Work

A Robin–Robin strongly coupled partitioned method for fluid–poroelastic structure interaction

Year: 2025

Type: article

Abstract: This work focuses on the development of a novel, strongly-coupled, second-order partitioned method for fluid–poroelastic structure interaction. The flow is assumed to be viscous and incompressible, and the poroelastic material is described using the Biot model. To solve this problem, a numerical method is proposed, based on Robin interface conditions combined with the refactorization of the Cauchy’s one-legged ‘ ϑ -like’ method. This approach allows the use of the mixed formulation for the Biot model. The proposed algorithm consists of solving a sequence of Backward Euler–Forward Euler steps. In the Backward Euler step, the fluid and poroelastic structure problems are solved iteratively until convergence. Then, the Forward Euler problems are solved using equivalent linear extrapolations. We prove that the iterative procedure in the Backward Euler step is convergent, and that the converged method is stable when ϑ ∈ [1/2, 1]. Numerical examples are used to explore convergence rates with varying parameters used in our scheme, and to compare our method to a monolithic method based on Nitsche’s coupling approach.

Source: Journal of Numerical Mathematics

DOI: 10.1515/jnma-2024-0057

Authors: Connor Parrow, Martina Bukač

Institution: University of Notre Dame

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,712

Funder: National Science Foundation