Speaker
Description
We introduce a numerical framework for moving-interface problems that integrates the Virtual Element Method (VEM) [1] within an immersed-boundary-type strategy [2,3]. In the proposed approach, the interface is represented in a Lagrangian manner and evolves within a fixed Eulerian finite element mesh. As the interface moves, it cuts the background structured grid, generating arbitrary polygonal subcells that are naturally handled as virtual elements.
Although a reconstruction of these polygonal regions is required at each update, achieved using standard computational-geometry procedures, this process avoids traditional mesh deformation, ensuring that elements never become distorted and eliminating the need for projection methods or sub-partitioning strategies [2,3]. The Eulerian–Lagrangian coupling enables accurate interface tracking while maintaining a stable and consistent solution of the governing equations on the fixed grid.
We demonstrate the effectiveness and versatility of the method in challenging scenarios involving tissue growth, third-medium contact, and erosion, all of which feature complex evolving geometries and large deformations. Numerical experiments show robust interface resolution and computational efficiency, highlighting the promise of this approach for multiphysics problems with moving boundaries.
References.
[1] P. Wriggers, F. Aldakheel, B. Hudobivnik. Virtual element methods in engineering sciences. Berlin: Springer, 2024.
[2] L. Foucard, A. Aryal, R. Duddu, F. Vernerey, 2015, A coupled Eulerian–Lagrangian extended finite element formulation for simulating large deformations in hyperelastic media with moving free boundaries, Computer Methods in Applied Mechanics and Engineering, Volume 283, Pages 280-302.
[3] L. Kudela, N. Zander, T. Bog, S. Kollmannsberger, E. Rank, 2015, Efficient and accurate numerical quadrature for immersed boundary methods. Advanced Modeling and Simulation in Engineering Sciences, Volume 2, Pages 10(22).