Validation of an Open Source Framework for the Simulation of Blood Flow in Rigid and Deformable Vessels

Abstract

SUMMARYWe discuss in this paper the validation of an open source framework for the solution of problems arising in hemodynamics. The proposed framework is assessed through experimental data for fluid flow in an idealized medical device with rigid boundaries and a numerical benchmark for flow in compliant vessels. The core of the framework is an open source parallel finite element library that features several algorithms to solve both fluid and fluid-structure interaction problems. The numerical results for the flow in the idealized medical device (consisting of a conical convergent, a narrow throat, and a sudden expansion) are in good quantitative agreement with the measured axial components of the velocity and pressures for three different flow rates corresponding to laminar, transitional, and turbulent regimes. We emphasize the crucial role played by the accuracy in performing numerical integration, mesh, and time step to match the measurements. The numerical fluid-structure interaction benchmark deals with the propagation of a pressure wave in a fluid-filled elastic tube. The computed pressure wave speed and frequency of oscillations, and the axial velocity of the fluid on the tube axis are close to the values predicted by the analytical solution associated with the benchmark. A detailed account of the methods used for both benchmarks is provided.

Deconvolution‐based nonlinear filtering for incompressible flows at moderately large Reynolds numbers

“…except in the convergent where the simulated pressure difference overestimates almost all the measurements. The reason for this overestimation is explained in [16]. Figure 2 shows that even mesh 1200k has a sufficient level of refinement to obtain numerical results in excellent agreement with the measurements in terms of average quantities, despite its h avg being roughly 20 times larger than the Kolmogorov length scale at Re t D 3500 (Tables I and II).…”

“…All the computational results presented in this article have been performed with LifeV [15], an open-source library of algorithms and data structures for the numerical solution of partial differential equations with high-performance computing techniques. In [16], we validated one Navier-Stoker solver implemented in LifeV with DNS up to Reynolds number 3500 and showed that a properly refined mesh is able to capture accurately the average flow features observed in the experiments. The LES technique used in this article makes the simulation of higher Reynolds numbers computationally affordable without sacrificing accuracy.…”

“….2ı 2 a.u/r s u I/n D 0 on @ N .t 0 ; T /; (16) while no initial condition is required for u, because there is no time derivative in Equations (13) and (14). The impact of non-Dirichlet boundary conditions has not been investigated thoroughly in literature.…”

About the numerical robustness of biomedical benchmark cases: Interlaboratory FDA's idealized medical device

“…With the exception of the lattice Boltzmann method [10], which had difficulties to estimate meaningful velocity profiles in this complex test case and exhibited a large dependency on the lattices orientation, all other works reported flow averages in good agreement with the experimental quantitative data. DNS simulations performed on the open platform LifeV in [9] yielded surprisingly good results with coarse grids. However, for some transitional Reynolds number values, results were unstable and reported to depend on the numerical scheme and on the size of the computational domain.…”

The FDA nozzle benchmark: “In theory there is no difference between theory and practice, but in practice there is”

“…Interestingly, none of the CFD benchmark participants obtained results in agreement with the in vitro measurements for Reynolds numer (Re) 3500, although good agreement and excellent CFD results have been reported by multiple authors retrospectively. [12][13][14][15] The FDA nozzle benchmark model remains highly relevant for biomedical problems and our aim was to further validate the open-source CFD solver Oasis 16 that we have extensively used to study turbulent-like cardiovascular flows. [17][18][19][20][21][22][23] We focus on the flow at Re = 3500, which is in the particularly challenging transitional flow regime, for which the in vitro experiments displayed the least variability.…”