Discrete Lie Advection of Differential Forms
Discrete Lie Advection of Differential Forms
复制标题
差分形式的离散平流
DOI：
10.1007/s10208-010-9076-y
复制
发表时间：
2009
影响因子：
3
通讯作者：
M. Desbrun
中科院分区：
文献类型：
--
作者：
Patrick Mullen;A. McKenzie;D. Pavlov;L. Durant;Y. Tong;E. Kanso;J. Marsden;M. Desbrun
在本文中，我们提出了一种用于执行任意微分形式的李平流的数值技术。利用标量双曲守恒定律的高分辨率有限体积方法的进步，我们首先通过对挤压的欧拉近似进行积分来离散化内部积（也称为收缩）。然后，将其与嘉当同伦公式和离散外导数一起用于导出离散李导数。该算子的实用性通过规则网格上标量场和 1-形式的数值平流得到证明。
In this paper, we present a numerical technique for performing Lie advection of arbitrary differential forms. Leveraging advances in high-resolution finite-volume methods for scalar hyperbolic conservation laws, we first discretize the interior product (also called contraction) through integrals over Eulerian approximations of extrusions. This, along with Cartan’s homotopy formula and a discrete exterior derivative, can then be used to derive a discrete Lie derivative. The usefulness of this operator is demonstrated through the numerical advection of scalar fields and 1-forms on regular grids.