Collaborative Research: New Formulation and Algorithms for Fluid-Structure Interaction, with Application to Tumor Growth

合作研究：流固相互作用的新配方和算法，及其在肿瘤生长中的应用

• 批准号: 1216907
• 负责人: Jianjun Paul Tian
• 金额: $ 13万
• 依托单位: College of William and Mary
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-15 至 2014-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1216907&HistoricalAwards=false
• 关键词: Collaborative; Research; New; Formulation; Algorithms

Fluid-structure interaction (FSI) problems play prominent roles in many scientific and engineering fields, yet an accurate study of such problems remains highly challenging due to the strong nonlinearity and multi-physics involved. Current computational theory and methods for fluid-structure interactions lack sufficient accuracy and realistic material representations, and are limited to relatively simple structural configurations. The goal of this project is to overcome such limitations by establishing a new computational mathematical framework for accurate and efficient numerical investigation of complex FSI problems, particularly for tumor growth modeling and simulation. The PIs will derive new mathematical formulation that allows the study of general FSI problems with sophisticated structural settings, develop efficient numerical algorithms that ensure high accuracy in FSI computations, and apply the proposed mathematical formulation and computational methods to the individual-cell-based modeling and simulation of tumor growth. This proposal builds on the PIs? solid background in computational and applied mathematics and significant work on tumor modeling.The proposed research will improve the understanding of the nonlinear dynamics in highly complex FSI problems through a combined mathematical and computational framework. Experimental measurements will also be used for validating the numerical results. The success of this project will not only provide a solid knowledge base for advancing the current state of computational FSI study, but also enable important discoveries in the fundamental mechanism of early tumor formation and development. The project experiences and findings will strengthen the research collaboration and curriculum development in computational mathematics and mathematical biology at both Old Dominion University and the College of William and Mary. Due to the close geographical proximity between the two schools, project impacts will be maximized through convenient communication between faculty and students and through joint programs between the two schools. Education and outreach activities will involve graduate and undergraduate students in the theory, methods and application of computational mathematics.

流固耦合（FSI）问题在许多科学和工程领域中发挥着重要作用，但由于涉及强非线性和多物理场，对此类问题的准确研究仍然极具挑战性。当前的流固耦合计算理论和方法缺乏足够的精度和现实的材料表示，并且仅限于相对简单的结构配置。该项目的目标是通过建立新的计算数学框架来克服这些限制，以准确有效地数值研究复杂的 FSI 问题，特别是肿瘤生长建模和模拟。 PI将推导出新的数学公式，允许研究具有复杂结构设置的一般FSI问题，开发有效的数值算法以确保FSI计算的高精度，并将所提出的数学公式和计算方法应用于基于个体细胞的肿瘤生长建模和模拟。该提案建立在 PI 的基础上？扎实的计算和应用数学背景以及在肿瘤建模方面的重要工作。所提出的研究将通过组合的数学和计算框架提高对高度复杂的 FSI 问题中的非线性动力学的理解。实验测量也将用于验证数值结果。该项目的成功不仅将为推进计算FSI研究的现状提供坚实的知识基础，而且有助于在早期肿瘤形成和发展的基本机制方面取得重要发现。该项目的经验和发现将加强奥多明尼恩大学和威廉玛丽学院在计算数学和数学生物学方面的研究合作和课程开发。由于两校地理位置相近，通过师生之间的便捷沟通以及两校之间的联合项目，项目的影响将最大化。教育和推广活动将让研究生和本科生参与计算数学的理论、方法和应用。