LEAPS-MPS: Computational Methods for Many-Physics Problems Involving Multi-Material Flows

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). In recent years, physical and mechanical systems that contain more than two entities have become common in applications. Some examples include fuel mixing in a deforming engine chamber, wind and ocean waves impacting on offshore wind power generation systems, and heart blood flow simulations.

Although there are many numerical methods that can be used individually, most do not work well with each other for solving challenges in these more complex situations. To this end, this project aims at developing a computational framework and software suite for the high-fidelity simulation of multi-material flows. Upon completion, this project will provide a powerful tool for studying the coupling between multi-material fluids and any number of structures.

The project also involves collaboration in two related subjects – a computational method to capture under-resolved structural boundaries in fluid-structure interaction problems and a machine-learning based reduced order modeling of embedded flow computations to realize real-time flow predictions in complex environments. In carrying out the project, the PI will train two graduate students.

In addition, the PI will improve two graduate courses for a new PhD program in Data Science at The University of Texas at El Paso to better prepare a majority Hispanic student body to solve data and computing related challenges. Furthermore, the project involves the organization of a new annual one-day workshop to promote a STEM-related career among young students from underrepresented groups and low-income families in the Borderplex region.

The major component of the project is an efficient and reliable embedded boundary method on moving computational grids, called the ALE-EBM method. Traditionally, the interface between fluids and structures are tracked by mesh points and it necessarily causes the grid to move, a strategy commonly known as the Arbitrary Lagrangian-Eulerian or ALE methods, whereas the interface between two fluids are usually captured implicitly by various embedded boundary methods (EBM), due to its large deformation or topological changes.

The two strategies, however, cannot be combined per se to enable computation of multi-fluid/structure interaction problems or multi-material shock hydrodynamics, as existing EBMs rely heavily on the assumption of a fixed grid. The new ALE-EBM method attempts to fill this gap by providing a proved methodology to perform embedded boundary computations on a computational grid that is allowed to move freely.

In particular, the project includes: (1) analyzing multi-material Riemann problems to enforce various transmission conditions between materials while maintaining the physical relevance of the numerical solutions, (2) utilizing multiple level sets to capture the motion of multiple fluid sub-domains while preserving the signed distance meaning of each level set and conserving the mass of each fluid, (3) using a Nitsche-type method to capture adjacent structural boundary with a much smaller physical scale, and (4) a machine learning approach to achieve efficient reduced-order modeling computations of these problems.

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.