A mechanically consistent model for fluid–structure interactions with contact including seepage

Burman, Erik; Fernández, Miguel Ángel; Frei, Stefan; Gerosa, Fannie

doi:10.1016/j.cma.2022.114637

Cited by 15 publications

(7 citation statements)

References 39 publications

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“…For p = 1, the backward Euler method is usually applied as a relaxation for steady problems, because the first-order accuracy in time is generally insufficient for time-dependent simulations. However, for some simulations like the fluid–structure interaction via the arbitrary Lagrangian–Eulerian method (Burman et al , 2022; Wang et al , 2020), the backward Euler method is still popular for time-dependent simulations, and hence the present work is still useful for p = 1 in these simulations. For p ⩾ 3, the BDF methods are conditionally stable and users have to be careful about the time step size selection.…”

Section: Methodsmentioning

confidence: 99%

Toward a simple and accurate Lagrangian-based error estimator for the BDF algorithms and adaptive time-stepping

Wang,

Luo,

Zhang

et al. 2023

HFF

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Purpose The purpose of this paper is to design a simple and accurate a-posteriori Lagrangian-based error estimator is developed for the class of backward differentiation formula (BDF) algorithms with variable time step size, and the adaptive time-stepping in BDF algorithms is demonstrated for efficient time-dependent simulations in fluid flow and heat transfer. Design/methodology/approach The Lagrange interpolation polynomial is used to predict the time derivative, and then the accurate primary result is obtained by the Gauss integral, which is applied to evaluate the local error. Not only the generalized formula of the proposed error estimator is presented but also the specific expression for the widely applied BDF1/2/3 is illustrated. Two essential executable MATLAB functions to implement the proposed error estimator are appended for practical applications. Then, the adaptive time-stepping is demonstrated based on the newly proposed error estimator for BDF algorithms. Findings The validation tests show that the newly proposed error estimator is accurate such that the effectivity index is always close to unity for both linear and nonlinear problems, and it avoids under/overestimation of the exact local error. The applications for fluid dynamics and coupled fluid flow and heat transfer problems depict the advantage of adaptive time-stepping based on the proposed error estimator for time-dependent simulations. Originality/value In contrast to existing error estimators for BDF algorithms, the present work is more accurate for the local error estimation, and it can be readily extended to practical applications in engineering with a few changes to existing codes, contributing to efficient time-dependent simulations in fluid flow and heat transfer.

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Section: Methodsmentioning

confidence: 99%

Toward a simple and accurate Lagrangian-based error estimator for the BDF algorithms and adaptive time-stepping

Wang,

Luo,

Zhang

et al. 2023

HFF

View full text Add to dashboard Cite

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“…This assumption holds generally true for the simulation of plaque growth, unless the interest is to simulate a complete closure of the artery. To simulate a full closure, a Fully Eulerian formalism [21,27,46] has been used in [27,30], see also [2,13,14] for further works on FSI-contact problems in a Fully Eulerian or Lagrange-Eulerian formalism.…”

Section: Numerical Frameworkmentioning

confidence: 99%

Towards parallel time-stepping for the numerical simulation of atherosclerotic plaque growth

Frei¹,

Heinlein²

2022

Preprint

Self Cite

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The numerical simulation of atherosclerotic plaque growth is computationally prohibitive, since it involves a complex cardiovascular fluid-structure interaction (FSI) problem with a characteristic time scale of milliseconds to seconds, as well as a plaque growth process governed by reaction-diffusion equations, which takes place over several months. In this work we combine a temporal homogenization approach, which separates the problem in computationally expensive FSI problems on a micro scale and a reactiondiffusion problem on the macro scale, with parallel time-stepping algorithms. It has been found in the literature that parallel time-stepping algorithms do not perform well when applied directly to the FSI problem. To circumvent this problem, a parareal algorithm is applied on the macro-scale reaction-diffusion problem instead of the micro-scale FSI problem. We investigate modifications in the coarse propagator of the parareal algorithm, in order to further reduce the number of costly micro problems to be solved. The approaches are tested in detailed numerical investigations based on serial simulations.

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“… 2021 ; Burman et al. 2022 ; Fernández and Gerosa 2021 ). From the point of view of applications, FSI computations have primarily focused on the influence of valve shape and properties in the blood flow dynamics (Marom et al.…”

Section: Introductionmentioning

confidence: 99%

A parametric geometry model of the aortic valve for subject-specific blood flow simulations using a resistive approach

Pase

Brinkhuis²,

Vries³

et al. 2023

Biomech Model Mechanobiol

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Cardiac valves simulation is one of the most complex tasks in cardiovascular modeling. Fluid–structure interaction is not only highly computationally demanding but also requires knowledge of the mechanical properties of the tissue. Therefore, an alternative is to include valves as resistive flow obstacles, prescribing the geometry (and its possible changes) in a simple way, but, at the same time, with a geometry complex enough to reproduce both healthy and pathological configurations. In this work, we present a generalized parametric model of the aortic valve to obtain patient-specific geometries that can be included into blood flow simulations using a resistive immersed implicit surface (RIIS) approach. Numerical tests are presented for geometry generation and flow simulations in aortic stenosis patients whose parameters are extracted from ECG-gated CT images.

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A mechanically consistent model for fluid–structure interactions with contact including seepage

Cited by 15 publications

References 39 publications

Toward a simple and accurate Lagrangian-based error estimator for the BDF algorithms and adaptive time-stepping

Toward a simple and accurate Lagrangian-based error estimator for the BDF algorithms and adaptive time-stepping

Towards parallel time-stepping for the numerical simulation of atherosclerotic plaque growth

A parametric geometry model of the aortic valve for subject-specific blood flow simulations using a resistive approach

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