[Paper Review] High order finite element simulations for fluid dynamics validated by experimental data from the fda benchmark nozzle model

Vincent Chabannes, Christophe Prud'Homme+2 more|arXiv (Cornell University)|Jan 9, 2017

Cardiovascular Function and Risk Factors3 citations

TL;DR

This paper presents high-order finite element simulations of blood flow in the FDA benchmark nozzle using the open-source Feel++ FEM library, validating results against experimental data across laminar, transitional, and turbulent regimes (Re = 500, 2000, 3500). The study demonstrates excellent agreement with experimental data for axial velocity and pressure difference, with validation metrics $E_z$ and $E_Q$ showing high accuracy and robustness, especially with high-order geometry and velocity-pressure discretization.

ABSTRACT

The objective of the present work is to construct a sound mathematical, numerical and computational framework relevant to blood flow simulations and to assess it through a careful validation against experimental data. We perform simulations of a benchmark proposed by the FDA for fluid flow in an idealized medical device, under different flow regimes. The results are evaluated using metrics proposed in the literature and the findings are in very good agreement with the validation experiment.

Motivation & Objective

• To establish a reliable, reproducible, and high-fidelity mathematical and computational framework for patient-specific blood flow simulations.
• To validate a high-order finite element method (FEM) solver in the open-source Feel++ library against experimental data from the FDA's benchmark nozzle model.
• To assess the impact of mesh refinement, polynomial order (P2, P3), and geometry approximation (G1, G2) on simulation accuracy in complex flow regimes.
• To evaluate key validation metrics $E_z$ and $E_Q$ across different Reynolds numbers to quantify agreement with experimental data.
• To contribute to improving the reliability and reproducibility of CFD in medical device development.

Proposed method

• Solving the incompressible unsteady Navier-Stokes equations in conservative form using a stabilized Galerkin finite element method.
• Employing the generalized Taylor-Hood finite element pair $P_{N+1}P_NG_{k_{\text{geo}}}$ for velocity, pressure, and geometry approximation.
• Using the open-source Feel++ library with PETSc-based preconditioning (e.g., PCD) and domain decomposition for efficient parallel solution.
• Generating structured, anisotropic tetrahedral meshes with Gmsh, refined in critical regions such as the throat and wall boundaries.
• Applying initial condition $\mathbf{u} = \mathbf{0}$, Poiseuille inlet profile on $\Gamma_{\text{inlet}}$, no-slip on $\Gamma_{\text{wall}}$, and free outflow on $\Gamma_{\text{outlet}}$.
• Implementing time discretization with $\Delta t = 10^{-3}$ s for Re = 500 and $\Delta t = 10^{-4}$ s for Re = 2000 and 3500 to resolve transient behavior.

Experimental results

Research questions

• RQ1 How accurately can high-order finite element methods reproduce experimental velocity and pressure profiles in the FDA nozzle benchmark?
• RQ2 What is the impact of mesh refinement and polynomial order (P2, P3) on the convergence and accuracy of the simulation metrics $E_z$ and $E_Q$?
• RQ3 How does high-order geometry approximation (G1 vs G2) affect the agreement with experimental data, especially in transitional and turbulent regimes?
• RQ4 Why does the numerical jet breakdown location in Re = 2000 simulations occur further downstream than in experiments?
• RQ5 Can the open-source Feel++ FEM framework achieve robust, accurate, and reproducible results comparable to experimental benchmarks in hemodynamic simulations?

Key findings

• For Re = 500, the normalized axial velocity and pressure difference show excellent agreement with experimental data across all mesh refinements and polynomial orders.
• The validation metric $E_z$ remains consistently low (< 0.05) across all simulations, indicating strong agreement between computed and experimental axial velocities.
• The mass conservation error $E_Q$ is below 2% for all but the coarsest mesh (M0), where it reaches ~10% in two locations, indicating sensitivity to mesh resolution.
• The $P_2P_1G_2$ approximation achieves $E_Q < 2\%$ on the coarsest mesh, while $P_3P_2G_1$ does not improve accuracy on M0, suggesting geometry approximation is more critical than velocity order in coarse grids.
• The numerical jet breakdown point in Re = 2000 simulations is located further downstream than in experiments, possibly due to numerical integration accuracy or boundary condition tuning.
• The study confirms that high-order FEM with proper meshing and geometry approximation enables highly accurate and reproducible CFD simulations in complex hemodynamic flows.