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

基本信息

批准号：
2310340
负责人：
Daozhi Han
金额：
$ 15.28万
依托单位：
SUNY at Buffalo
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：
2022-12-01 至 2025-07-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2310340&HistoricalAwards=false
关键词：
Efficient Hybridizable Discontinuous Galerkin Methods

项目摘要

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普遍存在。常见的例子包括波浪破碎和晃动、含水层中的污染物输送、石油工程中的石油回收、血流中的药物输送、燃烧反应器中的气体颗粒流、聚合物电解质膜燃料电池技术中的废气管理等等。扩散界面流体模型在与多相流相关的界面现象的数值模拟中变得越来越流行。它们能够捕获流体界面的平滑过渡，并且可以在固定网格上进行模拟，而无需显式界面跟踪。求解扩散界面模型的一个特殊挑战是，小宽度的扩散界面通常表现出不稳定性，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产生寄生振荡，这会污染界面区域之外的数值解，甚至由于负粘度、密度或迁移率而导致代码爆炸。该项目的目的是开发高阶数值方法，能够准确捕获多相流的移动界面。现实世界的应用既可以看到扩散主导的流动，也可以看到平流主导的流动。研究人员首先开发并分析了可证明的超收敛杂交不连续伽辽金方法 (HDG)，用于求解扩散主导状态下的扩散界面流体模型。设计的关键思想是通过比数值迹和梯度变量更高阶的多项式来近似解变量，并探索基于局部投影的稳定性。然后，PI 设计了稳定的高阶 HDG 方法，该方法通过标量辅助变量 (SAV) 时间步进方案实现平流主导流。这些方法稳定了非线性四阶平流扩散方程中的平流，同时保留了基本的能量定律。稳定的 SAV-HDG 算法使扩散界面方法能够准确捕获平流主导区域中的尖锐锋面和不稳定界面，并允许在每个时间步对较小系统进行高效并行计算。最后，PI 开发并实现了用于扩散界面流体模型的快速非线性 HDG 多重网格求解器。实用求解器将进一步解决 HDG 方法缺乏高效迭代求解器/预处理器的问题研究生参与该项目的工作。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响进行评估，被认为值得支持审查标准。