二维和三维质量守恒特征基格式的有效实现
An efficient implementation of mass conserving characteristic-based schemes in 2D and 3D
摘要：
在本文中，我们开发了球近似的特征（B-char）的方法，这是一种算法，有效地实现基于特征的计划在2D和3D。实施数值方案的核心是积分的评估，在基于特征的方案中，分段常数近似归结为计算两个区域之间的交点。在文献中，这些区域由多面体（2D中的多边形和3D中的多面体）近似，因此，3D中的实现是不平凡的。本文的主要新颖之处是近似的区域的球，其交叉点是便宜得多的计算比那些多面体。当然，球不能完全细分区域，因此可能会损失一些质量。我们进行了一些调整，并解决了优化问题，以产生一个计划，是本地和全球质量守恒。该算法可以实现的结果是类似的，从一个实现，使用多面体相交，具有更便宜的计算成本。
英文摘要：
In this paper, we develop the ball-approximated characteristics (B-char) method, which is an algorithm for efficiently implementing characteristic-based schemes in 2D and 3D. Core to the implementation of numerical schemes is the evaluation of integrals, which in the context of characteristic-based schemes with piecewise constant approximations boils down to computing the intersections between two regions. In the literature, these regions are approximated by polytopes (polygons in 2D and polyhedra in 3D) and, due to this, the implementation in 3D is nontrivial. The main novelty in this paper is the approximation of the regions by balls, whose intersections are much cheaper to compute than those of polytopes. Of course, balls cannot fully tessellate a region, and hence some mass may be lost. We perform some adjustments, and also solve an optimisation problem, in order to yield a scheme that is both locally and globally mass conserving. This algorithm can achieve results that are similar to those obtained from an implementation which uses polytopal intersections, with a much cheaper computational cost.
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