Goal-based angular adaptivity for Boltzmann transport in the presence of ray-effects
Goal-based angular adaptivity for Boltzmann transport in the presence of ray-effects
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DOI：
10.1016/j.jcp.2020.109759
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发表时间：
2019-11
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通讯作者：
Steven Dargaville-;R. Smedley-Stevenson;Paul N. Smith;C. Pain
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作者：
Steven Dargaville-;R. Smedley-Stevenson;Paul N. Smith;C. Pain
玻尔兹曼输运问题通常涉及重流，由于平流对粒子相互作用的主导作用，粒子在长距离传播。如果使用不充分细化的非旋转不变角度离散化，则问题的某些区域不会传播粒子。这些“射线效应”对于具有角度自适应性的基于目标的误差度量来说是有问题的，因为渐进前区域中的度量将为零/不正确并且不会发生角度自适应性。在这项工作中，我们使用低阶滤波球谐函数（旋转不变，因此不受射线效应影响）来“引导”我们的误差度量，并通过 Haar 小波角度离散实现高度精细的各向异性角度自适应性。我们在纯流式处理的三个简单问题上对此进行了测试，在这些问题中，传统的错误指标会失败。我们证明了我们的方法是稳健的，并且产生了适应的角度离散，与固定先验细化产生的结果相匹配，即使在角度细化的情况下，也可以减少运行时间或恒定的额外成本。
Boltzmann transport problems often involve heavy streaming, where particles propagate long distance due to the dominance of advection over particle interaction. If an insufficiently refined non-rotationally invariant angular discretisation is used, there are areas of the problem where no particles will propagate. These “ray-effects” are problematic for goal-based error metrics with angular adaptivity, as the metrics in the pre-asymptotic region will be zero/incorrect and angular adaptivity will not occur. In this work we use low-order filtered spherical harmonics, which are rotationally invariant and hence not subject to ray-effects, to “bootstrap” our error metric and enable highly refined anisotropic angular adaptivity with a Haar wavelet angular discretisation. We test this on three simple problems with pure streaming in which traditional error metrics fail. We show our method is robust and produces adapted angular discretisations that match results produced by fixeda priorirefinement with either reduced runtime or a constant additional cost even with angular refinement.