基于通量非结构网格有限体积法的Level Set方程求解

A Flux-based Unstructured Grids Finite Volume Method for Level Set Equation

在非结构网格上,采用基于通量的格心有限体积法求解Level Set方程,并给出了其数值离散格式.对Zalesak圆盘、旋转收缩圆及圆面剪切三个经典界面运动问题进行了数值模拟,其质量盈亏量与收敛阶的计算结果表明,该方法克服了传统数值方法造成的质量不守恒的缺点,能准确有效地求解拓扑结构发生变化的复杂运动界面问题,且计算量较格点格式大为减少.

A flux-based cell-centered finite volume method for solving the Level Set equation on unstructured grids is presented and the discretization scheme is deduced as well. Three benchmark numerical problems about interface evolution, namely Zalesak＇s disk rotation, circle rotation and shrink and vortex-in-a-box, are solved numerically by the proposed finite volume method. The mass errors and the order of the convergence are calculated and compared with those obtained by the traditional methods. The results show that the proposed method more accurately solves the mass loss problem that exists in the traditional methods. In addition, the proposed method can capture moving interface with complex topological structure accurately and efficiently. Compared with the node-centered finite volume method, the computation cost is greatly decreased by utilizing our method.