中文标题#
自适应网格加密在液滴模拟中的误差估计
英文标题#
Error Estimation for Adaptive Mesh Refinement in Droplet Simulations
中文摘要#
我们提出一个由剪切力驱动的一维液滴形成模型，该模型采用基于通量的误差估计。 所提出的模型通过渐近展开和前缘追踪方法推导出来，用于模拟液滴界面。 然后使用混合形式的伽辽金有限元方法对该模型进行离散化。 然而，由于高度对流的断裂过程，解梯度的跳跃是不连续的，并且可能增长得更快。 这会导致错误的液滴界面和不正确的曲率。 因此，必须对网格进行充分细化以准确捕捉界面。 控制方程的混合形式自然提供了平滑的界面梯度，可用于计算误差估计。 计算得到的误差估计随后被用来驱动自适应网格细化算法。
英文摘要#
We present a one-dimensional shear force driven droplet formation model with a flux-based error estimation. The presented model is derived using asymptotic expansion and a front-tracking method to simulate the droplet interface. The model is then discretized using the Galerkin finite element method in the mixed form. However, the jumps in the solution gradients are discontinuous and can grow faster due to the highly convective pinch-off process. This leads to an erroneous droplet interface and incorrect curvature. Therefore, the mesh must be sufficiently refined to capture the interface accurately. The mixed form of the governing equation naturally provides smooth interface gradients that can be used to compute the error estimate. The computed error estimate is then used to drive the adaptive mesh refinement algorithm.
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