论文标题
具有移动网格和精确未完成的源处理的准确解决方案针对时间依赖的运输问题
Accurate solutions to time dependent transport problems with a moving mesh and exact uncollided source treatment
论文作者
论文摘要
为了找到针对时间依赖的SN传输问题的基准质量解决方案，我们在不连续的Galerkin（DG）框架中开发了一种数值方法，该框架利用了时间依赖的细胞边缘，我们称之为移动的网格和未填充的源处理。离散空间的DG方法是对平滑问题的强大解决方案技术，并且在非平滑问题上具有鲁棒性。为了实现DG方法在光谱解决平稳问题的潜力，我们设计了移动的网格和未完成的源处理，以绕过解决方案中的不连续性或运输计算中接收的解决方案的第一个衍生物。最终的方法在平滑问题上实现了光谱收敛，例如标准DG实现。当应用于引起不连续性的非平滑源问题时，我们的移动网格无效的源方法将返回比标准DG方法更准确的解决方案。关于光滑来源的问题，我们即使在波浪前的问题中也观察到光谱收敛。在角度通量本质上是非平滑的问题中，与Ganapol（2001）众所周知的平面脉冲基准测试一样，与静态网格相比，我们不会观察到准确性的升高，但是误差的减少降低是近三个学位。
For the purpose of finding benchmark quality solutions to time dependent Sn transport problems, we develop a numerical method in a Discontinuous Galerkin (DG) framework that utilizes time dependent cell edges, which we call a moving mesh, and an uncollided source treatment. The DG method for discretizing space is a powerful solution technique on smooth problems and is robust on non-smooth problems. In order to realize the potential of the DG method to spectrally resolve smooth problems, our moving mesh and uncollided source treatment is devised to circumvent discontinuities in the solution or the first derivative of the solutions that are admitted in transport calculations. The resulting method achieves spectral convergence on smooth problems, like a standard DG implementation. When applied to problems with nonsmooth sources that induce discontinuities, our moving mesh, uncollided source method returns a significantly more accurate solution than the standard DG method. On problems with smooth sources, we observe spectral convergence even in problems with wave fronts. In problems where the angular flux is inherently non-smooth, as in Ganapol's (2001) well known plane pulse benchmark, we do not observe an elevated order of accuracy when compared with static meshes, but there is a reduction in error that is nearly three orders of magnitude.
