论文标题
一个新的Hodge运算符，中的外部演算。应用流体力学
A new Hodge operator in Discrete Exterior Calculus. Application to fluid mechanics
论文作者
论文摘要
本文在离散的外部演算（DEC）的背景下介绍了离散Hodge操作员的新的一般构造。这个离散的霍奇操作员可以限制与流行的对角线霍奇在网格上的良好中心限制。它允许基于任何内部点（例如矿物）或重中心的双网格。它为网格优化的离散霍奇操作员打开了道路。在以良好为中心的三角剖分的特定情况下，如果双网格是圆周的，则将其减少到对角线。基于分析发展，该离散的杂物不利用惠特尼形式，并且确切地符合分段恒定形式，无论是在双网格的构建中选择哪个内部点。进行了针对流体力学问题和热传递的分辨率的数值测试。研究了各种类型网格的收敛性。
This article introduces a new and general construction of discrete Hodge operator in the context of Discrete Exterior Calculus (DEC). This discrete Hodge operator enables to circumvent the well-centeredness limitation on the mesh with the popular diagonal Hodge. It allows a dual mesh based on any interior point, such as the incenter or the barycenter. It opens the way towards mesh-optimized discrete Hodge operators. In the particular case of a well-centered triangulation, it reduces to the diagonal Hodge if the dual mesh is circumcentric. Based on an analytical development, this discrete Hodge does not make use of Whitney forms, and is exact on piecewise constant forms, whichever interior point is chosen for the construction of the dual mesh. Numerical tests oriented to the resolution of fluid mechanics problems and thermal transfer are carried out. Convergence on various types of mesh is investigated.
