任意网格上的单调等高线集无需再距离化
Monotone level-sets on arbitrary meshes without redistancing
AI总结：
本文针对工程实践中使用等高线方法模拟双流体流动时出现的两个问题，提出了解决方案：通过考虑局部网格尺寸改进非均匀网格上的Heaviside函数正则化，以及通过强耦合方法减少再距离化步骤的计算成本和脆弱性。
摘要：
本文提出了针对工程实践中使用等高线方法模拟双流体流动时出现的两个问题的解决方案。第一个问题是关于在任意网格上正则化Heaviside函数。我们证明在非均匀网格上正则化的Heaviside函数可能不光滑。引入了确实光滑且单调的替代正则化定义，这些新定义通过考虑变化的局部网格尺寸产生光滑的Heaviside函数。第二个问题是由于必须重新距离化等高线场而导致的计算成本和脆弱性。在以前的论文中已显示，将等高线传播与流求解器强耦合可以提供鲁棒性和潜在的效率和准确性优势。下一步是将再距离化包含在算法的强耦合部分中。当前再距离化过程的计算成本禁止这一点。提出了四种替代方法来绕过昂贵的再距离化步骤。这应促进完全耦合的等高线方法。一些基准案例展示了所提方法的有效性。这些包括标准的箱中涡旋测试案例。基于这些结果，选择了最有利的再距离化方法。
英文摘要：
In this paper we present approaches that address two issues that can occur when the level-set method is used to simulate two-fluid flows in engineering practice. The first issue concerns regularizing the Heaviside function on arbitrary meshes. We show that the regularized Heaviside function can be non-smooth on non-uniform meshes. Alternative regularizing definitions that are indeed smooth and monotonic, are introduced. These new definitions lead to smooth Heaviside functions by taking the changing local meshsize into account. The second issue is the computational cost and fragility caused by the necessity of redistancing the level-set field. In previous papers it is shown that strongly coupling the level-set convection with the flow solver provides robustness and potentially efficiency and accuracy advantages. The next step would be to include redistancing within the strong coupling part of the algorithm. The computational cost of current redistancing procedure prohibit this. Four alternative approaches for circumventing the expensive redistancing step are proposed. This should facilitate a fully coupled level-set approach. Some benchmark cases demonstrate the efficacy of the proposed approaches. These includes the standard test case of the vortex in a box. Based on these results the most favorable redistancing approach is selected.
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