Discontinuous Galerkin methods for two-phase flows with soluble surfactants

用于可溶性表面活性剂两相流的不连续伽辽金方法

• 批准号: 166796982
• 负责人: Professor Dr.-Ing. Martin Oberlack
• 金额: --
• 依托单位: Fachgebiet Strömungsdynamik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2016-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/166796982?language=en
• 关键词: Discontinuous; Galerkin; methods; two; phase

The general research objective is to develop and implement a high-accurate numerical solver for the computation of multiphase flows including phase interfaces and interfacial transport equations with the Discontinuous Galerkin (DG) method. Specifically, it is intended to extend the newly developed DG library BoSSS (Bounded Support Spectral Solver) for single phase flows by an interface tracking method combined with the cut-cell method and non-smooth basis functions. The cut-cell method is proposed to accurately compute surface and volume integrals for those cells which are split by the phase interface. Further the non-smooth basis functions such as the Heaviside function allow for a sharp delimitation between different fluid properties. In this connection the interface tracking method is based on level-set and volume-of-fluid, or most likely a combination of both, to ensure both local mass preservation and a highly accurate front position. Finally, the interfacial equation is intended to be solved in an analogous fashion to the level-set formulation where the interface, a two-dimensional manifold, is embedded and solved in a manifold of dimension three. Similar to the signed-distance function for the level-set method certain embedding conditions are to be developed to couple the interfacial transport equations, which live on a two-dimensional manifold, into a three-dimensional manifold. The key goal is that the combination of the latter methods may avoid serious shortcomings of classical schemes such as mass deficit at the interface or artificially induced flows due to numerical errors in the computation of surface curvature to name only a few.

一般研究的目标是开发和实施一个使用不连续的Galerkin（DG）方法的多相流量计算的高精确数值求解器。具体而言，它旨在通过接口跟踪方法与Cut-Cell方法和非平滑基础基础函数相结合，以扩展新开发的DG库Boss（有界支持光谱求解器）对单相流进行。提出了切割方法，以准确计算那些被相界面分裂的单元格的表面和体积积分。进一步的非平滑基函数，例如重质函数，可以在不同的流体特性之间进行急剧的划界。在这方面，接口跟踪方法基于级别和流体量，或者最有可能是两者的组合，以确保局部质量保存和高度准确的前部位置。最后，界面方程旨在以类似的方式求解级别公式，在这种情况下，界面（二维歧管）嵌入并溶解在维度三的歧管中。与级别方法的签名距离函数相似，要开发某些嵌入条件，以将生存在二维歧管上的界面传输方程与三维歧管。关键目的是，后一种方法的组合可以避免经典方案的严重缺点，例如界面处的质量不足或由于表面曲率计算中的数值错误而导致的人为诱发的流量，仅举几例。