Seminar Event Detail


Applied Interdisciplinary Mathematics (AIM)

Date:  Friday, March 11, 2022
Location:  Virtual (3:00 PM to 4:00 PM)

Title:  Towards high-fidelity multiresolution simulations of interface-coupled multiphysics problems

Abstract:   Interface-coupled multiphysics simulations like fluid-structure interaction and two-phase flows pose several challenges to computational methods. Among these, the interface geometry is typically complex and time-dependent, which requires solvers to discretize PDEs within arbitrary domains with moving boundaries. Further, accurately enforcing the boundary conditions of the coupled problem requires local high fidelity results on and near the interface. Lastly, the computational cost of such problems, especially in 3D, means the use of adaptive grid resolution methods to exploit scale separations is indispensable.

In this talk I will detail our progress towards a high-fidelity multiresolution solver for interface-coupled multiphysics problems that addresses this challenges, by covering two main contributions.
First, I will discuss our approach for boundary discretization based on a reformulation of the immersed interface method (IIM). This has led to a locally second-order 2D vorticity-velocity based Navier-Stokes solver that can handle multiple bodies, moving boundaries and two-way coupling. I will also briefly discuss current work on high-order enforcement of embedded boundary conditions within 3D domains.
Second, I will present our approach to multiresolution grid adaptation using a wavelet-based analysis implemented within a scalable parallel software framework. In this approach, we use first- and second-generation interpolating wavelets to decompose any field in a multiresolution analysis, and use this to inform grid adaptation. Combined with standard finite-difference discretizations, we can provide a convergence analysis on wavelet-based multilevel grids and demonstrate high-order accuracy of our results. Finally, I will briefly discuss software implementation choices that have lead to parallel scalability of our 3D multiresolution solver on many thousands of compute cores.

Files:


Speaker:  Wim van Rees
Institution:  MIT

Event Organizer:   Silas Alben    alben@umich.edu

 

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