A high-order and interface-preserving discontinuous Galerkin method for level-set reinitialization
A high-order and interface-preserving discontinuous Galerkin method for level-set reinitialization
复制标题
DOI：
10.1016/j.jcp.2018.11.029
复制
发表时间：
2019-02
期刊：
影响因子：
--
通讯作者：
Jiaqi Zhang;P. Yue
中科院分区：
文献类型：
--
作者：
Jiaqi Zhang;P. Yue
本文提出了一种保留界面的水平集重新初始化的高阶数值方法。在界面单元中，水平集函数的梯度由加权局部投影方案确定，并且确定缺失的加性常数，从而保留零水平集的位置。在非界面单元中，我们遵循 Hu 和 Shu 的工作 [SIAM J. Sci.计算。 21（1999）660-690]；然后，在考虑特征的同时，通过水平集函数的连续性来恢复丢失的常数。为了处理高度扭曲的初始条件，我们开发了一种混合数值通量，它将 Lax-Friedrichs 通量和罚通量相结合。我们的方法对于重要的测试用例是稳定的，并且可以很好地处理远离界面的奇点。当界面上存在导数奇点时，设计二阶导数限制器来抑制振荡。当使用 N 次多项式时，对于平滑解，至少可以观察到接口单元中的 (N+1) 阶精度和整个域中的 N 阶精度。二维测试用例展示了卓越的性能，例如准确性、长期稳定性、界面保持能力以及接触线的轻松处理。我们还展示了悬滴夹断过程的一些初步结果，其中涉及流体界面的拓扑变化。我们的方法很容易扩展到三维和自适应网格。
A high-order numerical method for interface-preserving level-set reinitialization is presented in this paper. In the interface cells, the gradient of the level-set function is determined by a weighted local projection scheme and the missing additive constant is determined such that the position of the zero level set is preserved. In the non-interface cells, we compute the gradient of the level-set function by solving a Hamilton–Jacobi equation as a conservation law system using the discontinuous Galerkin method, following the work by Hu and Shu [SIAM J. Sci. Comput. 21 (1999) 660–690]; the missing constant is then recovered by the continuity of the level-set function while taking into account the characteristics. To handle highly distorted initial conditions, we develop a hybrid numerical flux that combines the Lax–Friedrichs flux and the penalty flux. Our method is stable for non-trivial test cases and handles singularities away from the interface very well. When derivative singularities are present on the interface, a second-derivative limiter is designed to suppress the oscillations. At least (N+ 1) th order accuracy in the interface cells and Nth order in the whole domain are observed for smooth solutions when N th degree polynomials are used. Two dimensional test cases are presented to demonstrate superior properties such as accuracy, long-term stability, interface-preserving capability, and easy treatment of contact lines. We also show some preliminary results on the pinch-off process of a pendant drop, where topological changes of the fluid interface are involved. Our method is readily extendable to three dimensions and adaptive meshes.