Finite Element Framework for Computational Fluid Dynamics in FEBio.

Area of Science:

• Biomechanics
• Computational Fluid Dynamics (CFD)
• Finite Element Analysis (FEA)

Background:

• Analyzing biological fluid mechanics often requires advanced computational tools for complex geometries and material properties.
• Existing methods may have limitations in handling nearly incompressible flows and require specialized element formulations.

Purpose of the Study:

• To formulate and implement a novel finite element framework for CFD within the FEBio software.
• To enable accurate simulation of nearly incompressible fluid flow for biomechanics and biophysics applications.

Main Methods:

• A compressible isothermal formulation was used for nearly incompressible flow, employing fluid velocity and dilatation as primary variables.
• The virtual work integral enforces momentum balance and kinematic constraints, allowing for equal-order interpolations.
• The formulation accommodates Newtonian, non-Newtonian, and inviscid fluid behaviors, enhanced by Broyden's quasi-Newton method for efficiency.

Main Results:

• The FEBio CFD framework successfully reproduced results from benchmark problems and other established codes.
• The novel formulation demonstrated accuracy and efficiency in simulating fluid dynamics.
• The approach simplifies element formulation by avoiding explicit satisfaction of the inf-sup condition.

Conclusions:

• The developed FEBio CFD framework provides a robust and versatile tool for biomechanical fluid dynamics research.
• Its formulation is analogous to solid mechanics FEA, paving the way for future fluid-structure interaction (FSI) studies.
• The software is freely available, supporting the wider biomechanics and biophysics communities.