Fully Automated Surface Mesh Adaptation in Strand Grid Framework

SummaryAn enhanced goal‐oriented mesh adaptation method is presented based on aerodynamic functional total derivatives with respect to mesh nodes in a Reynolds‐Averaged Navier‐Stokes (RANS) finite‐volume mono‐block and non‐matching multi‐block‐structured grid framework. This method falls under the category of methods involving the adjoint vector of the function of interest. The contribution of a Spalart–Allmaras turbulence model is taken into account through its linearization. Meshes are adapted accordingly to the proposed indicator. Applications to 2D RANS flow about a RAE2822 airfoil in transonic, and detached subsonic conditions are presented for the drag coefficient estimation. The asset of the proposed method is patent. The obtained 2D anisotropic mono‐block mesh well captures flow features as well as global aerodynamic functionals. Interestingly, the constraints imposed by structured grids may be relaxed by the use of non‐matching multi‐block approach that limits the outward propagation of local mesh refinement through all of the computational domain. The proposed method also leads to accurate results for these multi‐block meshes but at a fraction of the cost. Finally, the method is also successfully applied to a more complex geometry, namely, a mono‐block mesh in a 3D RANS transonic flow about an M6 wing. Copyright © 2016 John Wiley & Sons, Ltd.

In the adaptive mesh generation, the space mesh should be adequate to the surface mesh. When the analytical surface representation is not known, additional surface information may be extracted from triangular surface meshes. We describe a new surface reconstruction method which uses approximate Hessian of a piecewise linear function representing the discrete surface. Efficiency of the proposed method is illustrated with two CFD applications.

Thanks to advances in medical imaging technologies and numerical methods, patient-specific modelling is more and more used to improve diagnosis and to estimate the outcome of surgical interventions. It requires the extraction of the domain of interest from the medical scans of the patient, as well as the discretisation of this geometry. However, extracting smooth multi-material meshes that conform to the tissue boundaries described in the segmented image is still an active field of research. We propose to solve this issue by combining an implicit surface reconstruction method with a multi-region mesh extraction scheme. The surface reconstruction algorithm is based on multi-level partition of unity implicit surfaces, which we extended to the multi-material case. The mesh generation algorithm consists in a novel multi-domain version of the marching tetrahedra. It generates multi-region meshes as a set of triangular surface patches consistently joining each other at material junctions. This paper presents this original meshing strategy, starting from boundary points extraction from the segmented data to heterogeneous implicit surface definition, multi-region surface triangulation and mesh adaptation. Results indicate that the proposed approach produces smooth and high-quality triangular meshes with a reasonable geometric accuracy. Hence, the proposed method is well suited for subsequent volume mesh generation and finite element simulations.

This paper presents a novel statistical methodology for exerting control over adaptive surface meshes. The work builds on a recently reported adaptive mesh which uses split and merge operations to control the distribution of planar or quadric surface patches. Hitherto, we have used the target variance of the patch fit residuals as a control criterion. The novelty of the work reported in this paper is to focus on the variance-bias tradeoff that exists between the size of the fitted patches and their associated parameter variances. In particular, we provide an analysis which shows that there is an optimal patch area which minimises the variance in the fitted patch parameters. This area offers the best compromise between the noise-variance, which decreases with increasing area, and the model-bias, which increases in a polynomial manner with area. The computed optimal areas of the local surface patches are used to exert control over the facets of the adaptive mesh. We use a series of split and merge operations to distribute the faces of the mesh so that each resembles as closely as possible its optimal area. In this way the mesh automatically selects its own model-order by adjusting the number of control-points or nodes. We provide experiments on both real and synthetic data. This experimentation demonstrates that our mesh is capable of efficiently representing high curvature surface detail.KeywordsNoise VarianceAdaptive MeshSurface PatchPatch AreaBias TermThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The cutting operation of 3D surface meshes plays an important role in surgery simulators. One of the important requirements for surgical simulators is the visual reality. We propose a new strategy for cutting on surface meshes: refinement and separate strategy consisting of the refinement followed by the separation of the refined mesh element.The proposed strategy gives the faithful representation of interaction paths of a surgical tool

Adaptive stochastic morphology simulation and mesh generation of high-quality 3D particulate composite microstructures with complex surface texture

We present a particle-based approach for generating adaptive triangular surface and tetrahedral volume meshes from computer-aided design models. Input shapes are treated as a collection of smooth, parametric surface patches that can meet non-smoothly on boundaries. Our approach uses a hierarchical sampling scheme that places particles on features in order of increasing dimensionality. These particles reach a good distribution by minimizing an energy computed in 3D world space, with movements occurring in the parametric space of each surface patch. Rather than using a pre-computed measure of feature size, our system automatically adapts to both curvature as well as a notion of topological separation. It also enforces a measure of smoothness on these constraints to construct a sizing field that acts as a proxy to piecewise-smooth feature size. We evaluate our technique with comparisons against other popular triangular meshing techniques for this domain.

A difficulty of voxel-based sculpturing and modeling is the limitation of the design space by the fixed boundaries of the voxel volume.We present the concept of an infinite voxelized virtual modeling space. A finite shape located in the virtual modeling space is embedded in a voxel window which is enlarged if required by the spatial development of the shape. In order to cope with highly resolved or large shapes, the voxel windows are stored in a virtual voxel memory which implements a paging mechanism to secondary memory. Visualization is performed by meshes obtained by the marching cubes algorithm. Because highly resolved or large shapes may cause a considerable number of triangles, an adaptive meshing approach based on a filtered hierarchy of voxel volumes is presented. The surface mesh is represented in a surface octree which allows for fast rendering by e.g. the Performer library.

Advancing our understanding of spinal biomechanics through Finite Element Analysis (FEA) is essential for clinical decision-making and biomechanical research. Traditional FEA workflows are hindered by manual segmentation and meshing, introducing inconsistencies, user variability, and lengthy processing times. This study presents a streamlined, patient-specific modeling methodology for the lumbar spine that fundamentally transforms the FEA preprocessing pipeline. By integrating deep learning-based segmentation with advanced computational tools such as the GIBBON library and FEBio, our approach minimizes manual intervention, accelerates model preparation, and enhances both accuracy and reproducibility. The proposed workflow enables precise extraction and meshing of key anatomical structures including cortical and cancellous bone, intervertebral discs, ligaments, and cartilage directly from clinical CT imaging data. Robust segmentation techniques ensure accurate identification and separation of these components, which are subsequently converted into high-resolution surface and volumetric meshes. To optimize model fidelity and computational efficiency, the pipeline incorporates geometric smoothing and adaptive mesh decimation. Ligament attachment is addressed through an innovative coordinate-based framework that leverages anatomical landmarks for automated placement and orientation, overcoming a major challenge in FEA preprocessing. The results demonstrate that the resulting subject-specific models reproduce physiological biomechanics with high fidelity. Range of Motion and stress distribution outcomes closely match experimental data and established numerical models, confirming the pipeline’s accuracy. Importantly, preparation time is reduced from days to just hours, delivering an efficient, reproducible workflow. By unifying segmentation, meshing, and ligament modeling in a single efficient framework, this study establishes a scalable platform for rapid, reliable, and anatomically accurate FEA of the lumbar spine, with significant implications for clinical diagnostics and preoperative planning.

Exploiting high-resolution measurements from Laser induced Detection and Ranging (LiDAR) for floodplain modeling is a current challenge for research in hydrodynamics. This challenge aims to improve efficiency in finite element mesh generation and consistency of simulations results. This concept reduces huge LiDAR data sets based on slope classification, routinely deriving case specific, adaptive surface meshes for hydrodynamic simulations and provides a mean for fast data exploitation. Applications of computational fluid dynamics commonly recognize, that mesh resolution is the only unbounded parameter value where specific boundaries and error bands have not yet been considered up to now [8]. Providing this model concept seeks stimulation for further efforts in that particular field of hydrodynamic mesh generation.

A new, three-dimensional boundary integral method is used to study the evolution of an isolated precipitate growing by diffusion in an infinite, elastic matrix. An adaptive surface mesh[23] is used to accurately and efficiently discretize the precipitate boundaries in three dimensions. The model accounts for diffusion, surface energy, interface kinetics and elastic energy, which are coupled through a modified Gibbs-Thomson boundary condition at the precipitate-matrix interface. The precipitate and matrix phases are taken to have different elastic-stiffness tensors, and there is a mismatch strain between the phases. Both isotropic and anisotropic elasticity are investigated. In this article, the coarsening and growth of a single precipitate are simulated under various conditions. For isotropic elasticity, coarsened shapes are found to be consistent with the equilibrium-shape analysis of Johnson and Cahn.[29] Growth shapes are found to become rapidly nonlinear and to develop regions of high curvature. In elastically anisotropic systems, coarsened shapes are found to be consistent with the equilibrium-shape calculations of Mueller and Gross.[7,8] Simulations of coarsening in which the cubic axes of the precipitate are different from those of the matrix suggest that there may be more than one local minima in the energy, so that the observed shapes depend on the growth path. Finally, non-convex precipitate morphologies are seen for the growth of soft Ni3Al precipitates in a Ni matrix, consistent with experimental observations. In the case of a hard Ni3Si precipitate grown under the same conditions, we find self-similar growth of a convex shape.

We present a topographic simulation platform that simultaneously considers 3D surface movement, neutral and ion transport, and surface reactions in plasma high-aspect-ratio (HAR) oxide etching. The hash map data structure is considered for an effective 3D level-set algorithm with parallelized computations to calculate surface moving speed. Neutral and ion transport within nanoscale semiconductor geometry is parallelized with a graphics processing unit (GPU) so that the speedup ratio, as compared to a single central processing unit (CPU), is approximately 200. The surface reaction based on a two-layer model was incorporated into a 3D feature profile simulation platform with CPU parallelization. Finally, our simulation platform demonstrates that adaptive surface meshing can drastically decrease the computational load with a parallelized numerical platform.

How to improve strength-to-weight ratio of printed models is an important topic in 3D printing. We in this paper propose a novel structure modeling method based on the implicit function technique and the finite element method (FEM). Our method first obtains a set of sampled points in a given surface mesh model by using a probability-based strategy, and generates an adaptive tetrahedral mesh from the points. FEM is then used to analyze the stress of the tetrahedral mesh and a stress map of the input model is created. The method finally builds a result model composed of a shell and an interior single-gyroid lattice. The lattice is defined by a piecewise 3D implicit function, and has several special structural properties just like the structure of the light but strong butterfly wing. The lattice together with the shell forms a natural 3D structure for 3D printing. Local thickness of lattice rods in the structure adaptively changes with stress distribution for withstanding external loads. Experimental results show that our method can deal with various surface mesh models in rapid way, and the resulted models for 3D printing have high strength-to-weight ratios.

High Reynolds number helical vortex system possesses a dominant characteristic of helicopter rotor flow field, whose spatiotemporal evolution is one of the most important factors affecting the aerodynamic performance. In such a type of flow field, vortex interaction due to flow unsteadiness and non-linearity possesses the most common characteristic, whose complexity and tightly coupling property make it very hard to understand its physical behaviors. Also, the multi-scale characteristic of the helical vortex evolution poses a severe challenge to the computational fluid dynamics community. In this paper, a hybrid numerical method, blending 5th order weighted essentially non-oscillatory and 6th order cenitral schemes, implemented in a finite volume overset grid framework based on adaptive mesh refinement technique, are adopted to capture the evolution of vortical structure in a high resolution manner. The highly-resolved flow field of Caradonna-Tung rotor with two blades in hover, with a tip Mach number of 0.439 and a tip Reynolds number of 1.92×106, is obtained using delayed detached eddy simulation method. The averaged pressure coefficient distributions at 50%R, 68%R, 80%R, and 96%R stations show good agreement with experiment data, and the vortex trajectories during the stable stage, as well as the instantaneous turbulent kinetic energy distribution in the wake region, and also validate the computed result. In order to reveal the underlying physical mechanism of the helical vortex structure evolution, proper orthogonal decomposition analysis and Lagrangian coherent structures are adopted as a post processing procedure, which brings more details about the unsteady vortex system. The evolution characteristics of the vortex system are revealed as follows. 1) Trailing edge vortex sheet rolling-up and interaction with tip vortex strongly affect vortical stability and downstream nonlinear vortex-vortex behaviors. 2) The vortical system exhibits the spatiotemporal stability at an age less than 720°, and the vorticity decays with age and trajectories by power law, the distribution of circumferential velocity and the evolution of vortex core radius agree well with theoretical models. 3) Results of proper orthogonal decomposition analysis show that the mode of free stream and point vortex combination plays critical roles in the state transition of flow field. 4) Lagrangian coherent structure further gives the evolution process of helical vortex, and reveals the flow characteristics of vortex pairing and co-rotating, showing the effect of trailing edge vortex roll up phenomenon in the vortical system evolution.

While recent advances in Gaussian Splatting have enabled fast reconstruction of high-quality 3D scenes from images, extracting accurate surface meshes remains a challenge. Current approaches extract the surface through costly post-processing steps, resulting in the loss of fine geometric details or requiring significant time and leading to very dense meshes with millions of vertices. More fundamentally, the a posteriori conversion from a volumetric to a surface representation limits the ability of the final mesh to preserve all geometric structures captured during training. We present MILo, a novel Gaussian Splatting framework that bridges the gap between volumetric and surface representations by differentiably extracting a mesh from the 3D Gaussians. We design a fully differentiable procedure that constructs the mesh—including both vertex locations and connectivity—at every iteration directly from the parameters of the Gaussians, which are the only quantities optimized during training. Our method introduces three key technical contributions: (1) a bidirectional consistency framework ensuring both representations—Gaussians and the extracted mesh—capture the same underlying geometry during training; (2) an adaptive mesh extraction process performed at each training iteration, which uses Gaussians as differentiable pivots for Delaunay triangulation; (3) a novel method for computing signed distance values from the 3D Gaussians that enables precise surface extraction while avoiding geometric erosion. Our approach can reconstruct complete scenes, including backgrounds, with state-of-the-art quality while requiring an order of magnitude fewer mesh vertices than previous methods. Due to their light weight and empty interior, our meshes are well suited for downstream applications such as physics simulations and animation. The code for our approach and an online gallery are available at https://anttwo.github.io/milo/.