[论文解读] voFoam { A geometrical Volume of Fluid algorithm on arbitrary unstructured meshes with local dynamic adaptive mesh renement using OpenFOAM

Tomislav Mari, Holger Marschall+1 more|arXiv (Cornell University)|May 15, 2013

Fluid Dynamics and Heat Transfer参考文献 37被引用 26

一句话总结

本论文提出了一种新颖的、并行化的、非拆分几何体积分数（VoF）算法，应用于OpenFOAM中，支持任意非结构化网格及动态局部自适应网格加密（AMR），适用于二维和三维两相流。通过使用拉格朗日离散轨迹和二次收敛的迭代通量校正方法，该方法确保了高体积守恒性、有界性以及低界面重构误差——在非结构化网格上实现了迄今为止报道的最低对称差值误差。

ABSTRACT

A new parallelized unsplit geometrical Volume of Fluid (VoF) algorithm with support for ar- bitrary unstructured meshes and dynamic local Adaptive Mesh Renement (AMR), as well as for two and three dimensional computation is developed. The geometrical VoF algorithm supports arbitrary unstruc- tured meshes in order to enable computations involving ow domains of arbitrary geometrical complexity. The implementation of the method is done within the framework of the OpenFOAM library for Compu- tational Continuum Mechanics (CCM) using the C++ programming language with modern policy based design for high program code modularity. The development of the geometrical VoF algorithm signicantly extends the method base of the OpenFOAM library by geometrical volumetric ux computation for two- phase ow simulations. For the volume fraction advection, a novel unsplit geometrical algorithm is developed, which inherently sustains volume conservation utilizing unique Lagrangian discrete trajectories located in the mesh points. This practice completely eliminates the possibility of an overlap between the ux polyhedra and hence sig- nicantly increases volume conservation. A new ecient (quadratic convergent) and accurate iterative ux correction algorithm is developed, which avoids topological changes of the ux polyhedra. Our geometri- cal VoF algorithm is dimension agnostic, providing automatic support for both 2D and 3D computations, following the established practice in OpenFOAM. The geometrical algorithm used for the volume fraction transport has been extended to support dynamic local AMR available in OpenFOAM. Furthermore, the existing dynamic mesh capability of OpenFOAM has been modied to support the geometrical mapping algorithm executed as a part of the dynamic local AMR cycle. The method implementation is fully paral- lelized using the domain decomposition approach. The majority of the standard established test cases for verication and validation of VoF algorithms has been thoroughly tested with varying Courant numbers. Our results for the rst time show a VoF algorithm on unstructured meshes to be robust, mass conservative and boundedness-preserving for complex time-varying velocity elds. The obtained volume of symmetric dierence interface reconstruction errors are the lowest reported so far in the literature for unstructured meshes.

研究动机与目标

• 将OpenFOAM的功能扩展为支持一种鲁棒的、适用于非结构化网格的VoF算法，以处理复杂几何形状。
• 通过一种新颖的非拆分几何通量计算方法结合拉格朗日轨迹，确保两相流中严格的体积守恒。
• 在保持质量和界面精度的前提下，将VoF方法与动态局部自适应网格加密（AMR）集成。
• 在非结构化网格上，实现时间变化速度场下的高精度和有界性。
• 在不同Courant数的标准测试案例中，展示该方法的鲁棒性及低界面重构误差。

提出的方法

• 该方法采用几何VoF方法，通过在网格点上使用独特的拉格朗日离散轨迹来计算体积通量，消除了通量多面体之间的重叠。
• 采用一种新型的具有二次收敛特性的迭代通量校正算法，以提高精度，同时不改变通量多面体的拓扑结构。
• 该算法与维度无关，通过OpenFOAM已有的框架原生支持二维和三维模拟。
• 实现采用现代C++策略式设计，具有高度模块化，并通过域分解实现完全并行化。
• 扩展了OpenFOAM中的动态网格功能，以在AMR周期内支持几何映射，从而实现局部加密。
• 体积分数的对流通过一种保守的、非拆分的几何通量方案完成，该方案保持了有界性和质量守恒。

实验结果

研究问题

• RQ1 能否开发一种几何VoF算法，使其在任意非结构化网格上实现严格的体积守恒？
• RQ2 如何将非拆分几何通量计算与动态局部AMR相结合，同时保持质量和界面精度？
• RQ3 在非结构化网格上，使用迭代通量校正的VoF方法能实现多高的界面重构误差水平？
• RQ4 该方法在复杂的时间变化速度场下能否保持有界性和鲁棒性？
• RQ5 与现有VoF方法相比，该算法在标准测试案例中的性能和精度如何？

主要发现

• 所提出的VoF算法在非结构化网格上实现了迄今为止报道的最低对称差值界面重构误差。
• 该方法在不同Courant数的多种测试案例中表现出鲁棒性及有界性保持能力。
• 由于使用了拉格朗日离散轨迹和无重叠的通量多面体，体积守恒得到严格保持。
• 迭代通量校正算法实现二次收敛，显著提高了通量精度，且未改变拓扑结构。
• 与动态局部AMR的集成无缝，网格移动和几何映射均在AMR周期内处理。
• 实现完全并行化并使用域分解实现可扩展性，支持高效的大规模模拟。