TY - JOUR

T1 - Efficient split-step schemes for fluid–structure interaction involving incompressible generalised Newtonian flows

AU - Schussnig, Richard

AU - Pacheco, Douglas R.Q.

AU - Fries, Thomas Peter

N1 - Funding Information:
The authors gratefully acknowledge Graz University of Technology for the financial support of the Lead-project: Mechanics, Modeling and Simulation of Aortic Dissection.
Publisher Copyright:
© 2021 The Author(s)

PY - 2022/2

Y1 - 2022/2

N2 - Blood flow, dam or ship construction and numerous other problems in biomedical and general engineering involve incompressible flows interacting with elastic structures. Such interactions heavily influence the deformation and stress states which, in turn, affect the engineering design process. Therefore, any reliable model of such physical processes must consider the coupling of fluids and solids. However, complexity increases for non-Newtonian fluid models, as used, e.g., for blood or polymer flows. In these fluids, subtle differences in the local shear rate can have a drastic impact on the flow and hence on the coupled problem. There, existing (semi-) implicit solution strategies based on split-step or projection schemes for Newtonian fluids are not applicable, while extensions to non-Newtonian fluids can lead to substantial numerical overhead depending on the chosen fluid solver. To address these shortcomings, we present here a higher-order accurate, added-mass-stable fluid–structure interaction scheme centered around a split-step fluid solver. We compare several implicit and semi-implicit variants of the algorithm and verify convergence in space and time. Numerical examples show good performance in both benchmarks and an idealised setting of blood flow through an abdominal aortic aneurysm considering physiological parameters.

AB - Blood flow, dam or ship construction and numerous other problems in biomedical and general engineering involve incompressible flows interacting with elastic structures. Such interactions heavily influence the deformation and stress states which, in turn, affect the engineering design process. Therefore, any reliable model of such physical processes must consider the coupling of fluids and solids. However, complexity increases for non-Newtonian fluid models, as used, e.g., for blood or polymer flows. In these fluids, subtle differences in the local shear rate can have a drastic impact on the flow and hence on the coupled problem. There, existing (semi-) implicit solution strategies based on split-step or projection schemes for Newtonian fluids are not applicable, while extensions to non-Newtonian fluids can lead to substantial numerical overhead depending on the chosen fluid solver. To address these shortcomings, we present here a higher-order accurate, added-mass-stable fluid–structure interaction scheme centered around a split-step fluid solver. We compare several implicit and semi-implicit variants of the algorithm and verify convergence in space and time. Numerical examples show good performance in both benchmarks and an idealised setting of blood flow through an abdominal aortic aneurysm considering physiological parameters.

KW - Fluid–structure interaction

KW - Incompressible flow

KW - Non-Newtonian fluid

KW - Semi-implicit coupling

KW - Split-step scheme

KW - Time-splitting method

UR - http://www.scopus.com/inward/record.url?scp=85121123031&partnerID=8YFLogxK

U2 - 10.1016/j.compstruc.2021.106718

DO - 10.1016/j.compstruc.2021.106718

M3 - Article

AN - SCOPUS:85121123031

VL - 260

JO - Computers & Structures

JF - Computers & Structures

SN - 0045-7949

M1 - 106718

ER -