Discretization Of Geometry Research Articles

Shutdown dose rate calculation for fission reactors: An application of the MS-CADIS method to OPAL

There have been considerable advances of shutdown dose rate (SDDR) calculation methods for fusion related problems, however applications of these methods in the fission reactor field have hitherto been sparse. The present study attempts to bridge this gap by investigating the applicability of SDDR calculation methods for fission reactor problems. Specifically, we aim to assess and validate whether recent advances in SDDR methods can be successfully applied in fission research reactors. To this end, we estimate the shutdown dose rate distribution at the Open Pool Australian Light water reactor (OPAL) using the rigorous two step (R2S) computational method, and we compare the calculated results with the experimental data. This method utilizes a 3D reactor model implemented in the Monte Carlo N-Particle (MCNP) transport code, the AutomeD VAriaNce reduction Generator (ADVANTG) code for geometry discretization and variance reduction calculations, and the Oak Ridge Isotope GENeration (ORIGEN) inventory code for activation calculations. To ensure robustness, we employ two variance reduction techniques, Forward Weighted Consistent Adjoint Driven Importance Sampling (FW-CADIS) and Multi-Step Consistent Adjoint Driven Importance Sampling (MS-CADIS). To the best of our knowledge, this is the first MS-CADIS method implementation for fission reactor problems. The SDDR is estimated at ten locations within the experimental hall, all situated more than 4 m away from the reactor core.The paper shows that, the experimental observations are within the lower and upper bounds of the simulation results for 4 out of 10 locations, while the remaining observations are within a factor of 7, with one significant outlier. The calculated average dose rate is within 5% of the nominal values of the experimental observations for 3 locations. The computational results are within statistical uncertainty by using two different variance reduction techniques, with significant computational advantage of MS-CADIS over FW-CADIS for SDDR calculations. The results indicate that the combination of SDDR distribution maps, estimated dose rate energy dependance, and activation information are powerful tools in identifying the radioisotopes and reactor components dominating the SDDR. These results can contribute to better radiation safety practices in contaminated areas, by enabling the minimal dose path planning or by improving radiation shielding.

Nonlinear topology optimization on thin shells using a reduced-order elastic shell model

We present a novel numerical algorithm to perform nonlinear topology optimization on elastic thin shells. The main component of our method is a differentiable thin-shell simulator based on discrete differential geometry (DDG) discretization and the projected Newton method to solve geometrically nonlinear elasticity and its derivatives on a triangle mesh. We build a density-based topology optimization algorithm, enhanced by a density filter and a Heaviside projection scheme, to emerge and optimize topologically complex shell structures on curved surfaces. We validate our approach using standard test cases for nonlinear topology optimization and demonstrate the efficacy of our method by tackling highly nonlinear topology optimization problems by producing complex and high-resolution shell structural designs under various load conditions.

A CutFEM method for phase change problems with natural convection

In this paper, we present a Nitsche-based CutFEM approach for solving phase change problems while taking natural convection into account in the liquid phase. In the proposed algorithm, the interface is implicitly tracked through a level-set approach, where the level-set function is updated by solving a transport equation. To stabilize the finite element formulation of this equation, we use the continuous interior penalty method (CIP). We use the Backward Euler scheme for the time discretization and the of continuous piecewise linear polynomials (P1) for the spatial discretization of the temperature and the level-set function. For flow velocity and pressure in the liquid phase, the finite element formulation is based on the inf-sup stable pair of Hood-Taylor finite element function spaces P2−P1. As we are dealing with unfitted finite element methods, stability issues may arise due to geometry discretization. To address this issue, we incorporate ghost penalty terms into the finite element formulations of the heat and Navier–Stokes equations. According to Stefan’s condition, the normal velocity of the interface is proportional to the jump in the interfacial flux. For an efficient approximation of this jump, we use a ghost penalty-based domain integral approach which has shown to be highly accurate. To validate the proposed method, we first provide two manufactured solutions that confirm optimal convergence in both temporal and spatial discretizations. We next consider challenging problems such as the melting of n-octadecane in a differentially heated cavity, the multi-cellular melting of gallium, and the freezing of water to further validate our algorithm. We compare our results to existing numerical and experimental data.

Code verification of non‐linear immersed boundary simulations using the method of manufactured solutions

AbstractNon‐standard finite element technologies, such as immersed boundary approaches, are typically based on novel algorithms and advanced methods, which require reliable testing of the implemented code. For this purpose, the method of manufactured solutions (MoMS) offers a great framework, enabling an easy and straightforward derivation of closed‐form reference solutions. In this contribution, the focus is kept on non‐linear analysis via the finite cell method (FCM), which is typically based on an unfitted geometry discretization and higher‐order shape functions. The code verification via MoMS generally requires the application of boundary conditions to all boundaries of the simulation domain, which need to be enforced in a weak sense on the immersed boundaries. To avoid this, we propose a novel way of deriving manufactured solutions, for which the necessary constraints on the embedded boundaries are directly fulfilled. Thus, weak boundary conditions can be eliminated from the FCM simulation, and the simulation complexity is reduced when testing other relevant features of the immersed code. In particular, we focus on finite strain analysis of 3D structures with a Neo‐Hookean material model, and show that the proposed technique enables a reliable code verification approach for all load steps throughout the deformation process.

Numerical approaches in simulating Trichel pulse characteristics in point-plane configuration

In this work, a detailed comparison is made of a few different approaches to numerical modeling of non-equilibrium gas discharge plasmas in dry ambient air at atmospheric conditions, leading to Trichel pulse discharge. Simulation models are based on a two-dimensional axisymmetric finite element discretization of point-plane geometry. The negative corona discharge and the hydrodynamic approximation for generic ionic species (electrons, positive and negative ions) are used. The models account for the drift, diffusion, and reactions of the species. They comprise continuity equations coupled to Poisson’s equation for the electric field. Three different formulations were used to specify the ionic reaction rate coefficients. In the first one, the reaction coefficients are approximated by the analytical expressions as a function of the electric field intensity. Two others extract the reaction coefficients from the solution of the Boltzmann equation as a function of the reduced electric field or the electron energy. The effect of gas flow and heating on the pulse characteristics is also investigated. The accuracy of the models has been validated by comparing them with the experimental data.

A hybrid implicit-explicit discontinuous Galerkin spectral element time domain (DG-SETD) method for computational elastodynamics

SUMMARY A hybrid implicit-explicit (IMEX) discontinuous Galerkin spectral element time domain (DG-SETD) algorithm is proposed to simulate 3D elastic wave propagation in inhomogeneous media. In this method, the original problem can be divided into a number of well designed subdomains, and the mesh generation of different subdomains is completely independent, thus allowing flexible spatial discretization of complex geometry. The neighboring subdomains are connected by a Riemann transmission condition (RTC), and spectral elements with different interpolation orders can be used in different subdomains to maximize the computational efficiency of multiscale problems to facilitate parallel computing for different subdomains. In particular, the explicit or implicit time iteration scheme can be appropriately selected for a subdomain according to the size of its mesh elements to increase the global time step increment, thus giving higher computational efficiency: For subdomains with coarse meshes, the explicit time integration scheme is used and the time step increment is limited by the Courant−Friedrichs−Lewy (CFL) stability condition; for subdomain with fine structures and thus fine meshes, an implicit time integration scheme is used so that a large time step increment can be used without affecting the stability. In addition, a jump condition of displacement and velocity is introduced to accurately simulating fractures and faults, including lossless and viscous fractures with plane, curve or cross structures. This avoids the volume modeling of the extremely thin fracture structures, and effectively reduces the number of degrees of freedoms (DoFs) in the discretized system without the loss of accuracy. The accuracy, robustness and efficiency of the DG-SETD algorithm are demonstrated by quantitative comparisons of the waveforms with the commercial finite element software COMSOL.

Enhancing three-dimensional convolutional neural network-based geometric feature recognition for adaptive additive manufacturing: a signed distance field data approach

Abstract In the context of additive manufacturing, the adjustment of process data to individual geometric features offers the potential to further increase manufacturing speed and quality, while being widely underestimated in recent research. Unfortunately, the current non-uniform data handling in the CAD-CAM-Link results in a downstream data loss, that prevents the availability of geometric knowledge from being present at any time to apply the more advanced approaches of adaptive slicing and tool path generation. Automatic detection of various geometric entities would be beneficial for classifying partial surfaces and volumetric ranges to gain customized informational insights of geometric parameterization. In this work, an enhanced approach of geometric deep learning for the analysis of voxelized engineering parts will be presented to align the inference representations to modeling paradigms for complex design models like architected materials. Although the baseline voxel representation offers distinct advantages in detection accuracy, it comes with an adversely large memory footprint. The geometry discretization leads to high resolutions needed to capture various detail levels that prevent the analysis of fine-grained objects. To achieve efficient usage of three-dimensional (3D) deep learning techniques, we propose a 3D-convolutional neural network-based feature recognition approach using signed distance field data to limit the needed resolution. These implicit geometric data leverage the advantages of volumetric convolution while alleviating their disadvantages through the use of the continuous signed distance function. When analyzing computer-aided design data for geometric primitive features, a common application task in surface reconstruction of reverse engineering the proposed methodology, achieves a detection accuracy that is in line with the accuracy values achieved by comparable algorithms. This enables the recognition of fine-grained surface instances. The unambiguous shape information extracted could be used in subsequent adaptive slicing algorithms to achieve individual geometry-based hatch generation.

Peridynamics topology optimization of three-dimensional structures with surface cracks for additive manufacturing

Additive manufacturing (AM) is an effective approach to fabricating intricate shapes obtained from topology optimization (TO). However, it may cause undesired manufacturing-induced defects/cracks due to high thermal residual stresses. This study proposes a PeriDynamics-enabled three-dimensional Topology Optimization method (PD-TO) for designing structures by considering surface cracks for the AM processes. The PD-TO approach employs a bi-directional evolutionary structural optimization method and uses particle discretization of geometry for mechanical analysis. Crack surfaces are generated by breaking three-dimensional nonlocal interactions of the particles, and thus, during the optimization process, complex multiple structural discontinuities can be diligently modeled. First, the proposed approach is validated by solving benchmark problems without cracks. For each benchmark geometry, the PD-TO analysis is then performed by considering different positions and numbers (single/multiple) of cracks. These analyses extensively investigate and demonstrate the effects of a priori knowledge of residual stress-induced damages/cracks on the optimum topology for additive manufacturing. Besides, the smoothing operation is applied to the optimum designs to transform voxel shapes into AM-friendly smooth surfaces. These geometries are manufactured by an extrusion-based AM process to demonstrate the practical engineering application of the proposed method. Finally, the comparison of numerical results is also supported by the experimental tests conducted on the optimized topologies. Overall, it is confirmed that the PD-TO approach is a viable and accurate optimization tool for additive manufacturing considering possible process-induced damages.

Finite Element Analysis of Continuous Plates Using a High-Performance Programming Language (MATLAB)

This paper uses MATLAB, a finite element software program to compare the results of several finite analysis methods for continuous plates and check the degree of correlation with the exact values obtained by Timoshenko (1959) and Cheung (1996). The results showed little or no significant difference between plates in finite elements. Two different finite Numerical techniques are used. The Finite Strip and Exact methods and their results are compared to the results from the MATLAB program. Finite element analysis (FEA) workflow using MATLAB includes generation of meshes, geometry creation, defining physics of load, initial conditions and boundary problems, calculation, and results from visualization. FEA is a very general approach for solving Equations in science and engineering. This work offers solutions to the increasing errors associated with several other numerical methods when solving any equations of plates (сontinuous). It makes it easier to calculate and design larger structures through geometry discretization of plates and plains into more minor elements.

Design and optimization of free-form surfaces for modular concrete 3D printing

Although they are very efficient structures, concrete shells have lost popularity due to the complexity of the traditional construction process using cast-in-place concrete. A key concept to overcome the labor-intensive formwork in situ is the segmentation of the shells into prefabricated parts. In order to avoid individual formworks during prefabrication as well, the authors rely on extrusion-based 3D printing of strain-hardening cement-based composite (SHCC). The goal is a highly automated, scalable, and adaptable flow-prefabrication of modules controlled by a holistic digital design process. Such the creation of modular free-form shell structures can be accelerated significantly, resulting in structures comparable with gridshells. Starting with the problem statement and the elaboration of the technology used, the main contribution of this research is the development of geometrical methods for modularization based on given production conditions. The challenge lies in the free-form geometry discretization with respect to the structural analysis and within the defined constraints such as planar quads, no edge torsion, and minimal material consumption. Methods of discrete differential geometry for circular PQ (planar quad) mesh generation are combined with Response Surface Methodology (RSM) for multi-objective optimization of the global parameterized shape. The results were illustrated in a study case where the geometrical and structural production parameters of starting and final shell are compared.

A mid-fidelity numerical method for blood flow in deformable vessels

In this work, a novel fluid–structure interaction algorithm for the simulation of blood flow in three-dimensional deformable vessels is addressed. The method extends the mid-fidelity strategy named as Transversally Enriched Pipe Element Method, extensively tested as an efficient approach to simulate the blood flow under rigid wall hypothesis, by taking into account the distensibility of the lumen boundary by means of an independent ring structural model. The Navier–Stokes equations, in Arbitrary Lagrangian–Eulerian framework, are used as the governing equations for the blood flow dynamics, the vessel wall mechanics is represented through an elastic constitutive law, and the fluid domain deformation problem is explicitly solved by exploiting the layered structure of the geometry discretization associated to the mid-fidelity model. The result is an approximation strategy able to take into account the wall deformation at nearly zero added cost when compared with a rigid wall model. An extensive numerical validation and verification of the proposed methodology is reported employing simple domains and complex patient-specific geometries to highlight the potential for real applications.

Dynamical analysis of sliding connections with mesh independent roughness by a total Lagrangian FEM

Sliding connections are present in several applications on the mechanics, civil and aerospace industries. A framework consisting on an accurate and stable formulation to describe the dynamics of flexible systems with sliding connections is developed. The total Lagrangian positional approach of the Finite Element Method is employed using 2D solid and frame elements to discretize bodies and connections. This allows a wide range of applications, particularly the local modelling of joints. The proposed formulation includes roughness along sliding paths independent from the finite element geometry discretization. Following variational principles, Lagrange multipliers are used to impose sliding constraints on the equations of motion. A direct time integration is performed by the generalized-α method and its stability in the present finite deformation context is evaluated. The resulting nonlinear equations are solved by the Newton-Raphson method. Examples are presented where the proposed framework is evaluated regarding its dynamical behavior and to solve practical scenarios for which sliding modelling is a necessity.

A fast boundary element method using the Z‐transform and high‐frequency approximations for large‐scale three‐dimensional transient wave problems

SummaryThree‐dimensional (3D) rapid transient acoustic problems are difficult to solve numerically when dealing with large geometries, because numerical methods based on geometry discretization (mesh), such as the boundary element method (BEM) or the finite element method (FEM), often require to solve a linear system (from the spacial discretization) for each time step. We propose a numerical method to efficiently deal with 3D rapid transient acoustic problems set in large exterior domains. Using the ‐transform and the convolution quadrature method, we first present a straightforward way to reframe the problem to the solving of a large amount (the number of time steps, M) of frequency‐domain BEMs. Then, taking advantage of a well‐designed high‐frequency approximation, we drastically reduce the number of frequency‐domain BEMs to be solved, with little loss of accuracy. The complexity of the resulting numerical procedure turns out to be O(1) in regard to the time discretization and for the spacial discretization, the latter being prescribed by the complexity of the used fast BEM solver. Examples of applications are proposed to illustrate the efficiency of the procedure in the case of fluid‐structure interaction: the radiation of an acoustic wave into a fluid by a deformable structure with prescribed velocity and the scattering of an abrupt wave by simple and realistic geometries.

Large deformation in bi-material components by XIGA and coupled FE-IGA techniques

In the recent years, isogeometric analysis (IGA) has found wide application in modeling different types of discontinuities produced by cracks, contact surfaces and bi-material interfaces. This technique eliminates the geometry discretization errors associated with the representation of complex geometries. The present paper employs the extended isogeometric analysis (XIGA) and the coupled finite element-isogeometric analysis (FE-IGA) to model large elasto-plastic deformations in bi-material engineering components. XIGA models all types of discontinuities independent of the grid chosen for analysis. Instead, the standard displacement-based approximation is enriched with additional enrichment functions to include the effects of these discontinuities in the formulation. In the coupled FE-IGA technique, IGA is used in the weak portion of the domain to eliminate the problems of mesh distortion and conventional finite element method is used in the stronger portion where mesh distortions do not occur. The transition elements are employed to couple the finite element and isogeometric portions of the domain. Finally, several numerical problems are solved by XIGA and coupled FE-IGA techniques to illustrate the applicability, efficiency and accuracy of the proposed techniques in modeling large elasto-plastic deformations in bi-material specimens. The results obtained in the present study are compared with finite element solutions which have been taken as the reference solution for the given problems.

On the importance of spiral-flow inflow boundary conditions when using idealized artery geometries in the analysis of liver radioembolization: A parametric study.

In the last decades, the numerical studies on hemodynamics have become a valuable explorative scientific tool. The very first studies were done over idealized geometries, but as numerical methods and the power of computers have become more affordable, the studies tend to be patient specific. We apply the study to the numerical analysis of tumor-targeting during liver radioembolization (RE). RE is a treatment for liver cancer, and is performed by injecting radiolabeled microspheres via a catheter placed in the hepatic artery. The objective of the procedure is to maximize the release of radiolabeled microspheres into the tumor and avoid a healthy tissue damage. Idealized virtual arteries can serve as a generalist approach that permits to separately analyze the effect of a variable in the microsphere distribution with respect to others. However, it is important to use proper physiological boundary conditions (BCs). It is not obvious, the need to account for the effect of tortuosity when using an idealized virtual artery. We study the use of idealized geometry of a hepatic artery as a valid research tool, exploring the importance of using realistic spiral-flow inflow BC. By using a literature-based cancer scenario, we vary two parameters to analyze the microsphere distribution through the outlets of the geometry. The parameters varied are the type of microspheres injected and the microsphere injection velocity. The results with realistic inlet velocity profile showed that the particle distribution in the liver segments is not affected by the analyzed injection velocity values neither by the particle density. NOVELTY STATEMENT: In this article, we assessed the use of idealized geometries as a valid research tool and applied the use of an idealized geometry to the case of an idealized hepatic artery to study the particle-hemodynamics during radioembolization (RE). We studied three different inflow boundary conditions (BCs) to assess the usefulness of the geometry, two types of particle injection velocities and two types of commercially available microspheres for RE treatment. In recent years, the advent in computational resources allowed for more detailed patient-specific geometry generation and discretization and hemodynamics simulations. However, general studies based on idealized geometries can be performed in order to provide medical doctors with some basic and general guidelines when using a given catheter for a given cancer scenario. Moreover, using an idealized geometry can be a reasonable approach which allows us to isolate a given parameter and control other parameters, so that parameters can be independently assessed. Even though an idealized geometry does not match any patient's geometry, the use of an idealized geometry can be valid when drawing general conclusions that may be useful in patient-specific cases. However, we believe that even if an idealized hepatic artery geometry is used for the study, it is necessary to account for the upstream and downstream tortuosity of vessels through the BCs. In this work, we highlighted the need of modeling the tortuosity of upstream and downstream vasculatures through the BCs.

A modified conjugated bond-based peridynamic analysis for impact failure of concrete gravity dam

Description of the impact damage of dams subjected to projectile penetration objectively is a significant but difficult issue. To take the advantages of bond-based peridynamics (BB PD) in analyzing multiple crack growth and fragmentation, a modified conjugated BB PD model with two micro-moduli is established for analyzing the quasi-static deformation and the projectile impact damage of a typical concrete gravity dam. The nonlocal interaction force in the conjugated BB PD is not only related to the relative normal stretch of a bond, but also related to a series of relative rotation angle of a pair of conjugated bonds. This model can be regarded as considering the tensile spring and the rotation spring together, so that it can break through the fixed Poisson’s ratio limitation of the original BB PD model due to the central pairwise interaction. Furthermore, compared with the original conjugated BB PD model, the definitions of tangent bond force and rotation strain energy density are distinctly different, which will not varied with different geometry discretization; also an attenuation kernel function related to the bond length is incorporated to reflect the decreasing long-range force with the increasing distance between material points. Finally, the failure analysis of a dam subjected to high-velocity projectile impacting at the center of dam crest demonstrates the effectiveness of the PD method for simulating the projectile impact failure.

Efficient aerodynamic shape optimization through reduced order CFD modeling

Although computational power is increasingly available, high-fidelity simulation based aerodynamic shape optimization is still challenging for industrial applications. To make the simulation based optimization acceptable in the practice of engineering design, a technique combining mesh morphing and reduced order modeling is proposed for efficient aerodynamic optimization based on CFD simulations. The former technique avoids the time-consuming procedure of geometry discretization. And the latter speeds up the procedure of field solution by exploiting pre-computed solution snapshots. To test the efficiency of the proposed method, the windshield of a motorbike is analyzed and optimized. It is shown that even the total number of cells of the mesh is around 0.4 million, the CFD computation and the post-processing of the results can be completed in less than 10 s if the reduced order model is adopted. Running on a personal computer, the generic algorithm is applied to optimize the profile of the windshield. A 8% reduction of the drag coefficient is achieved after 800 queries of the reduced order CFD model and the total CPU time is only around 2 h.

Efficient aerodynamic shape optimization through free-form mesh morphing and reduced order CFD modeling

Although computational power is increasingly available, high-fidelity simulation based aerodynamic shape optimization is still challenging for industrial applications. To make the simulation based optimization acceptable in the practice of engineering design, a technique combining mesh morphing and reduced order modeling is proposed for efficient aerodynamic optimization based on CFD simulations. The former technique avoids the time-consuming procedure of geometry discretization. And the latter speeds up the procedure of field solution by combining pre-computed solution snapshots. To test the efficiency of the proposed method, the windshield of a motorbike is analyzed and optimized. It is shown that even the total number of cells of the mesh is around 0.4 million, the CFD computation and the post processing of the results can be completed in less than 10 seconds if the reduced order model is adopted. Running on a personal computer, the generic algorithm is applied to optimize the profile of the windshield. A 8% reduction of the drag coefficient is achieved after 800 queries of the reduced order CFD model and the total CPU time is only around 2 hours.

Voxel transformation: scalable scene geometry discretization for global illumination

In real-time computer graphics, efficient discretization of scenes is required in order to accelerate graphics related algorithms such as realistic rendering with indirect illumination and visibility checking. Sparse voxel octree (SVO) is a popular data structure for such a discretization task. Populating an SVO with data is challenging when dynamic object count is high, especially when data per spatial location is large. Problem of populating such trees is adressed with our Voxel Transformation method, where pre-generated voxel data is transformed from model space to world space on demand, in contrast to the common way of voxelizing each dynamic object over each frame. Additionally, an accompanying filtering technique for voxel transformation is also proposed. This technique serves proposed system in two ways: (1) resolves issues introduced by the proposed fast and scalable voxel transformation method, and (2) enables smooth transitions between frames and handles the aliasing problem naturally as shown in the supplementary video. As an application use case, the proposed Voxel Transformation method is demonstrated in order to achieve indirect illumination using the well-known voxel cone tracing method. Results, which is compared with the standard voxelization method and ground-truth, are visually appealing and also scalable over large number of dynamic objects as shown in the supplementary video.

Digital-Image-Driven Stochastic Homogenization for Recycled Aggregate Concrete Based on Material Microstructure

In this paper, a digital-image-driven stochastic homogenization method is developed to analyze elastic heterogeneous media such as recycled aggregate concrete (RAC), etc. This linking can be accomplished in an efficient manner by exploiting the excellent synergy of finite pixel-element method and Monte Carlo simulation for the computation of the effective properties of the random five-phase composite. The pixel-point discretization of system geometry is used for the approximation of the mechanical response of the elastic heterogeneous microstructure. Using nanoindentation technique and scanning electron microscopy, tens of digital images of modulus map of the five-phase heterogeneous material are made. Using the moving window technique and the Monte Carlo method, the random elastic moduli of the five phases at micro-scale are obtained. Then the effective elastic modulus of the meso-scale representative volume element (RVE) is computed based on spectral stochastic finite element method. Finally, the effective modulus is used to analyze the global behavior of RVE at macro-scale. Then the finite pixel-element method is used to investigate the effect of microscopic covariance noise on the global material properties, as well as the computational efficiency. The results show that the digital image method is an accurate and efficient tool to investigate the random material properties across scales.