Efficient Hybridizable Discontinuous Galerkin Methods for Phase Field Fluid Models

用于相场流体模型的高效可杂交不连续伽辽金方法

• 批准号: 2208231
• 负责人: Daozhi Han
• 金额: $ 15.28万
• 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: 2022
• 资助国家: 美国
• 起止时间: 2022-08-15 至 2023-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2208231&HistoricalAwards=false
• 关键词: Efficient; Hybridizable; Discontinuous; Galerkin; Methods

Multiphase flow is ubiquitous in natural phenomena and industrial applications. Common examples include wave-breaking and sloshing, contaminant transport in aquifers, oil recovery in petroleum engineering, drug delivery in blood flow, gas-particle flow in combustion reactors, exhaust management in Polymer Electrolyte Membrane fuel cell technology, and so forth. The diffuse interface fluid models have become increasingly popular in the numerical modeling of interfacial phenomena associated with multiphase flows. They are able to capture smooth transitions of fluid interface, and simulations can be carried out on a fixed grid without explicit interface tracking. A particular challenge in solving diffuse interface models is that the diffusive interface of small width often exhibits instability such as bubble merging or splitting. Traditional high order methods are prone to spurious oscillations around diffusive interfaces which can pollute the numerical solution beyond the interface region and even cause blow-up of the code due to negative viscosity, density or mobility. The aim of this project is to develop high order numerical methods that can accurately capture moving interfaces of multiphase flow.Real-world applications see both diffusion dominated flows and advection dominated flows. The investigator first develops and analyzes provably superconvergent hybridizable discontinuous Galerkin methods (HDG) for solving diffuse interface fluid models in the diffusion-dominated regime. The key idea in the design is to approximate solution variables by higher order polynomials than those for the numerical traces and gradient variables, and to explore local projection based stabilization. The PI then designs stabilized high order HDG methods effected with the Scalar Auxiliary Variable (SAV) time-stepping schemes for advection-dominated flows. The methods stabilize advection in the nonlinear fourth order advection-diffusion equation while preserve the underlying energy laws. The stabilized SAV-HDG algorithms enable diffuse interface methods to accurately capture sharp fronts and unstable interfaces in the advection-dominated regime, and allow efficient parallel computation of smaller systems at each time step. Finally the PI develops and implements fast nonlinear HDG multigrid solvers for diffuse interface fluid models. The practical solvers will further address the lack of efficient iterative solvers/preconditioners for HDG methods Graduate students 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.

多相流在自然现象和工业应用中无处不在。 常见的例子包括波浪和晃动，含水层中的污染物运输，石油工程中的石油回收，血流中的药物输送，燃烧反应堆中的气体流量，聚合物电解膜燃料电池技术中的排气管理等等。 弥漫性界面流体模型在与多相流相关的界面现象的数值模型中变得越来越流行。他们能够捕获流体接口的平滑转变，并且可以在固定网格上进行模拟而无需显式接口跟踪。 解决扩散界面模型的一个特殊挑战是，较小宽度的扩散界面通常表现出不稳定的范围，例如气泡合并或分裂。传统的高阶方法容易在扩散界面周围伪造振荡，这些界面可能会污染界面区域以外的数值解决方案，甚至由于负粘度，密度或迁移率而引起代码的爆炸。 该项目的目的是开发高阶数值方法，可以准确捕获多相流的运动界面。真实世界的应用程序，请参见扩散占主导的流量和对流占主导的流量。研究者首先开发和分析了可证明超融合的杂交不连续的盖金方法（HDG），用于在扩散为主导的方案中求解扩散界面流体模型。设计中的关键思想是通过高阶多项式近似解决方案变量，而不是数值轨迹和梯度变量的变量，并探索基于局部投影的稳定性。然后，PI设计了用标量辅助变量（SAV）时间稳定时间稳定的高阶HDG方法，用于向上主导的流量。这些方法稳定了非线性第四阶对流扩散方程的对流，同时保留了基本的能量法。 稳定的SAV-HDG算法可以使漫射界面方法准确地捕获以对流为主的态度，并在每个时间步骤中允许对较小系统的有效平行计算。 最终，PI开发并实现了扩散界面流体模型的快速非线性HDG Multigrid求解器。 实用的求解器将进一步解决HDG方法研究生缺乏有效的迭代求解器/预调节器参与该项目的工作。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的审查标准通过评估来进行评估的。