In this paper, we introduce a second-order unstructured finite-volume method developed to solve a conservative level-set equation in two- and three-dimensional geometries. The characteristic function for the flow is defined at the center of each cell while the face-normal velocities are calculated at the mid-points of the corresponding cell faces. An interpolation method independent of cell shape and based on a central scheme is applied for the approximations at the cell faces. The capabilities and performance of the proposed scheme are validated using several 2D and 3D tests. Results show that the present numerical method is quite suitable for working within the smooth framework resulting from the signed distance function. Moreover, this method yields very accurate results in interface-capturing problems such as the single vortex deformation.

在本文中，我们介绍了一种二阶非结构化有限体积方法，用于求解二维和三维几何中的保守水平集方程。在每个单元的中心定义流动的特征函数，而在相应单元面的中点计算面法向速度。独立于单元形状并基于中心方案的插值方法应用于单元面的近似值。所提出的方案的能力和性能已使用多个 2D 和 3D 测试进行验证。结果表明，目前的数值方法非常适合在有符号距离函数产生的平滑框架内工作。此外，这种方法在界面捕获问题（例如单涡旋变形）中产生了非常准确的结果。