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Modeling and Hybridizable Discontinuous Galerkin Methods for Two-phase Flows in Karstic Geometry

岩溶几何中两相流的建模和可混合间断伽辽金方法

基本信息

批准号：
1912715
负责人：
Daozhi Han
金额：
$ 10万
依托单位：
Missouri University of Science and Technology
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-08-01 至 2022-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1912715&HistoricalAwards=false
关键词：
Modeling Hybridizable Discontinuous Galerkin Methods

项目摘要

A prime example of multi-phase flow in karstic geometry is flow in natural karst aquifers. Karst aquifers supply about 40 percent of the drinking water in the United States, and are susceptible to contamination. During flooding seasons, the water pressure in the conduits is larger than that in the adjacent porous media so that conduit-borne contaminants are driven into the porous media. Likewise during dry seasons, contaminants sequestered in the porous media are released into flow in the conduits due to the pressure reversal, and exit through springs and wells into surface water systems. This exchange of flow between conduits and porous media poses an environmental issue in that sequestered contaminants may influence the quality of underground water sources and thus significantly decrease water availability. Besides applications in environmental science, multi-phase flows in karstic geometry are also important in oil recovery in petroleum engineering, in Polymer Electrolyte Membrane fuel cell technology, as well as in cardiovascular modeling and simulation in biomedical sciences. In these applications multi-phase flows in conduits and in porous media interact with each other, and therefore have to be considered together. Geometric configurations that consist of both conduits and porous media are termed as karstic geometry. Despite the importance of the subject, little work has been done in this direction, due to the nature of deforming boundary of the problem, the complex geometry, the coupling of different dynamics via domain interface, the vast disparity of spatial and temporal scales and so on.The investigator will examine modeling and the design of hybridizable discontinuous Galerkin (HDG) methods for two-phase flows in karstic geometry. Based on the phase field formalism and Onsager's variational principle, the PI will derive a degenerate Cahn-Hilliard-Stokes-Darcy model for two-phase flow of arbitrary density and viscosity contrast in karstic geometry. The derivation seeks to overcome a number of obstacles in modeling of multiphase flows in karstic geometry, including maintaining a divergence-free velocity, deriving an explicit degenerate mobility function, and incorporating multiphysics such as wetting and solute. The PI then will introduce and analyze superconvergent HDG methods for solving the diffuse interface model by exploiting approximation via polynomials of mixed orders and by carefully stabilizing the nonlinear advection in the presence of high-order diffusion. Finally, the PI and his collaborators will develop scalable HDG multigrid solvers for diffuse interface fluid models. The practical solvers will further address the lack of efficient iterative solvers in the HDG community. Graduate students will participate in the work of this project.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

岩溶几何学中多相流的一个主要例子是天然岩溶含水层中的流动。岩溶含水层提供了美国约40%的饮用水，而且很容易受到污染。在洪水季节，管道中的水压力大于相邻多孔介质中的水压力，从而将水携带的污染物驱入多孔介质中。同样，在旱季，由于压力逆转，多孔介质中封存的污染物被释放到管道中的水流中，并通过泉水和威尔斯进入地表水系统。管道和多孔介质之间的这种流动交换造成了一个环境问题，因为隔离的污染物可能影响地下水源的质量，从而显著降低水的可用性。除了在环境科学中的应用外，岩溶几何中的多相流在石油工程中的石油回收、聚合物电解质膜燃料电池技术以及生物医学科学中的心血管建模和模拟中也很重要。在这些应用中，管道中的多相流和多孔介质中的多相流相互作用，因此必须一起考虑。由管道和多孔介质组成的几何构型称为岩溶几何构型。尽管这一课题的重要性，但由于问题的变形边界的性质，复杂的几何形状，不同动力学通过域界面的耦合，空间和时间尺度的巨大差异等，在这方面的工作已经做得很少。研究者将研究建模和设计的杂交间断Galerkin（HDG）方法在岩溶几何两相流。基于相场理论和Onsager变分原理，PI将推导出适用于任意密度和粘度差的两相流的退化Cahn-Hilliard-Stokes-Darcy模型。推导旨在克服一些障碍，在岩溶几何多相流的建模，包括保持一个无发散的速度，推导出一个明确的退化流动性函数，并将多物理，如润湿和溶质。然后，PI将介绍和分析超收敛HDG方法，通过利用混合阶多项式近似和在高阶扩散存在下仔细稳定非线性平流来求解扩散界面模型。最后，PI和他的合作者将为扩散界面流体模型开发可扩展的HDG多重网格求解器。实用的求解器将进一步解决HDG社区缺乏有效的迭代求解器的问题。研究生将参与该项目的工作。该奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。