We are pleased to announce that Stephan B. Lunowa, post-doctoral researcher at the Technical University of Munich, will give the SFB 1313 "Pretty Porous Science Lecture" #61. His talk will be on "Solving Linear Poroelasticity with Lattice Boltzmann Methods".
Date: 21 January 2025
Time: 4 pm CET
Authors: Stephan B. Lunowa and Barbara Wohlmuth
Speaker: Dr. Stephan B. Lunowa, Technical University of Munich (Germany)
Title: "Solving Linear Poroelasticity with Lattice Boltzmann Methods"
Venue: Multi Media Lab (MML), U1.003, Pfaffenwaldring 61, 70569 Stuttgart, Campus Vaihingen
Abstract
Biot’s consolidation model is the standard model for the evolution of deformable porous media saturated by a fluid and has various interdisciplinary applications. While numerical solution methods to solve poroelasticity by classical methods such as finite differences, finite volumes or finite elements have been intensely studied in the past, lattice Boltzmann methods for poroelasticity have not been developed yet. In this talk, we propose a novel semi-implicit coupling of lattice Boltzmann methods to solve Biot’s consolidation model in two dimensions. To this end, we apply a single-relaxation-time lattice Boltzmann method for reaction-diffusion equations to solve the Darcy flow subproblem and combine it with a recent pseudo-time multi-relaxation-time lattice Boltzmann scheme for quasi-static linear elasticity [1]. For the coupling between the equations, we developed a centered update scheme, that incorporates both explicit and semi-implicit contributions. The numerical results demonstrate that naive coupling schemes lead to instabilities when the poroelastic system is strongly coupled, while the newly developed
centered coupling scheme is stable and accurate, even for the Biot–Willis coefficient being one. Moreover, the results for Terzaghi’s consolidation problem and a two-dimensional extension thereof highlight that the scheme is also able to capture discontinuous solutions arising from instantaneous loading.
References
[1] O. Boolakee, M. Geier, L. De Lorenzis, A new lattice Boltzmann scheme for linear elastic solids: periodic problems,
Comput. Methods Appl. Mech. Engrg. 404 (2023) 115756. doi:10.1016/j.cma.2022.115756.
[2] S.B. Lunowa, B. Wohlmuth, A lattice Boltzmann method for Biot’s consolidation model of linear poroelasticity,
arXiv:2409.11382 [math.NA] (2024), arxiv.org/abs/2409.11382.