Partitioned semi-implicit methods for simulation of biomechanical fluid-structure interaction problems

A Naseri,A Oliva,O Lehmkuhl,I Gonzalez

doi:10.1088/1742-6596/745/3/032020

A Naseri, A Oliva + Show 2 more

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https://doi.org/10.1088/1742-6596/745/3/032020

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Abstract

This paper represents numerical simulation of fluid-structure interaction (FSI) system involving an incompressible viscous fluid and a lightweight elastic structure. We follow a semi-implicit approach in which we implicitly couple the added-mass term (pressure stress) of the fluid to the structure, while other terms are coupled explicitly. This significantly reduces the computational cost of the simulations while showing adequate stability. Several coupling schemes are tested including fixed-point method with different static and dynamic relaxation, as well as Newton-Krylov method with approximated Jacobian. Numerical tests are conducted in the context of a biomechanical problem. Results indicate that the Newton-Krylov solver outperforms fixed point ones while introducing more complexity to the problem due to the evaluation of the Jacobian. Fixed-point solver with Aitken's relaxation method also proved to be a simple, yet efficient method for FSI simulations.

Highlights

We follow a semi-implicit approach in which we implicitly couple the added-mass term of the fluid to the structure, while other terms are coupled explicitly. This significantly reduces the computational cost of the simulations while showing adequate stability
Fluid-structure interaction (FSI) refers to problems that deal with mutual interaction between fluid flow and a moving or deforming structure
Partitioned methods, on the other hand, use separate solvers for fluid and structural equations and adopt a coupling scheme to account for the interaction of the domains

Summary

Introduction

Fluid-structure interaction (FSI) refers to problems that deal with mutual interaction between fluid flow and a moving or deforming structure. Solving the fluid and structural equations only once at each time step, does not precisely satisfy the coupling condition at the fluid-structure interface Semi-implicit methods try to mitigate this problem by splitting the fluid equations and applying implicit coupling only to the terms associated with the added-mass effect. This modification prevents excessive computational cost while maintaining the stability [10,11,12].

Fluid domain

Findings

Conclusions