Research

At hypersonic speeds, the interplay of shock waves, boundary layer instabilities, and thermophysical nonequilibrium presents modeling and control challenges. Our recent work focuses on simulating blunt cones at hypersonic speeds, related to Stetson's experiments, to develop and validate computationally high-fidelity aerothermal flows. By coupling steady-state Navier-Stokes simulations with a heat conduction solver, we resolve the characteristics of roughness-induced surface heating. This effort details the limitations of classical energy models in capturing the vibrational excitation and dynamic dissociation that govern high-enthalpy flows. Future integration of chemical kinetics and thermochemical nonequilibrium is essential to advance preventative capabilities. These insights will not only enhance the physical fidelity of simulations. Still, they will also inform the design of thermal protection and transition control strategies, ultimately contributing to the development of robust high-speed aerospace systems.

Partition-of-Unity Physics-Informed Neural Networks (POU-PINNs) represent a fusion of classical numerical analysis and modern machine learning, aiming to address the challenges of solving parameterized partial differential equations in heterogeneous domains. Unlike traditional PINNs, which exhibit convergence and accuracy difficulties in the presence of spatial discontinuities, the POU-PINN architecture supports domain decomposition in partition-of-unity theory, facilitating locality- and physics-based approaches. Each subdomain features spatially varying learning parameters and is governed by a physics-based residual loss, promoting the unsupervised discovery of latent physical regimes. This formulation enables scalability to multiscale conductivity problems, as demonstrated in pore mass ablation and ice sheet dynamics. By disentangling spatial structure and physics through flexible subdomain assignments, the framework provides interpretable expert mixtures that seamlessly respect interface conditions and flow continuity. Our work contributes to the growing body of research focused on physics-based unsupervised learning and surrogate probabilistic modeling for high-consequence systems, enabling the integration of scientific constraints directly into learning architectures for predictive simulation under uncertainty.

Venous valves play a crucial role in maintaining unidirectional blood flow and preventing reflux in the lower extremities. Dysfunction of these valves can contribute to deep vein thrombosis (DVT), a serious and life-threatening condition. In this study, we used computational fluid dynamics (CFD) to model blood flow through a two-dimensional venous valve over a range of relevant Reynolds numbers. Simulations in ANSYS Fluent analyze flow separation, vortex shear, shear stress, and the formation of recirculation and stagnation regions, all of which are closely linked to thrombus formation. To deepen our understanding, we conducted simulations under both normal and dysfunctional valve configurations to assess the influence of valve competence on hemodynamics. We also compared results across various fluid models, including Newtonian and non-Newtonian representations of blood rheology, and observed significant differences in flow behavior, particularly at transitional Reynolds numbers. Both linear and nonlinear blood flow models were examined to capture the shear-thinning, non-Newtonian nature of blood under different physiological conditions. Simulations included scenarios with variable leaflet positions, such as fully open, partially closed, and asymmetric closure, to study how leaflet motion and positioning influence local vortex shedding and overall circulation patterns. While recent work has focused on broad digital twin frameworks and experimental platforms, our study offers high-resolution, physics-based insights into the specific flow structures that contribute to clot formation. By isolating and quantifying the fluid dynamic mechanisms behind valve dysfunction and DVT risk, our work provides a level of mechanistic clarity and predictive detail that is often generalized in hybrid or data-driven approaches. These findings inform the design of more effective valves, risk stratification, and the development of targeted therapeutic strategies.