A second-order face-centred finite volume method on general meshes with automatic mesh adaptation
A second-order face-centred finite volume method on general meshes with automatic mesh adaptation
复制标题
具有自动网格自适应功能的通用网格二阶面心有限体积法
DOI：
10.1002/nme.6428
复制
发表时间：
2020
影响因子：
2.9
通讯作者：
Giacomini M
中科院分区：
文献类型：
--
作者：
Giacomini M
提出了一种适用于一般网格的二阶面心有限体积策略。该方法使用混合公式，其中在网格的表面上计算未知的常数近似值。然后，这些信息被用来求解一组独立的单元格问题，以检索解的局部值及其梯度。这种方法的主要新颖之处在于引入了一个新的基函数，用于每个单元中原始变量的线性逼近。与常用的节点基不同，该基适用于一般网格的计算，包括不同单元类型的网格。所得到的方法提供了二阶精度的解和一阶梯度，无需重建程序，在不可压缩极限下具有鲁棒性，并且对细胞畸变和拉伸不敏感。利用该方法的二阶精度设计了一种自动网格自适应策略。通过计算一个额外的局部问题，获得一个有效的误差指标，独立的单元格，并用于驱动网格自适应。给出了数值算例，说明了该方法的逼近特性和网格自适应过程。在微流控的背景下，该方法具有自动网格自适应的潜力。
A second‐order face‐centred finite volume strategy on general meshes is proposed. The method uses a mixed formulation in which a constant approximation of the unknown is computed on the faces of the mesh. Such information is then used to solve a set of problems, independent cell‐by‐cell, to retrieve the local values of the solution and its gradient. The main novelty of this approach is the introduction of a new basis function, utilised for the linear approximation of the primal variable in each cell. Contrary to the commonly used nodal basis, the proposed basis is suitable for computations on general meshes, including meshes with different cell types. The resulting approach provides second‐order accuracy for the solution and first‐order for its gradient, without the need of reconstruction procedures, is robust in the incompressible limit and insensitive to cell distortion and stretching. The second‐order accuracy of the solution is exploited to devise an automatic mesh adaptivity strategy. An efficient error indicator is obtained from the computation of one extra local problem, independent cell‐by‐cell, and is used to drive mesh adaptivity. Numerical examples illustrating the approximation properties of the method and of the mesh adaptivity procedure are presented. The potential of the proposed method with automatic mesh adaptation is demonstrated in the context of microfluidics.