Tetrahedral Volume Mesh Research Articles

A workflow for building surface-based reservoir models using NURBS curves, coons patches, unstructured tetrahedral meshes and open-source libraries

Surface-based models have been built to represent complex reservoir geometries. This paper presents a workflow for building surface-based reservoir models using NURBS curves, Coons patches and unstructured tetrahedral volume meshes. Surfaces are created as Coons patches based on NURBS curves. The surface mesh of the entire model is hybrid consisting of quadrilaterals and triangles. Geological regions are represented as volumes bounded by surfaces. Unstructured tetrahedral meshes are built to adapt to the bounding surfaces. Well configurations of location and geometry are particularly flexible, facilitated by mesh adaptation. All libraries for curve, surface and mesh generation are open-source. They are free-of-charge for non-commercial uses. The workflow provides a flexible alternative to commercial software packages for building surface-based models and unstructured meshes. The workflow is validated by simulating two-phase immiscible displacement and comparing to the analytical solution.

Aerodynamics and Flight Dynamics Simulation of Basic Finner Supersonic Flight in Aeroballistic Experiment

This paper presents some results of aerodynamics and flight dynamics modeling of Basic Finner supersonic flight in an aeroballistic experiment [1]. Three dimensional surface based on the experiment description was formed. Unstructured tetrahedral volume mesh is formed after it. Aerodynamics computations were done by software package for CFD numerical computation of free form high-speed vehicle ug3D developed in the Institute for Problems in Mechanics. Obtained from CFD calculations aerodynamic coefficients became initial data for unguided Basic Finner flight dynamics calculations. Flight dynamics computations were done by developed solver MODIN for typical high speed vehicles flight dynamics calculations [2]. Six degrees of freedom motion without considering Earth rotation and form are adopted. Results of experimental and obtained numerical aerodynamic coefficients and flight parameters data comparison are also presented.

Efficient and robust strain limiting and treatment of simultaneous collisions with semidefinite programming

We present an efficient and robust method which performs well for both strain limiting and treatment of simultaneous collisions. Our method formulates strain constraints and collision constraints as a serial of linear matrix inequalities (LMIs) and linear polynomial inequalities (LPIs), and solves an optimization problem with standard convex semidefinite programming solvers. When performing strain limiting, our method acts on strain tensors to constrain the singular values of the deformation gradient matrix in a specified interval. Our method can be applied to both triangular surface meshes and tetrahedral volume meshes. Compared with prior strain limiting methods, our method converges much faster and guarantees triangle flipping does not occur when applied to a triangular mesh. When performing treatment of simultaneous collisions, our method eliminates all detected collisions during each iteration, leading to higher efficiency and faster convergence than prior collision treatment methods.

Mooney-Rivlin biomechanical modeling of lung with Inhomogeneous material.

In this study, the Mooney-Rivlin material with hyperelastic strain energy was proposed for biomechanical modeling of the lung. We modeled the lung as an inhomogeneous Mooney-Rivlin material with uncoupled deviatoric and volumetric behavior. The proposed method was evaluated on the lungs of eight lung cancer patients. For each patient, the lung was segmented from the 4D-CT images and tetrahedral volume mesh of the lung in phase 50% was created by using the adaptive mesh generation toolkit. The demons deformable registration algorithm was used to extract the displacement vector fields (DVFs). The Jacobian of the deformation gradient was calculated from DVFs, and the lung strain energy function was optimized to improve the tumor center of mass (TCM) motion simulation accuracy between respiratory phase 50% and 0%. The average TCM motion simulation error for the proposed strategy is 1.95 mm for eight patients. We observed 13% improvement in the TCM position prediction compared with the homogeneous Mooney-Rivlin modeling.

TU‐F‐CAMPUS‐J‐02: Mooney‐Rivlin Biomechanical Modeling of Lung with Inhomogeneous Material Property

Purpose:The Mooney‐Rivlin material with hyperelastic strain energy has been proposed for realistic biomechanical modeling of lung. In this study, the lung is modeled as an inhomogeneous Mooney‐Rivlin material with the incompressibility factors being optimized to improve the tumor center of mass (TCM) motion simulation accuracy during respiration.Method:ITK‐SNAP was used to segment lungs of eight lung cancer patients from the 4D‐CT images and tetrahedral volume meshes of the lungs in phase 50% were created by using adaptive mesh generation toolkit. The interphase deformation vector fields (DVFs) are calculated by demons deformable registration algorithm and the barycentric coordinate system of tetrahedral elements is obtained from the resulted DVFs. Mooney‐Rivlin hyperelastic material is used to model the lung volume. Each element is considered unique where the incompressibility factor (k‐factor) for each element is assumed to be proportional to the magnitude of normalized DVF. The incompressibility factor for each element was optimized by minimizing the tumor center of mass motion simulation error.Results:If lung is considered as a homogenous material in Mooney‐Rivlin modeling, the average TCM motion simulation error is 2.26 mm. By considering inhomogeneous properties of lung in the proposed strategy, the average TCM motion simulation error is reduced to 2.04 mm.Conclusions:We proposed a method for assigning the inhomogeneous biomechanical material in the Mooney‐Rivlin model of lung based on the lung regional deformation vector fields. Inhomogeneous material property of lung improves the simulation accuracy.

Biomechanical modeling constrained surface-based image registration for prostate MR guided TRUS biopsy.

Adding magnetic resonance (MR)-derived information to standard transrectal ultrasound (TRUS) images for guiding prostate biopsy is of substantial clinical interest. A tumor visible on MR images can be projected on ultrasound (US) by using MR-US registration. A common approach is to use surface-based registration. The authors hypothesize that biomechanical modeling will better control deformation inside the prostate than a regular nonrigid surface-based registration method. The authors developed a novel method by extending a nonrigid surface-based registration algorithm with biomechanical finite element (FE) modeling to better predict internal deformations of the prostate. Data were collected from ten patients and the MR and TRUS images were rigidly registered to anatomically align prostate orientations. The prostate was manually segmented in both images and corresponding surface meshes were generated. Next, a tetrahedral volume mesh was generated from the MR image. Prostate deformations due to the TRUS probe were simulated using the surface displacements as the boundary condition. A three-dimensional thin-plate spline deformation field was calculated by registering the mesh vertices. The target registration errors (TREs) of 35 reference landmarks determined by surface and volume mesh registrations were compared. The median TRE of a surface-based registration with biomechanical regularization was 2.76 (0.81-7.96) mm. This was significantly different than the median TRE of 3.47 (1.05-7.80) mm for regular surface-based registration without biomechanical regularization. Biomechanical FE modeling has the potential to improve the accuracy of multimodal prostate registration when comparing it to a regular nonrigid surface-based registration algorithm and can help to improve the effectiveness of MR guided TRUS biopsy procedures.

Simulation analysis of airflow alteration in the trachea following the vascular ring surgery based on CT images using the computational fluid dynamics method

This study presents a computational fluid dynamics (CFD) model to simulate the three-dimensional airflow in the trachea before and after the vascular ring surgery (VRS). The simulation was based on CT-scan images of the patients with the vascular ring diseases. The surface geometry of the tracheal airway was reconstructed using triangular mesh by the Amira software package. The unstructured tetrahedral volume meshes were generated by the ANSYS ICEM CFD software package. The airflow in the tracheal airway was solved by the ESI CFD-ACE+ software package. Numerical simulation shows that the pressure drops across the tracheal stenosis before and after the surgery were 0.1789 and 0.0967 Pa, respectively, with the inspiratory inlet velocity 0.1 m/s. Meanwhile, the improvement percentage by the surgery was 45.95%. In the expiratory phase, by contrast, the improvement percentage was 40.65%. When the inspiratory velocity reached 1 m/s, the pressure drop became 4.988~Pa and the improvement percentage was 43.32%. Simulation results further show that after treatment the pressure drop in the tracheal airway was significantly decreased, especially for low inspiratory and expiratory velocities. The CFD method can be applied to quantify the airway pressure alteration and to evaluate the treatment outcome of the vascular ring surgery under different respiratory velocities.

Tetrahedral mesh generation based on space indicator functions

SUMMARYAn algorithm for the generation of tetrahedral volume meshes is developed for highly irregular objects specified by volumetric representations such as domain indicator functions and tomography data. It is based on red–green refinement of an initial mesh derived from a body‐centered cubic lattice. A quantitative comparison of alternative types of initial meshes is presented. The minimum set of best‐quality green refinement schemes is identified. Boundary conformity is established by deforming or splitting surface‐crossing elements. Numerical derivatives of input data are strictly avoided. Furthermore, the algorithm features surface‐adaptive mesh density based on local surface roughness, which is an integral property of finite surface portions. Examples of applications are presented for computer tomography of porous media. Copyright © 2012 John Wiley & Sons, Ltd.

Particle systems for adaptive, isotropic meshing of CAD models

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.

CubeCover– Parameterization of 3D Volumes

AbstractDespite the success of quad‐based 2D surface parameterization methods, effective parameterization algorithms for 3D volumes with cubes, i.e. hexahedral elements, are still missing. CubeCover is a first approach for generating a hexahedral tessellation of a given volume with boundary aligned cubes which are guided by a frame field.The input of CubeCover is a tetrahedral volume mesh. First, a frame field is designed with manual input from the designer. It guides the interior and boundary layout of the parameterization. Then, the parameterization and the hexahedral mesh are computed so as to align with the given frame field. CubeCover has similarities to the QuadCover algorithm and extends it from 2D surfaces to 3D volumes. The paper also provides theoretical results for 3D hexahedral parameterizations and analyses topological properties of the appropriate function space.

力覚提示を伴う高品質な穿刺シミュレーションのためのマルチレート・オンラインリメッシュ法

Recently, there are growing needs for fast and accurate needle insertion simulations with realistic sensations. However, it takes large computation time to realize such simulations. Our goal is to construct a needle insertion training system for trainee doctors to practice the needle insertion operations. In this paper, we propose a multi-rate online remesh method to achieve a real time and accurate needle insertion simulation. In this approach, tetrahedral volume mesh that located near the needle is rapidly subdivided by binary bisection algorithm. And then, accurate friction force of the needle is calculated from relative velocities between the needle and nodes of subdivided small tetrahedra.

3D numerical simulation of flow and conjugate heat transfer through a pore scale model of high porosity open cell metal foam

A 3D numerical simulation methodology for the flow and heat transfer at the pore scale level of high porosity open cell metal foam is presented. The pore scale topology is directly represented with a 3D numerical model of the geometry, which is discretised using a tetrahedral volume mesh for both its void and solid phases. The conjugate flow and temperature fields are obtained by solution of the Navier–Stokes and energy equations for two different foam pore densities under various flow and temperature conditions. Model validation is performed against macroscopic parameters such as pressure drop and heat transfer coefficient; the results are found in reasonable agreement with the experimental measurements.

Interactive Point-Based Rendering of Higher-Order Tetrahedral Data

Computational simulations frequently generate solutions defined over very large tetrahedral volume meshes containing many millions of elements. Furthermore, such solutions may often be expressed using non-linear basis functions. Certain solution techniques, such as discontinuous Galerkin methods, may even produce non-conforming meshes. Such data is difficult to visualize interactively, as it is far too large to fit in memory and many common data reduction techniques, such as mesh simplification, cannot be applied to non-conforming meshes. We introduce a point-based visualization system for interactive rendering of large, potentially non-conforming, tetrahedral meshes. We propose methods for adaptively sampling points from non-linear solution data and for decimating points at run time to fit GPU memory limits. Because these are streaming processes, memory consumption is independent of the input size. We also present an order-independent point rendering method that can efficiently render volumes on the order of 20 million tetrahedra at interactive rates.

Three-Dimensional Digital Microstructure

Abstract : We report on a systematic means of generating a finite element (FE) mesh for realistic three-dimensional (3D) microstructure systems that are suitable for FE analysis. The relationship between a materials microstructure and its properties are well documented and drive efforts to model the substructure evolution of textured materials. An accurate 3D computer representation of the microstructure arrangement of a material is essential to modeling the behavior and performance of materials at the microstructure level. We describe a method that uses a combination of experimental and computational techniques to produce an accurate statistical representation of its microstructure arrangement. The experimental results are used to guide the construction of the abstract 3D digital model and to provide a quantitative measure for gauging the accuracy and quality of the model upon completion. Information about the size, shape, and orientation of the grains as well as the crystallographic orientation and miss-orientation between adjacent grains can be reproduced. A 3D advancing front grid-generating technique then uses this information to produce a tetrahedral volume mesh for the material that is suitable for FE analysis.

Template-based finite-element mesh generation from medical images

The finite-element (FE) method is commonly used in biomedical engineering to simulate the behaviour of biological structures because of its ability to model complex shapes in a subject-specific manner. However, generating FE meshes from medical images remains a bottleneck. We present a template-based technique for semi-automatically generating FE meshes which is applicable to prospective studies of individual patients in which FE meshes must be generated from scans of the same structure taken at different points in time to study the effects of disease progression/regression. In this "template-based" meshing approach, the baseline FE (tetrahedral) volume mesh is first manually aligned with the follow-up images. The triangulated surface of the mesh is then automatically deformed to fit the imaged organ boundary. The deformed surface nodes are then smoothed using a Laplacian smoothing algorithm to correct triangle (surface nodes) distortion and thus preserve triangle quality. Finally, the internal mesh nodes are smoothed to correct distorted tetrahedral elements and thus preserve tetrahedral element quality. This template-based approach is shown to be as accurate and precise as the previous technique used by our group, while preserving element quality and volume.

Octree-Advancing Front Method for Generation of Unstructured Surface and Volume Meshes

Amethodisdescribedforthegeneration ofunstructuredgridsforcomplexthree-dimensionalgeometriesincluding multibodydomains.Acombinedoctree-advancing frontmethod ispresentedforgenerationoftheunstructured surface mesh as well as the tetrahedral volume mesh. The unique feature of this generator is that a special octree provides the local length scales of the mesh, which can vary signi® cantly. This octree is automatically created and eliminates the need for a user-constructed background mesh to determine the grid-spacing and stretching parameters. The grid generator isrobust, isgeometry independent, and requires minimal userinteraction. A techniqueis also presented for generation of anisotropic surface meshes that result in a signi® cant reduction in the number of triangular faces. Automatic local remeshing is also employed to improve the quality of the tetrahedral mesh. The geometry independence of the octree-advancing front method is demonstrated through both surface and volume