Modelling and simulation of complex flows with multiple scales and multi-physics

当今计算科学家面临的一些最具挑战性的问题来自于 流体动力学，以及最显著的问题，其中流体流动与一些其他物理 进程。在这个提议中，我们关注两类这样的多物理现象：流体-结构 可变形的固体结构与流体相互作用的相互作用问题； 流经多孔性材料的多孔性介质对流体产生附加阻力。 例如，心脏和动脉中的血液流动；弹性木浆纤维的悬浮液 在造纸过程中；氢燃料电池中反应物的运输；以及混凝土的降解 通过水分运输来调节。虽然这些问题表面上看起来是从根本上 不同的是，所有的都可以用非线性偏微分方程组建模，并且是 以复杂的、耦合的物理为特征的，其发生的长度和时间尺度变化很大。它是 要在解决方案中同时解决这些不同规模的问题是一个主要的计算挑战 保持一定程度的效率。 在这项研究中，我的基本方法有两个：第一，推导出解析解或渐近解 提供对解决方案行为的一些洞察的近似；第二，使用分析的 作为设计更准确和更有效的数值求解策略的指导。一大专业 本工作的应用是利用浸没边界法对柔性纤维进行模拟 悬浮物；游动的海洋生物；生物膜的动力学。我也在调查 具有工业应用的多孔介质中的流动的各种问题，例如混凝土 燃料电池催化层设计，以及地下水污染和修复。

Some of the most challenging problems facing computational scientists today arise from applications in fluid dynamics, and most notably problems where a fluid flow interacts with some other physical process. In this proposal we focus on two classes of such multi-physics phenomena: fluid-structure interaction problems in which a deformable, solid structure interacts with a fluid; and transport in porous media for which flow through a porous material introduces an additional drag force on the fluid. Examples include the flow of blood in the heart and arteries; suspensions of flexible wood pulp fibers in the paper making process; transport of reactants in a hydrogen fuel cell; and concrete degradation mediated by moisture transport. While these problems seem on the surface to be fundamentally different, all can be modelled using nonlinear systems of partial differential equations, and are characterised by complex, coupled physics that occur over widely-varying length and time scales. It is a major computational challenge to resolve these various scales in the solution while at the same time maintaining some degree of efficiency. In this research, my basic approach is two-fold: first, to derive analytical solutions or asymptotic approximations that afford some insight into solution behaviour; and second, to use the analytical results as a guide in designing more accurate and efficient numerical solution strategies. One major application of this work is the use of the "immersed boundary method" to simulate flexible fiber suspensions; swimming marine organisms, and dynamics of biological membranes. I am also investigating a variety of problems involving flow in porous media with industrial applications, such as concrete degradation, fuel cell catalyst layer design, and groundwater contamination and remediation.