3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the Finite Element Method. In this paper, we describe the use of our recently rewritten mesh processing software, GAMer 2, to bridge the gap between poorly conditioned meshes generated from segmented micrographs and boundary marked tetrahedral meshes which are compatible with simulation. We demonstrate the application of a workflow using GAMer 2 to a series of electron micrographs of neuronal dendrite morphology explored at three different length scales and show that the resulting meshes are suitable for finite element simulations. This work is an important step towards making physical simulations of biological processes in realistic geometries routine. Innovations in algorithms to reconstruct and simulate cellular length scale phenomena based on emerging structural data will enable realistic physical models and advance discovery at the interface of geometry and cellular processes. We posit that a new frontier at the intersection of computational technologies and single cell biology is now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies available upon reques

Geometry Modeling for Unstructured Mesh Adaptation

The quantification and control of discretization error is critical to obtaining reliable simulation results. Adaptive mesh techniques have the potential to automate discretization error control, but have made limited impact on production analysis workflow. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic mesh adaptation mechanics. However, the poor integration of initial mesh generation and adaptive mesh mechanics to typical sources of geometry has hindered adoption of adaptive mesh techniques, where these geometries are often created in Mechanical Computer- Aided Design (MCAD) systems. The difficulty of this coupling is compounded by two factors: the inherent complexity of the model (e.g., large range of scales, bodies in proximity, details not required for analysis) and unintended geometry construction artifacts (e.g., translation, uneven parameterization, degeneracy, self-intersection, sliver faces, gaps, large tolerances be- tween topological elements, local high curvature to enforce continuity). Manual preparation of geometry is commonly employed to enable fixed-grid and adaptive-grid workflows by reducing the severity and negative impacts of these construction artifacts, but manual process interaction inhibits workflow automation. Techniques to permit the use of complex geometry models and reduce the impact of geometry construction artifacts on unstructured grid workflows are models from the AIAA Sonic Boom and High Lift Prediction are shown to demonstrate the utility of the current approach

Generation of curved high-order meshes with optimal quality and geometric accuracy

We present a novel methodology to generate curved high-order meshes featuring optimal mesh quality and geometric accuracy. The proposed technique combines a distortion measure and a geometric L2-disparity measure into a single objective function. While the element distortion term takes into account the mesh quality, the L2-disparity term takes into account the geometric error introduced by the mesh approximation to the target geometry. The proposed technique has several advantages. First, we are not restricted to interpolative meshes and therefore, the resulting mesh approximates the target domain in a non-interpolative way, further increasing the geometric accuracy. Second, we are able to generate a series of meshes that converge to the actual geometry with expected rate while obtaining high-quality elements. Third, we show that the proposed technique is robust enough to handle real-case geometries that contain gaps between adjacent entities.Peer ReviewedPostprint (published version

Finite Element Flow Simulations of the EUROLIFT DLR-F11 High Lift Configuration

This paper presents flow simulation results of the EUROLIFT DLR-F11 multi-element wing configuration, obtained with a highly scalable finite element solver, PHASTA. This work was accomplished as a part of the 2nd high lift prediction workshop. In-house meshes were constructed with increasing mesh density for analysis. A solution adaptive approach was used as an alternative and its effectiveness was studied by comparing its results with the ones obtained with other meshes. Comparisons between the numerical solution obtained with unsteady RANS turbulence model and available experimental results are provided for verification and discussion. Based on the observations, future direction for adaptive research and simulations with higher fidelity turbulence models is outlined.Comment: 52nd Aerospace Sciences Meetin

Free and smooth boundaries in 2-D finite-difference schemes for transient elastic waves

A method is proposed for accurately describing arbitrary-shaped free boundaries in single-grid finite-difference schemes for elastodynamics, in a time-domain velocity-stress framework. The basic idea is as follows: fictitious values of the solution are built in vacuum, and injected into the numerical integration scheme near boundaries. The most original feature of this method is the way in which these fictitious values are calculated. They are based on boundary conditions and compatibility conditions satisfied by the successive spatial derivatives of the solution, up to a given order that depends on the spatial accuracy of the integration scheme adopted. Since the work is mostly done during the preprocessing step, the extra computational cost is negligible. Stress-free conditions can be designed at any arbitrary order without any numerical instability, as numerically checked. Using 10 grid nodes per minimal S-wavelength with a propagation distance of 50 wavelengths yields highly accurate results. With 5 grid nodes per minimal S-wavelength, the solution is less accurate but still acceptable. A subcell resolution of the boundary inside the Cartesian meshing is obtained, and the spurious diffractions induced by staircase descriptions of boundaries are avoided. Contrary to what occurs with the vacuum method, the quality of the numerical solution obtained with this method is almost independent of the angle between the free boundary and the Cartesian meshing.Comment: accepted and to be published in Geophys. J. In