An Energy Stable One-Field Fictitious Domain Method for Fluid-Structure Interactions

TL;DR

This paper introduces an energy-stable, one-field fictitious domain method for fluid-structure interactions that simplifies computations by solving a single velocity field and decouples interactions until the final step, validated through numerical tests.

Contribution

It presents a novel energy-stable method that uses a single velocity field and separate meshes for fluid and solid, improving computational efficiency and stability in fluid-structure interaction simulations.

Findings

Proves energy stability of the method theoretically.

Validates stability through numerical experiments in 2D and 3D.

Demonstrates accurate simulation of fluid-structure interactions.

Abstract

In this article, the energy stability of a one-field fictitious domain method is proved and validated by numerical tests in two and three dimensions. The distinguishing feature of this method is that it only solves for one velocity field for the whole fluid-structure domain; the interactions remain decoupled until solving the final linear algebraic equations. To achieve this the finite element procedures are carried out separately on two different meshes for the fluid and solid respectively, and the assembly of the final linear system brings the fluid and solid parts together via an isoparametric interpolation matrix between the two meshes. The weak formulations are introduced in the continuous case and after discretization in time. Then the stability is analyzed through an energy estimate. Finally, numerical examples are presented to validate the energy stability properties.