Dr. Hu’s research interests primarily focus on mathematical modeling, scientific computing, and scientific machine learning. His early works include developing numerical methods based on immersed boundary method and immersed interface method for solving complex fluid dynamical systems, such as vesicle hydrodynamics with inextensibility constraint, interfacial problems with soluble surfactants, electrohydrodynamic systems, etc. These problems are known to be challenging in scientific computing community and he has achieved fruitful and outstanding results on those topics.
Recently, he developed a theoretical analysis and efficient numerical method for solving diffusiophoretic systems in three dimensions. Using technique of linear stability analysis, it is found that a symmetric breaking spontaneous swimming motion exists under certain condition. In addition, the particle exhibits a complicated chaotic locomotion with high Péclet numbers. With absence of inertia effect in a fluid, the finding of chaotic behavior is quite rare. The result has been published in the prestigious journal Physical Review Letters in 2019.
As the latest research topic, Dr. Hu propose a discontinuity capturing shallow neural network that can effectively work as an approximator for discontinuous functions in high dimensions. The network model is further applied to solve sharp interface problems, such as elliptic interface problems and anisotropic elliptic interface problems with multiple interfaces.