An adaptive mesh refinement solver for large‐scale simulation of biological flows

Abstract

SUMMARYThe observation that hemodynamic forces play an important role in the pathophysiology of the cardiovascular system has led to the need for characterizing in vivo hemodynamics on a patient-specific basis. However, the introduction of computational hemodynamics in clinical research contexts is bound to the availability of integrated workflows for analyses on large populations. Since such workflows must rely on automated geometry-driven mesh generation methods, the availability of robust solvers featuring adaptive mesh refinement strategies is essential to ensure that the approach can be adopted on a large scale. In this paper, we present an open-source solver for the incompressible Navier-Stokes equations based on the libMesh finite elements library, featuring adaptive mesh refinement and parallelization. The solution scheme is a second-order velocity correction in rotational form. By presenting numerical tests on benchmark cases, we demonstrate that the coupling of this solution strategy with adaptive mesh refinement leads to a solver with good accuracy characteristics despite the relative simplicity of the scheme adopted. The availability of this solver within the Vascular Modeling Toolkit project leads to a widely available, seamless pipeline from images to simulation ready to be applied in clinical research environments.

Quality meshing based on STL triangulations for biomedical simulations

“…As can be seen in Figure 8, the high-quality isotropic volume meshes converge well toward an azimuthal WSS distribution. The WSS for the anisotropic mesh exhibits more numerical noise that is due to the velocity gradient computations involved in (7) that are less accurate for highly anisotropic meshes [41][42][43]. Meanwhile, the mean values (max and min WSS) converge toward the one obtained with the finest isotropic mesh within a smaller computational time (mesh of only 20k).…”

“…We fist compute an isotropic surface mesh with our remeshing algorithm and then produce two different types of volume meshes: (i) isotropic volume meshes of different prescribed mesh sizes, (ii) adapted anisotropic volume meshes and (ii) a boundary layer mesh obtained by extrusion of the surface mesh over a number of layers (five layers in the boundary bl = 1/ √ Re). Adaptive refinement in the boundary with either anisotropic metric fields or boundary layers is indeed attractive [41][42][43] to increase the solution accuracy in the region of interest (at the wall) and this way decrease the load on the solver by reducing the number of finite elements used. With the presented approach of harmonic map, we do have a parametric description of the initial triangulation that enables us to use anisotropic mesh adaptation libraries such as our open-source MadLib library [44].…”

An Adaptive Approach to Solutions of Fredholm Integral Equations of the Second Kind

“…In their paper, the studies on solving integral equations with adaptive FEM in that period are given with [25][26][27][28]. Adaptive FEM are usually used to solve partial differential equations; but in literature these methods are also seen to be used for solving different type of problems in various branches of science such as hydrodynamics [29], optimal design [30], elliptic stochastic equations [31], parabolic problems [32], parabolic systems [33], elliptic problems [34], elliptic partial differential equations [35], elliptic boundary value problems [36,37], electrostatics [38], electromagnetic problems [39], biological flows [40], and Laplace eigenvalue problem [41]. 2 < ⋅ ⋅ ⋅ < = be the node points of a given (finite element) mesh which is accepted as the coarse mesh and denote the list of these node points as follows:…”

Flexible composition and execution of high performance, high fidelity multiscale biomedical simulations

“…We have constructed a distributed multiscale model in which we combine the open source HemeLB lattice-Boltzmann application for blood flow modelling in 3D [38,39] with the open source one-dimensional Python Navier-Stokes (pyNS) blood flow solver [40]. HemeLB is optimized for sparse geometries such as vascular networks, and has been shown to scale linearly up to at least 32,768 cores [41].…”