Collaborative Research: Optimal-Complexity Spectral Methods for Complex Fluids

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Complex fluids, such as microbial suspensions in biology or quantum fluids in physics, exhibit a wealth of intriguing phenomena, ranging from spontaneous transport and non-equilibrium pattern formation to the emergence of superfluid and superconductive currents. Computational techniques for simulating and predicting the dynamics of these fluids in realistic 3D configurations found in laboratories are not keeping pace with the recent breakthroughs in experimental design and mathematical modeling. The Principal Investigators (PIs) will develop a collection of computational advancements that are urgently needed to validate current mathematical models and explore relevant parameter regimes to guide current and next-generation experiments. These efforts will pave the way for a better understanding of biological and physical transport phenomena, promising improved designs of micro-fluidic and quantum-fluidic devices. The project also provides research training opportunities for graduate students. The PIs will be developing highly efficient numerical methods based on a hybrid of Fourier/ultraspherical spectral methods that are ideally suited for accurately and robustly treating the high-order derivatives that appear in the complex fluid models. This computational framework will enable the fast simulation of non-equilibrium fluid flows through scientifically relevant geometries composed of cylinders, spheres, and ellipsoids. The algorithms will be parallelizable for efficient simulation on next-generation hardware accelerators. Working with two experimental collaborators, the PIs will investigate chaotic mixing, transport properties, and topological nature of geometrically confined non-Newtonian 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.