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Ateshian GA, Shim JJ, Maas SA, et al. Finite Element Framework for Computational Fluid Dynamics in FEBio. J Biomech Eng. 2018;140(2)doi: 10.1115/1.4038716.
Ateshian, G. A., Shim, J. J., Maas, S. A., & Weiss, J. A. (2018). Finite Element Framework for Computational Fluid Dynamics in FEBio. Journal of biomechanical engineering, 140(2), . https://doi.org/10.1115/1.4038716
Ateshian, Gerard A, et al. "Finite Element Framework for Computational Fluid Dynamics in FEBio." Journal of biomechanical engineering vol. 140,2 (2018). doi: https://doi.org/10.1115/1.4038716
Ateshian GA, Shim JJ, Maas SA, Weiss JA. Finite Element Framework for Computational Fluid Dynamics in FEBio. J Biomech Eng. 2018 Feb 01;140(2). doi: 10.1115/1.4038716. PMID: 29238817; PMCID: PMC5816258.
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J Biomech Eng. 2018 Feb 01;140(2). doi: 10.1115/1.4038716.

Finite Element Framework for Computational Fluid Dynamics in FEBio.

Journal of biomechanical engineering

Gerard A Ateshian, Jay J Shim, Steve A Maas, Jeffrey A Weiss

Affiliations

  1. Department of Mechanical Engineering, Columbia University, New York, NY 10027.
  2. Department of Bioengineering, University of Utah, Salt Lake City, UT 84112.

PMID: 29238817 PMCID: PMC5816258 DOI: 10.1115/1.4038716

Abstract

The mechanics of biological fluids is an important topic in biomechanics, often requiring the use of computational tools to analyze problems with realistic geometries and material properties. This study describes the formulation and implementation of a finite element framework for computational fluid dynamics (CFD) in FEBio, a free software designed to meet the computational needs of the biomechanics and biophysics communities. This formulation models nearly incompressible flow with a compressible isothermal formulation that uses a physically realistic value for the fluid bulk modulus. It employs fluid velocity and dilatation as essential variables: The virtual work integral enforces the balance of linear momentum and the kinematic constraint between fluid velocity and dilatation, while fluid density varies with dilatation as prescribed by the axiom of mass balance. Using this approach, equal-order interpolations may be used for both essential variables over each element, contrary to traditional mixed formulations that must explicitly satisfy the inf-sup condition. The formulation accommodates Newtonian and non-Newtonian viscous responses as well as inviscid fluids. The efficiency of numerical solutions is enhanced using Broyden's quasi-Newton method. The results of finite element simulations were verified using well-documented benchmark problems as well as comparisons with other free and commercial codes. These analyses demonstrated that the novel formulation introduced in FEBio could successfully reproduce the results of other codes. The analogy between this CFD formulation and standard finite element formulations for solid mechanics makes it suitable for future extension to fluid-structure interactions (FSIs).

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