Splitting Method for a Multilayered Poroelastic Solid Interacting with Stokes Flow

TL;DR

This paper introduces a novel partitioned numerical scheme for simulating the interaction between Stokes flow and multilayered poroelastic structures, validated through stability analysis and biological applications.

Contribution

It develops a stable, decoupled numerical method combining Stokes-Biot and Biot splitting techniques for complex fluid-poroelastic interactions.

Findings

The scheme is stable under various conditions.

Validation with manufactured solutions confirms accuracy.

Application to blood vessel flow demonstrates biological relevance.

Abstract

Multilayered poroelastic structures are found in many biological tissues such as cartilage and the cornea, and play a key role in the design of bioartificial organs and other bioengineering applications. Motivated by these applications, we study the interaction between a free fluid flow, governed by the time-dependent Stokes equations, and a multilayered poroelastic structure composed of a thick Biot layer and a thin, linear poroelastic plate located at the interface. The resulting equations are linearly coupled across the thin structure domain through physical coupling conditions. We develop a partitioned numerical scheme for this poroelastic fluid-structure interaction problem, combining the backward Euler Stokes-Biot splitting method with the fixed-strain Biot splitting approach. The first decouples the Stokes problem from the multilayered structure problem, while the second decouples the flow and mechanical subproblems within the poroelastic structures. Stability of the splitting scheme is proven under different combinations of time-step conditions and parameter constraints. The method is validated using manufactured solutions, and further applied to a biologically inspired blood vessel flow problem. We also demonstrate convergence of the solution to the limiting case without the plate as its thickness tends to zero, providing additional validation of the numerical method.