limiting strategy to 2D. In addition, we perform a numerical study of various combinations of the realizability limiter and the TVBM local slope limiter on a third order Discontinuous Galerkin (DG) scheme on both triangular and rectangular meshes. In several test cases, we demonstrate that in general, a combination of the realizability limiter and a TVBM limiter is necessary to obtain a robust and accurate numerical scheme. Our code is published so that all results can be reproduced by the reader.