Simulating particulate Stokes suspensions can be challenging because moving fluid–solid interfaces display arbitrary and time varying geometries; solid bodies are subject to both near-field and far-field hydrodynamic interactions; resolving point singularities that govern lubrication effects comes at stiff computational cost; and the presence of singularities challenges the numerical solutions by convergence order reduction. To tackle these challenges, we have developed a numerical method that is high-order accurate, meshless, consistent, stable, and spatially adaptive. It enables high-fidelity simulations for suspension flows and accurately resolving the lubrication effects in hydrodynamic interactions without invoking any artificial subgrid-scale lubrication model. However, for large-scale applications and the applications requiring multi-query loops (e.g., optimization and control), high-fidelity simulations that solve the full governing PDEs are too expensive. To address this limitation, we further investigate surrogate modeling for particulate suspensions. By harnessing the power of deep learning, we establish a graphic neural network model for fast computation of many-body hydrodynamic interactions. A preliminary study shows that using this approach can save the computer time by 2-3 orders, compared with the most commonly used solver for simulating the same suspension system.
About the Speaker
Dr. Wenxiao Pan is an assistant professor in the department of Mechanical Engineering at the University of Wisconsin-Madison. She received her PhD in applied mathematics at Brown University, and before joining UW-Madison in 2016, she worked at Pacific Northwest National Laboratory as a postdoc and a staff scientist. Her research group at UW-Madison focuses on modeling and simulating soft matter and complex fluids, through accurate, robust and scalable numerical methods as well as machine learning and data-driven model order reduction techniques.