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Partition of Unity Multivariate Approximation for the Volume of Fluid Method

流体体积法的单位多元近似的划分

基本信息

批准号：
2012011
负责人：
Alfa Heryudono
金额：
$ 20万
依托单位：
University of Massachusetts, Dartmouth
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-09-01 至 2024-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2012011&HistoricalAwards=false
关键词：
Partition Unity Multivariate Approximation Volume

项目摘要

This project will advance the understanding of multi-phase flows that are encountered in many scientific and engineering applications. Multi-phase flow problems exhibit highly dynamic, complex interfaces, and the project will develop computational tools to predict the evolution of such interfaces; the challenge is that these interfaces may be largely deformed with intricate localized patterns. Methods for numerically tracking and predicting the dynamics of the interfaces must be able to correctly capture local features with optimal computational costs and high accuracy. This project aims to develop and analyze techniques for fast and highly accurate interface reconstruction methods with emphasis on three-phase (liquid-gas-solid) flow. An application of interest here is deposition of eye drops onto 3D realistic eye geometries. The project also involves research training and integrated education of students in an interdisciplinary setting and the development of codes to support reproducible research.The volume-of-fluid (VOF) method is one of the most commonly used interface tracking methods in multi-phase flow simulations. Research in this project involves the development of techniques to improve the accuracy of the interface reconstruction scheme for the volume of fluid method for simulating multi-phase problems on complex geometries. The three most important aspects we are investigating are (1) robust and highly-accurate partition of unity multivariate approximation volume-of-fluid (PUMA-VOF) method; (2) simultaneous space-time schemes for advection-type partial differential equations (PDEs) on time-varying domains; (3) mathematical modeling and numerical simulation of problems with moving geometries. The research will include theory and practical application of PUMA-VOF on the field of scientific simulations on complex geometries.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.

该项目将增进对许多科学和工程应用中遇到的多相流的理解。多相流问题表现出高度动态、复杂的界面，该项目将开发计算工具来预测此类界面的演变；挑战在于，这些界面可能会因复杂的局部图案而大幅变形。用于数值跟踪和预测界面动态的方法必须能够以最佳的计算成本和高精度正确捕获局部特征。该项目旨在开发和分析快速且高精度的界面重建方法，重点关注三相（液-气-固）流。这里感兴趣的一个应用是将眼药水沉积到 3D 逼真的眼睛几何形状上。该项目还涉及跨学科环境中对学生的研究培训和综合教育，以及支持可重复研究的代码开发。流体体积（VOF）方法是多相流模拟中最常用的界面跟踪方法之一。该项目的研究涉及开发技术来提高流体体积法界面重建方案的准确性，以模拟复杂几何形状的多相问题。我们正在研究的三个最重要的方面是（1）稳健且高精度的单位多元近似流体体积划分（PUMA-VOF）方法； (2)时变域上对流型偏微分方程(PDE)的联立时空格式； (3)运动几何问题的数学建模和数值模拟。该研究将包括 PUMA-VOF 在复杂几何形状的科学模拟领域的理论和实际应用。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审查标准进行评估，被认为值得支持。