Towards High-order Adaptive-grid Simulations of Flow Problems with Embedded Moving Boundaries
Embedded boundary methods are widely used for flow simulations within complex, moving domains. The advantages of such methods are their ability to handle complex domains and moving boundaries on structured grids, without the need to generate body-fitted meshes and associated dynamic mesh adaptations. The vast majority of existing embedded boundary methods achieve first or second order accuracy in space. This makes them well-suited for exploring problems at moderate Reynolds numbers but limits their use for tackling higher Reynolds number flow problems, especially in three dimensions and/or when accurate resolution of boundary quantities are required.
In this talk I will detail our progress towards increasing the efficiency of adaptive-grid flow problems with embedded moving boundaries. First, I will discuss our approach for high-order boundary discretization based on a reformulation of the immersed interface method (IIM), and share our error and stability analyses. I will demonstrate the effectiveness of the approach in a second-order 2D vorticity-velocity Navier-Stokes solver, and show our higher order accurate solutions to advection-diffusion problems in 3D. Second, I will present our approach to 3D multiresolution grid adaptation techniques using a wavelet-based analysis implemented within a scalable parallel software framework. This leads to a predictable convergence of the solution error with respect to the adaptation criteria, as well as large control over the compression ratio through the wavelet order.
Bio:
Wim M. van Rees is Assistant Professor in the department of Mechanical Engineering at Massachusetts Institute of Technology. He received his BSc and MSc from Delft University of Technology in Marine Technology, and his PhD from ETH Zurich in 2014. In 2015 he performed research as a postdoctoral fellow in the School of Engineering and Applied Sciences at Harvard University, and he joined the MIT faculty in 2017. His awards and recognitions include an American Bureau of Shipping Career Development Chair (2017), a Seagrant Doherty Professorship in Ocean Utilization (2019), a Department of Energy Early Career Award (2020), and an Army Research Office Early Career Award (2021).
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