A multi-moment constrained finite volume method on arbitrary unstructured grids for incompressible flows
A multi-moment constrained finite volume method on arbitrary unstructured grids for incompressible flows
复制标题
DOI：
10.1016/j.jcp.2016.09.054
复制
发表时间：
2016-12
期刊：
影响因子：
--
通讯作者：
B. Xie;F. Xiao
中科院分区：
文献类型：
--
作者：
B. Xie;F. Xiao
提出了一种多矩约束有限体积法，可以模拟复杂几何形状的高雷诺数不可压流动。遵循体积平均/点值多矩（VPM）方法的基本思想（Xie et al.（2014）[71]），通过采用单元顶点和重心处的点值（PV）作为预测变量，在任意非结构化混合网格上开发了该公式。通过有限体积形式的约束条件推导出演化方程来更新网格中心值，保证了严格的数值保守性。提出了一种新的基于紧致模板上局部PV的数值计算公式，以提高混合单元和任意单元的非结构网格计算的精度、鲁棒性和效率。数值实验表明，该数值模型具有接近3阶的收敛速度，数值误差远小于VPM方法。数值耗散被显著抑制，这有利于复杂几何形状中高雷诺数流动的数值模拟。
We proposed a multi-moment constrained finite volume method which can simulate incompressible flows of high Reynolds number in complex geometries. Following the underlying idea of the volume-average/point-value multi-moment (VPM) method (Xie et al. (2014) [71]), this formulation is developed on arbitrary unstructured hybrid grids by employing the point values (PV) at both cell vertex and barycenter as the prognostic variables. The cell center value is updated via an evolution equation derived from a constraint condition of finite volume form, which ensures the rigorous numerical conservativeness. Novel numerical formulations based on the local PVs over compact stencil are proposed to enhance the accuracy, robustness and efficiency of computations on unstructured meshes of hybrid and arbitrary elements. Numerical experiments demonstrate that the present numerical model has nearly 3-order convergence rate with numerical errors much smaller than the VPM method. The numerical dissipation has been significantly suppressed, which facilitates numerical simulations of high Reynolds number flows in complex geometries.