Fast algorithms for high fidelity simulation of viscous suspension flows

用于粘性悬浮液流高保真模拟的快速算法

• 批准号: 2309661
• 负责人: Eduardo Corona
• 金额: $ 39.9万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-09-01 至 2026-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2309661&HistoricalAwards=false
• 关键词: Fast; algorithms; fidelity; simulation; viscous

Particle suspensions are ubiquitous in nature; their study is featured in many areas of fundamental science and technology. Simulating them helps us understand properties of matter like jamming and phase transition, enables us to study of spontaneous formation of biological structures like cell membranes and cytoskeletons, and it allows us to design a vast array of smart materials, from damping fluids in Kevlar and prosthesis to self-assembling nanomaterials. However, the very properties that define these particle systems make them very challenging to simulate, as we must accurately reproduce their behavior for long periods of time. The overarching goal of this research project is to provide transformative improvements to state-of-the-art solvers for the numerical simulation of these particulate systems. By design, each of the contributions in this project has, on its own, foreseeable broad impact in multiphysics simulation and in numerical methods for scientific computing, and ultimately, in advancing our scientific and technological capabilities by enabling simulation methods to bridge the gap between theory and experiment. This project is integrated with ongoing educational initiatives, including the development of novel applied mathematics curricula and providing research opportunities for a diverse group of students. The project will include training of graduate students.This research project involves the development of a fast simulation framework for rigid particulate suspensions. This work is centered around the formulation of long-range forces with Boundary Integral Methods and of short-ranged contact forces employing optimization-based methods, as this is ideal to effectively tackle the many-body interactions in dense particle systems. This framework features three separate contributions aimed at unlocking the full potential of this approach: (1) Fast singular and near-singular revaluation schemes to resolve long-range particle interactions and analyze integral operators for spheroidal, ellipsoidal and axis-symmetric geometries, enabling the study of a wide array of particle systems and confining geometries, (2) Structured preconditioners for boundary integral equations in evolving geometries leveraging prior work on structured matrices and tensor train decompositions to accelerate the solution of resulting linear systems of equations, and (3) Systematic, robust and adaptive acceleration method for optimization-based collision resolution using matrix-splitting schemes for viscous flow mobility matrices, which may be adapted to most formulations for particulate suspensions.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.

粒子悬浮液本质上是普遍存在的；他们的研究在许多基本科学技术领域都有特色。模拟它们有助于我们理解物质的特性，例如干扰和相位过渡，使我们能够研究生物结构的自发形成，例如细胞膜和细胞骨架，它使我们能够设计出大量的智能材料，从凯夫拉（Kevlar）和疾病中的阻尼液中，自组装纳米材料。但是，定义这些粒子系统的特性使它们非常具有挑战性，因为我们必须长时间准确地重现其行为。该研究项目的总体目标是为这些颗粒系统的数值模拟为最先进的求解器提供变革性改进。根据设计，该项目的每个贡献本身都在多物理模拟以及用于科学计算的数值方法中有可预见的广泛影响，并最终通过启用模拟方法来促进我们的科学和技术能力，以弥合理论之间的差距和实验。该项目与正在进行的教育计划相结合，包括开发新颖的应用数学课程，并为各种学生提供研究机会。该项目将包括对研究生的培训。该研究项目涉及为刚性颗粒悬架的快速模拟框架开发。这项工作以边界积分方法和采用基于优化方法的短距离接触力的长距离制定为中心，因为这是有效解决密集粒子系统中多体相互作用的理想选择。该框架具有三个独立的贡献，旨在解锁这种方法的全部潜力：（1）快速奇异和近乎含量的重估方案，以解决远程粒子相互作用，并分析了球体，椭圆形和轴对称几何的整体操作员研究各种粒子系统和限制几何形状的研究，（2）用于边界积分方程的结构化预处理，用于在结构化矩阵上利用先前的工作和张量的火车分解，以加速产生的线性系统的解决方案，以及（3） ，使用矩阵拆分方案用于粘性流动式矩阵，可用于优化基于优化的碰撞解决方案的鲁棒和适应性加速方法，这可以适应大多数颗粒悬架的配方。此奖项反映了NSF的法定任务，并且通过评估的支持值得一提基金会的智力优点和更广泛的影响审查标准。