By coupling the standard and the conservative level set methods, an improved conservative level set method is proposed to capture the free surface smoothly with excellent mass conservation properties. The improvement lies in the fact that the surface normal is computed from a signed distance function instead of the Heaviside function. Comparing with the conservative level set method, the inevitable numerical discretization errors to point the surface normal in arbitrary directions could be eliminated, and the instability of the numerical solution could be improved efficiently. The advantage is clear in the straightforward combination of the standard level set and the conservative level set and a little effort is taken in coding compared with other coupled methods. The present method is validated with several well-known benchmark problems, including the 2-D Zalesak’s disk rotating, the 3-D sphere stretching in deformation vortex and the dam break flow simulation. The results are shown to be in good agreement with the published experimental data and numerical results.

中文翻译：

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改进的保守水平集方法用于自由表面流模拟

通过将标准和保守水平集方法相结合，提出了一种改进的保守水平集方法来平滑捕获具有优良质量守恒性能的自由表面。改进之处在于，表面法线是根据有符号距离函数而不是Heaviside函数计算的。与保守水平集方法相比，可以消除将表面法线指向任意方向的不可避免的数值离散误差，并可以有效地提高数值解的不稳定性。在标准级别集和保守级别集的直接组合中，其优势显而易见，并且与其他耦合方法相比，在编码上花费了一些精力。本方法已通过几个众所周知的基准问题进行了验证，包括二维Zalesak的圆盘旋转，变形涡旋中的3-D球体拉伸以及溃坝流模拟。结果表明与公开的实验数据和数值结果高度吻合。