Divergence-free radial kernel for surface Stokes equations based on the surface Helmholtz decomposition
Divergence-free radial kernel for surface Stokes equations based on the surface Helmholtz decomposition
复制标题
基于表面亥姆霍兹分解的表面斯托克斯方程的无散径向核
DOI：
10.1016/j.cpc.2020.107408
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发表时间：
2020-11-01
影响因子：
6.3
通讯作者：
Feng, Xinlong
中科院分区：
文献类型：
--
作者：
Li, Jingwei;Gao, Zhiming;Feng, Xinlong
在本文中，我们开发并分析了一种新的无散核近似方法，用于解决曲面上瞬态不可压缩斯托克斯方程。我们提出的方法的新颖性来自于表面亥姆霍兹分解，它可以将表面斯托克斯方程转换为耦合方程，其中速度是致命的无散度，因此不必满足 inf-sup 条件。速度的空间离散是通过径向核无散度逼近空间实现的，只需要表面上的散点节点。利用空间径向基函数配置方法，得到了严格的稳定性和收敛性结果。给出了数值示例，证明了一些模型问题在更一般的表面上的效率。 (C) 2020 Elsevier B.V. 保留所有权利。
In this paper, we develop and analyze a new divergence-free kernel approximation method for the time-dependent incompressible Stokes equations on surfaces. The novelty of our proposed method comes from the surface Helmholtz decomposition, which can convert the surface Stokes equations into a coupled equations in which the velocity is deadly divergence-free so that no inf-sup conditions have to be satisfied. Spatial discretization of velocity is implemented by the radial kernel divergence-free approximation spaces, which only need scatter nodes on surfaces. Using the radial basis function collocation method in space, we derive the rigorous stability and convergence result. Numerical examples are presented, demonstrating the efficiency of some model problems on more general surfaces. (C) 2020 Elsevier B.V. All rights reserved.