Wim van Rees (MIT)

A high-order sharp immersed method for simulating PDEs with moving interfaces or boundaries on adaptive grids

Abstract: Immersed methods offer powerful advantages over traditional body-fitted techniques for solving differential equations in complex, moving domains, eliminating the need to create and maintain body-conforming grids. However, most existing immersed methods are only first- or second-order accurate, driving up resolution requirements for high-fidelity 3D nonlinear simulations. In this talk, I will present our work on a high-order finite-difference-based immersed boundary and interface discretization, along with our error and stability analyses for stationary and moving boundaries. I will show applications to both linear and nonlinear elasticity and the incompressible Navier–Stokes equations. I will also describe our 3D multiresolution grid adaptation approach, based on high-order interpolating wavelet transforms within a scalable parallel framework, achieving predictable convergence across different wavelet orders. Finally, I will demonstrate how combining high-order immersed methods with adaptive grids enables robust, accurate simulation of 3D Navier–Stokes flows with moving immersed boundaries.

Bio:
Wim M. van Rees is Associate Professor in the department of Mechanical Engineering at Massachusetts Institute of Technology. He is affiliated with the Center for Ocean Engineering. He received his BSc and MSc from Delft University of Technology in Marine Technology, and his PhD from ETH Zurich in 2014 in Computational Science and Engineering. In 2015 he performed research as a postdoctoral fellow in the School of Engineering and Applied Sciences at Harvard University on the mechanics and design of shape-shifting structures. Wim joined the MIT faculty in 2017, where he received Early Career awards from the Department of Energy in 2020, and from the Army Research Office in 2021. Wim's main research interests are to develop and apply advanced numerical simulations to solve bio-inspired forward and inverse problems in fluids, solids, and fluid-structure interaction.