论文标题
自动网格适应的一般网格的二阶以面部为中心的有限体积方法
A second-order face-centred finite volume method on general meshes with automatic mesh adaptation
论文作者
论文摘要
提出了对一般网格的二阶有限体积策略。该方法使用混合配方，其中在网格的面上计算未知的常数近似。然后，此类信息用于解决一组问题，即独立的单元格，以检索解决方案的局部值及其梯度。这种方法的主要新颖性是引入一个新的基础函数，用于每个单元格中原始变量的线性近似。与常用的淋巴结相反，所提出的基础适用于一般网格的计算，包括具有不同细胞类型的网格。最终的方法为溶液提供了二阶精度，而在不需要重建程序的情况下，在不需要重建程序的情况下，在不可压缩的限制中为其梯度提供了二阶精度，对细胞失真和拉伸不敏感。利用解决方案的二阶精度来设计自动网格适应性策略。从一个额外的局部问题（独立单元格）的计算中获得有效的误差指标，并用于驱动网格自适应。显示了说明该方法和网格适应性过程的近似特性的数值示例。在微流体学的背景下，证明了具有自动网格适应的建议方法的潜力。
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.
