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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >A Robust And Efficient Hybrid Cut-cell/ghost-cell Method With Adaptive Mesh Refinement For Moving Boundaries On Irregular Domains
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A Robust And Efficient Hybrid Cut-cell/ghost-cell Method With Adaptive Mesh Refinement For Moving Boundaries On Irregular Domains

机译：具有不规则域上的移动边界的鲁棒高效的带有自适应网格细化功能的混合剪切/幻像细胞方法

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摘要

A new robust and efficient Cartesian grid method is developed for the moving boundary problem on an arbitrary complex domain. A difficult problem in the application of cut-cell methods is the presence of degenerate cut-cells, which are defined as cut-cells that are intersected by a boundary curve at more than two points. A new strategy is proposed for handling the problem of degenerate cells within the cut-cell methodology. In the proposed approach, gradient fluxes through all sections of the boundary curve intersecting a cut-cell are computed using surface integrals, with the consequence that all cut-cells in the solution domain (whether they are regular or degenerate) are handled using the same procedure. Marker points on the boundary curve are used to define cubic splines, which provide a high-fidelity representation for the boundary curve from which various geometrical properties (e.g., volume, face areas, centroid, etc.) of cut-cells can be determined with high-accuracy. In order to enhance the robustness of the present approach, the concept of a "ghost point" for degenerate cut-cells is introduced, which facilitates the evaluation of gradient fluxes in the fluid domain. This is advantageous as there is no longer any need to deal individually with each (usually small) split cut-cell. In consequence, the method proposed here can be interpreted as a hybrid cut-cell/ghost-cell method, in which the conventional cut-cell method is used to deal with regular cut-cells and the ghost-cell method is used to handle degenerate cut-cells. The accuracy and efficiency of this method can be improved further by application of an adaptive mesh refinement (AMR) method, based on a fully threaded tree data structure, to the cut-cells. A multigrid acceleration technique is used to solve the resulting algebraic system of discretized equations. Six test cases, for which exact solutions are available, are used to demonstrate the accuracy and efficiency of the proposed algorithm for both fixed and moving boundary problems. Using a triangulated surface mesh to represent an internal boundary surface, our proposed approach is generalized to deal with three-dimensional fluid flow problems. A test case of a three-dimensional free surface problem is used to validate the generalization of our Cartesian grid approach for complex boundaries in three dimensions.
机译：针对任意复杂域上的运动边界问题，开发了一种新的鲁棒高效的笛卡尔网格方法。切割单元方法应用中的一个难题是存在简并的切割单元，其定义为在两个以上点处被边界曲线相交的切割单元。提出了一种新的策略来处理切细胞方法中的简并细胞问题。在提出的方法中，使用表面积分计算通过边界曲线与切割单元相交的所有部分的梯度通量，结果是，解决方案域中的所有切割单元（无论是规则的还是退化的）都使用相同的方法进行处理。程序。边界曲线上的标记点用于定义三次样条，三次方样条曲线为边界曲线提供了高保真度表示，从中可以确定切割单元的各种几何特性（例如，体积，表面积，质心等）。高精确度。为了增强本方法的鲁棒性，引入了用于简并切孔的“重影点”的概念，这有助于评估流体域中的梯度通量。这是有利的，因为不再需要单独处理每个（通常较小的）拆分剪切单元。因此，这里提出的方法可以解释为混合切割单元/鬼单元方法，其中常规切割单元方法用于处理常规切割单元，而幻影单元方法用于处理退化单元。切割单元。通过将基于全线程树数据结构的自适应网格细化（AMR）方法应用于剪切单元，可以进一步提高此方法的准确性和效率。多网格加速技术用于求解离散方程组的代数系统。六个测试用例（可提供精确的解决方案）用于证明所提出算法在固定和移动边界问题上的准确性和效率。使用三角表面网格来表示内部边界表面，我们提出的方法被通用化以处理三维流体流动问题。使用三维自由表面问题的测试案例来验证我们的笛卡尔网格方法对三维复杂边界的推广。

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