Collaborative Research: Robust and Scalable Methods for Simulation and Data-Driven Modeling of Particulate Flows

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Complex fluids are mixtures of homogeneous fluids and deformable or rigid particles or fibers. These fluids are ubiquitous in biological systems and engineering applications and accurate prediction of their behavior is important for a broad set of problems such as hemodynamics modeling, simulation of intracellular processes, and microfluidics device modeling. Currently, accurate models of complex fluids require highly expensive simulations at microscopic or mesoscopic level, resolving the behavior of each particle (e.g., a deforming cell or fiber) and their interactions. In contrast, macroscopic continuum models for complex fluids (when available) allow for a far more efficient computation. However, these models often lack accuracy, and cannot capture all important aspects of the flow behavior in realistic settings; hindering construction of fast predictive models. The goal of the project is to enable construction of such models in a data-driven way. The investigators will develop a framework based on microscopic numerical simulations. The challenge in developing efficient and accurate continuum computational models of such fluids is the hard-to-analyze transition from microscopic to macroscopic parameters. In this work, the investigators focus on (1) robust and scalable solvers for particulate flow in 2D and 3D; and (2) the utilization of our framework to explore data-driven macroscopic models for the complex flows in 2D, with an initial exploration of extensions to 3D. The team will develop the algorithms for accurate solution of large-scale 3D flows with a high volume fraction of immersed deformable particles handling viscosity contrast, complex geometric boundaries, and long simulation times. Key mathematical components for this include boundary integral formulation and computation, kernel-independent quadrature schemes for singular and near-singular integration on surfaces in 3D, contact handling and close interaction, and improving efficiency of time-stepping schemes. In the second component of the project, the investigators will apply this framework to explore macroscopic characteristics of complex flows and their dependence on microscopic parameters and local geometry; this will create a foundation for data-driven continuum models for complex fluids.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.