3D Problems Research Articles

Automatic surface mesh generation by a binary-tree method

In order to realize the automation of surface mesh generation for arbitrary complex models, this paper proposes a binary-tree method (BTM) which can generate discontinuous grids. Compared with continuous grids, the adjacency relationship between discontinuous grids generated by BTM is more flexible, so it is easier to discretize “dirty” geometry without geometry repair than continuous grids. The BTM can adaptively generate meshes by features based on the curvature of curves and surfaces, and thus it does not need to construct a sizing field. Anisotropic meshes can also be directly generated by selecting the direction of subdividing meshes. Moreover, according to the periodic characteristics of periodic surfaces, the topological structure of the initial mesh can be designed to achieve mesh generation on periodic surfaces. Successful numerical examples are used to illustrate the effectiveness and robustness of the presented methods for meshing various types of geometric surfaces and reveal the excellent performance of the BTM. In addition, the BTM has been employed by the dual interpolation boundary face method (DiBFM) to solve 3D problems.

Fast CO2 saturation simulations on large-scale geomodels with artificial intelligence-based Wavelet Neural Operators

Carbon capture and storage (CCS) projects rely on numerical reservoir simulations for determining where and how much CO2 can safely be stored underground. Conventional simulations are computationally expensive and time consuming, thereby increasing the turn-around time of decision-making processes and projects. Recent research on artificial intelligence (AI) based approaches for solving the underlying two-phase flow equations has shown enormous promise, as the computational burden can be shifted to the training time, while simulations can be performed in fractions of a second at test time. Applications of AI methods for simulating CO2 flow and other differential equations have so far been limited to 2D or small 3D problems with relatively simple geometries. We introduce a cloud-native framework for parallel simulations of large-scale training data sets using the Open Porous Media (OPM) simulator and we propose a new AI architecture based on Fourier Neural Operators (FNOs) with 3D wavelet transforms. This architecture performs better than FNOs on data with shock fronts, such as simulating CO2 saturation. We also provide a new training dataset for CO2 flow based on the Sleipner CO2 storage geomodel from the Norwegian continental shelf and show that both FNOs and Wavelet Neural Operators (WNOs) can be trained on models with over 200,000 cells and lead to significant speed-ups of up to 50,000× (FNOs) and 100× (Wavelet NOs) over numerical simulations of CO2 saturation with OPM.

Soft IsoGeometric analysis of the bound states of a quantum three-body problem in 1D

The study of quantum three-body problems has been centred on low-energy states that rely on accurate numerical approximation. Recently, isogeometric analysis (IGA) has been adopted to solve the problem as an alternative but more robust (with respect to atom mass ratios) method that outperforms the classical Born–Oppenheimer (BO) approximation, especially for the cases with small mass ratios. In this paper, we focus on the performance of IGA and apply the recently-developed softIGA to further reduce the spectral errors of the low-energy bound states. This is an extension to the recent work that was published as an ICCS conference paper in Deng (2022). The main idea of softIGA is to add high-order derivative-jump terms with a penalty parameter to the IGA bilinear forms. With an optimal choice of the penalty parameter, we observe eigenvalue error superconvergence. Herein, the optimal parameter coincides with the ones for the Laplace operator (zero potential) and can be heuristically computed for a general elliptic operator. We focus on linear and quadratic elements and demonstrate the outperformance of softIGA over IGA through a variety of examples including both two- and three-body problems in 1D.

3D Transient CFD Simulation of an In-Vessel Loss-of-Coolant Accident in the EU DEMO WCLL Breeding Blanket

The in-vessel Loss-of-Coolant Accident (LOCA) is one of the design basis accidents in the design of the EU DEMO tokamak fusion reactor. System-level codes are typically employed to analyse the evolution of these transients. However, being based on a lumped approach, they are unable to quantify localised quantities of interest, such as local pressure peaks on the vacuum vessel walls, to which the failure criteria are linked. To calculate local quantities, the 3D nature of the phenomenon needs to be considered. In this work, a 3D transient model of the in-vessel LOCA from a water-cooled blanket is developed. The model is implemented in the commercial CFD software STAR-CCM+. It simulates the propagation of the water jet in the vessel from the beginning of the accident, thus accounting for the phase change of the water, i.e., from the pressurised liquid phase to the vapour phase inside the vessel, being the latter at a much lower pressure than in the blanket coolant pipes. Due to the large pressure ratio (>1000), shocks are expected; therefore, an Adaptive Mesh Refinement (AMR) algorithm is employed. The physical models (in particular, the multiphase model) are benchmarked to a 2D reference problem before being applied to the 3D EU DEMO-relevant problem. The simulation results show that the pressure peaks in front of the vessel walls are not dangerous as they are below the design limit. The entire evolution of the water jet is followed up to the opening of the burst disks, in order to compare the average pressure evolution with that computed with system-level codes. A comparison with the in-vessel LOCA from a helium-cooled blanket is also carried out, showing that the accident evolution in the water case is less violent than in the helium case.

Achieving one-dimensionality with attractive fermions

In this article we discuss the accuracy of effective one-dimensional (1D) theories used to describe the behavior of ultracold atomic ensembles confined in quantum wires by a harmonic trap. We derive, within a fully many-body approach, the effective Hamiltonian describing this class of systems and we calculate the beyond-mean-field corrections to the energy of the ground state arising from virtual transitions towards the excited state of the confining potential. We find that, due to the Pauli principle, effective finite-range corrections are one order of magnitude larger than effective three-body interactions. By comparing to exact solutions of the purely 1D problem, we conclude that a 1D effective theory provides a good description of the ground state of the system for a rather large range of interaction parameters.

A coupled FETI-BDNM for solving 3D elastic frictional contact problem

Based on the B-differentiable Newton method (BDNM) and finite element tearing and interconnecting (FETI) algorithm, a coupled approach named FETI-BDNM is developed to solve the 3D elastic contact problem with friction. In this method, the contact bodies are decomposed into a number of subdomains. The interfaces between the two adjacent substructures will be skillfully considered as the special contact surfaces that are always in the stick state. By resorting to the generalized inverse of stiffness matrices of the subdomains, the relationships between the relative displacements and forces on contact/interface, i.e., contact flexibility matrices will be computed efficiently. The contact equations, displacement continuity equations and equilibrium equations for each subdomain are expressed in the form of B-differentiable equations (BDEs) uniformly, which can be solved by the damped Newton-Raphson method with 1D Armijo type linear search. The proposed method makes it possible to solve large-scale contact problems without compromising the solution accuracy compared to the original BDNM, and the good convergence of BDEs and parallel scalability of the FETI algorithm will be preserved. Numerical examples validate the accuracy, efficiency, robustness and effects of the number of subdomains on the computational time of the proposed method.

Coupled 3D evolutionary reconstruction technique for multi-simultaneous measurements

An integrated approach for the three-dimensional tomographic reconstruction of multiple scalar fields in premixed gaseous non-sooting reactive flow applications is presented. Measurement of different physical quantities are combined to enable an in-depth analysis of the combustion process in premixed turbulent flames. This is achieved by utilizing a flexible and versatile evolutionary reconstruction technique, where measured chemiluminescence signals and deflections of a background-oriented schlieren tomography (BOST) setup are processed in a coupled manner for the first time. The 3D tomographic inverse problem is stated as a coupled system and is holistically solved for the chemiluminescence intensity field and the refractive index field (from BOST data) in the flow domain. The chemiluminescence field is interpreted as a pseudo flame surface density function of a progress variable field that allows the analysis of flame front curvatures. The proposed method is tested for its consistency and sensitivities on synthetically generated measurement data of different complexities. Finally, the technique is applied to experimental measurement data of turbulent stratified flames with different levels of swirl.

Modeling Dynamic Rate Dependent Pore Closure with A Range of Pore Sizes

Previously we presented a model (which we call PORT) with rate dependent pore closing/opening, for which we assumed that all pores close/open with the same dynamics [1]. Here we upgrade PORT to take into account different dynamics as function of pore size. We represent different pore sizes by their volume (v), and we have k discrete pore sizes. We therefore call this model VK. For the ith pore size we have ni, i=1,k pores per unit mass. We’re not aware of information on pore size distributions of porous materials, and we assume arbitrarily that pore sizes are initially distributed with a log-normal distribution. Similar to PORT, we define quasistatic pore closure curves that depend on pore volume v, and we compute the rate of pore closure with a linear overstress equation relative to these curves. From the values of v and vdot (rate of change of v) we then compute (for each cell and for each time) the overall porosity j and its rate of change jdot. Finally, we compute Pdot and Tdot (P=pressure and T=temperature) in the same way as in PORT, using the equation of state of the porous material. To show how our VK model works, we apply it to a simple 1D problem: a 20GPa sustained pressure pulse enters a porous aluminum target. We show histories of pressure, temperature and porosity at several locations into the target. We compare these curves to the ones obtained for k=1 (which are as in PORT).

Numerical Identification of External Boundary Conditions for Time Fractional Parabolic Equations on Disjoint Domains

We consider fractional mathematical models of fluid-porous interfaces in channel geometry. This provokes us to deal with numerical identification of the external boundary conditions for 1D and 2D time fractional parabolic problems on disjoint domains. First, we discuss the time discretization, then we decouple the full inverse problem into two Dirichlet problems at each time level. On this base, we develop decomposition techniques to obtain exact formulas for the unknown boundary conditions at point measurements. A discrete version of the analytical approach is realized on time adaptive mesh for different fractional order of the equations in each of the disjoint domains. A variety of numerical examples are discussed.

Topology optimization using the lattice Boltzmann method for unsteady natural convection problems

This paper proposes a density-based topology optimization method for natural convection problems using the lattice Boltzmann method (LBM). As the LBM can be developed as a completely explicit scheme, its attractive features over the traditional ones, such as the finite element method, are (1) suitability for solving unsteady flow problems and (2) scalability for large-scale parallel computing. We develop an LBM code for solving unsteady natural convection problems and provide its sensitivity analysis based on the so-called adjoint lattice Boltzmann method. Notably, the adjoint equation is derived from the discrete particle velocity Boltzmann equation and can be solved similarly to the original LBM concerning unsteady natural convection problems. We first show that the proposed method can produce similar results to the previous work in a steady-state natural convection problem. We then demonstrate the efficacy of the proposed method through 2D numerical examples concerning unsteady natural convection. As a large-scale problem, we tackle a 3D unsteady natural convection problem on a parallel supercomputer. All the developed codes written in C++ are available at https://github.com/PANFACTORY/PANSLBM2.git.

Accelerated high-cycle phase field fatigue predictions

Phase field fracture models have seen widespread application in the last decade. Among these applications, its use to model the evolution of fatigue cracks has attracted particular interest, as fatigue damage behaviour can be predicted for arbitrary loading histories, dimensions and complexity of the cracking phenomena at play. However, while cycle-by-cycle calculations are remarkably flexible, they are also computationally expensive, hindering the applicability of phase field fatigue models for technologically-relevant problems. In this work, a computational framework for accelerating phase field fatigue calculations is presented. Two novel acceleration strategies are proposed, which can be used in tandem and together with other existing acceleration schemes from the literature. The computational performance of the proposed methods is documented through a series of 2D and 3D boundary value problems, highlighting the robustness and efficiency of the framework even in complex fatigue problems. The observed reduction in computation time using both of the proposed methods in tandem is shown to reach a speed-up factor of 32, with a scaling trend enabling even greater reductions in problems with more load cycles.

Three-Dimensional Geometry Reconstruction Method from Multi-View ISAR Images Utilizing Deep Learning

The three-dimensional (3D) geometry reconstruction method utilizing ISAR image sequence energy accumulation (ISEA) shows great performance on triaxial stabilized space targets but fails when there is unknown motion from the target itself. The orthogonal factorization method (OFM) can solve this problem well under certain assumptions. However, due to the sparsity and anisotropy of ISAR images, the extraction and association of feature points become very complicated, resulting in the reconstructed geometry usually being a relatively sparse point cloud. Therefore, combining the advantages of the above methods, an extended factorization framework (EFF) is proposed. First, the instance segmentation method based on deep learning is used for the extraction and association of a number of key points on multi-view ISAR images. Then, the projection vectors between the 3-D geometry of the space target and the multi-view ISAR images are obtained, using the improved factorization method. Finally, the 3D geometry reconstruction problem is transformed into an unconstrained optimization problem and solved via the quantum-behaved particle swarm optimization (QPSO) method. The proposed framework uses discretely observed multi-view range–Doppler ISAR images as an input, which can make full use of the long-term data of space targets from multiple perspectives and which is non-sensitive to movement. Therefore, the proposed framework shows high feasibility in practical applications. Experiments on simulated and measured data show the effectiveness and robustness of the proposed framework.

An adaptive mesh refinement strategy for 3D phase modeling of brittle fracture

In order to improve the calculation accuracy and efficiency of the phase field method (PFM), an adaptive mesh refinement strategy suitable for 3D problems is proposed. The refined area is selected in terms of both the phase field value and the phase field increment value. The transition area is then chosen based on the transition element determination algorithm. The corresponding areas are refined using three basic and two advanced refinement templates. The new mesh is made up of hexahedrons and has no hanging nodes. The improved backtracking algorithm based on distance judgment is used in 3D adaptive mesh refinement and has proven its capacity to increase calculation efficiency. The accuracy and applicability of PFM to low-quality meshes with 3D adaptive mesh refinement are verified through benchmark tests, and the errors are all within 1%. Compared with the global refinement mesh, the number of elements in the PF model with 3D adaptive mesh refinement is reduced by more than 80%, and the computational efficiency is increased by 16 times. Combined with virtual crack insertion technology, mode I-II-III fracture is successfully simulated. The accurate and efficient calculation of cracked structures is realized. 3D multi-level adaptive mesh refinement is preliminary developed, and compared with single-level adaptive mesh, the computational efficiency is about two times higher, which provides a potential way to solve the efficient simulation of crack propagation in large-volume structures.

The consistent boundary element method for potential and elasticity: Part III — Topologically challenging numerical assessments for 2D problems

The collocation boundary element method is consistently outlined in a companion (Part I) paper for the general three-dimensional, static case of elasticity on the basis of a weighted-residuals statement that leads to the Somigliana’s identity. Arbitrary rigid-body displacements, as for elasticity, are naturally taken into account, and traction force parameters are always in balance independently of problem scale and mesh discretization. For generally curved boundaries, the correct definition of traction force interpolation functions enables the enunciation of a general convergence theorem, the introduction of patch and cut-out tests and, not least, a considerable simplification of the numerical implementations. Simple code schemes are proposed in a second companion (Part II) paper for 2D problems of potential and elasticity, which rely exclusively on Gauss–Legendre quadrature and lead to arbitrarily high – actually only machine-precision dependent – computational accuracy of all results of interest independently of a problem’s geometry and topology. We present here numerical results and convergence assessments – including numerical illustration of convergence Theorem 1 of the companion paper I – for 2D potential and elasticity problems with very challenging topology issues and even for subnanometer source–field distances — maybe with approximations due to a coarse mesh discretization but never introducing unduly singularities. We dare say the present results cannot be replicated by any code implementation other than the ones of our own, which resort to no ad hoc means beyond the problem’s correct mathematics. In fact, we present the objective and controllable tools of separately assessing a mesh discretization for a given practical problem in terms of precision, accuracy and liability to round-off-errors. We also evaluate the distance threshold for a source point to be considered sufficiently close to demand the proposed exact mathematical treatment, as, for large distances, only Gauss–Legendre quadrature is required, be it in terms of quadrature adaptivity of even a fast multipole scheme.

A coarse-grained constitutive law for fracturing beams based on a sharp interface crack representation

Damage gradient models approximate fracture mechanics using a modulation of the material stiffness. To this aim a single scalar field, the damage, is used to degrade as a whole the elastic energy. If applied to the structural models of beams and shells, where the elastic energy is the sum of the stretching and bending contributions, a similar approach is not able to capture some important features. For instance, the coupling between axial and bending strains induced by cracks non-symmetric with respect to the center line is completely missed. In this contribution, we deduce a constitutive law for a beam having a crack non-symmetric with respect to the center line. To achieve this, we perform an asymptotic coarse-grained procedure from a 2D problem, using a sharp interface model. We deduce a homogenized 1D elastic energy, coupling the axial and bending strains, the constitutive parameters of which depend in a different way on the crack depth and we state how precisely they do. This should pave the way to a rational development of a phase-field gradient model for thin structures.

A strain based Lipschitz regularization for materials undergoing damage

Data Driven Computational Mechanics (DDCM) solves the boundary value problem by directly relying on the strain-stress data, bypassing the need for a constitutive model. In presence of materials exhibiting a softening response, Finite Element analyses performed with a constitutive model typically use a length scale, which can be introduced into the problem in multiple ways. A few commonly used ways include the addition of the gradient of damage variable in the energy density functional, using the gradient of strain while evaluating the internal variable, and so on. However, in the context of DDCM, these techniques may not be effective as the internal variables are not explicitly defined. Hence, the current article introduces a regularization technique, where the gradient of strain is constrained to lie within some interval. This prevents strain localization within an element by introducing a length scale into the problem. This article demonstrates the effectiveness of such a regularization technique in the case of 1D problems using a constitutive model while comparing its performance with strain gradient (SG) models.

Self-supervised Image-based 3D Model Retrieval

Image-based 3D model retrieval aims at organizing unlabeled 3D models according to the relevance to the labeled 2D images. With easy accessibility of 2D images and wide applications of 3D models, image-based 3D model retrieval attracts more and more attentions. However, it is still a challenging problem due to the modality gap between 2D images and 3D models. In spite of the remarkable progress brought by domain adaptation techniques for this research topic, which usually propose to align the global distribution statistics of two domains, these methods are limited in learning discriminative features for target samples due to the lack of label information in target domain. In this article, besides utilizing the label information of 2D image domain and the adversarial domain alignment, we additionally incorporate self-supervision to address cross-domain 3D model retrieval problem. Specifically, we simultaneously optimize the adversarial adaptation for both domains based on visual features and the contrastive learning for unlabeled 3D model domain to help the feature extractor to learn discriminative feature representations. The contrastive learning is used to map view representations of the identical model nearby while view representations of different models far apart. To guarantee adequate and high-quality negative samples for contrastive learning, we design a memory bank to store and update representative view for each 3D model based on entropy minimization principle. Comprehensive experimental results on the public image-based 3D model retrieval datasets, i.e., MI3DOR and MI3DOR-2, have demonstrated the effectiveness of the proposed method.

Identifying Critical Defect Sizes From Pore Clusters in Nickel-based Superalloys Using Automated Analysis and Casting Simulation

Porosity can form during investment casting as a result of the solidification conditions. Significant porosity can result in agglomerations (pore clusters) which are a primary crack initiation source and can result in reduced fatigue life of Nickel-based superalloys. Such clusters of porosity are today conventionally measured using 2D micrographs. An approach to accurately predict and analyze casting porosity from 2D cuts while facing in reality a 3D shape problem is currently missing. In this work, an approach that combines automation and simulation to assess the representative pore dimension, their interconnectivity and the porosity position is presented. On a LPT blade made of IN100, the porosity percentage and Feret diameter have been measured in multiple cuts and the porosity was found to be in the range of 0.88 to 5.4 pct. From the same micrographs the critical defect sizes were estimated with an automated tool to be in the range of 200 to 1800 mum. The simulated shrinkage porosity for the same part, was predicted to be in the range of 1.67 to 2.33 pct. This study shows that the scaling factor between the pore Feret diameter and the critical pore size is equal to 2.9, in accordance to the proportionality of critical pores size clusters calculated from a 2D and 3D dataset. Finally, the simulated casting porosity was compared to that measured on cast blades in critical regions and the predictive accuracy is discussed in detail.

A new Markov–Dubins hybrid solver with learned decision trees

In this paper, the applicability of machine learning models and techniques to the Markov–Dubins path planning problem have been explored. Machine learning techniques are already applied to several fields, which range from computer vision, to physics simulation, to item recommendation, to user profiling. This pervasiveness has led to marked improvements in the implementation and support for applying machine learning models, in particular for specialised use cases such as low-power devices, embedded hardware, and real-time applications. On the other hand, the Markov–Dubins path planning problem, which is central in robotic nonholonomic trajectory design, is already covered by established numerical and optimisation techniques. However, the benefits of applying machine learning approaches to this problem remain to be investigated. In particular, there is the need to research potential speed-ups or application domains that would be better solved by a machine learning approach compared to the traditional algorithmic approaches. In this study, we train a state-of-the-art machine learning model in a supervised setting on Markov–Dubins and use it in two different ways: to directly predict the solution, and to filter candidate solutions. Also, a comparison of the quality of these predictions with a state-of-the-art Markov–Dubins solver is made. The results obtained indicate that machine learning approaches are comparable to state-of-the-art solutions: our bare model, directly predicting the solution, appears to be 8.3 times faster than the current standard, sacrificing the accuracy, which amounts to a value close to 92%; the hybrid model that filters the solutions prior to finding the best candidate runs in times that are comparable to the classical solver (58 ms) and has over 98% accuracy. A further comparison with alternative solvers and techniques, such as Optimal Control, NonLinear Programming and Mixed Integer NonLinear Programming has been made, confirming the benefits of the machine learning approach over these, for which the computational times are in the range of seconds. This opens new avenues for interdisciplinary applications of machine learning to more general planning problems (e.g., the same problem in 3D), where the number of possible manoeuvres is large and the computation of each of them requires a considerable computational effort, which makes the brute force trial-and-error infeasible.

A Novel Multivariate Spectral Local Quasilinearization Method (MV-SLQLM) for Modelling Flow, Moisture, Heat, and Solute Transport in Soil

Conventionally, the problem of studying the transport of water, heat, and solute in soil or groundwater systems has been numerically solved using finite difference (FD) or finite element (FE) methods. FE methods are attractive over FD methods because they are geometrically flexible. However, recent studies demonstrate that spectral collocation (SC) methods converge exponentially faster than FD or FE methods using a few grid points or on coarse grids. This work proposes and applies a multivariate spectral local quasilinearization method (MV-SLQLM) to model the transportation and interaction of soil moisture, heat, and solute concentration in a nonbare soil ridge. The MV-SLQLM uses a quasilinearization method (QLM) to linearize any nonlinear equations and then employs a local linearization method (LLM) to decouple the linearized system of PDEs to form a sequence of equations that are solved in a computationally efficient manner. The MV-SLQLM is thus an extension of the bivariate spectral local linearization method (BI-SLLM) that fails to deal with a 2D problem and is a modification of the MV-SQLM whose efficiency is compromised when operating on high dense solution matrices. We use the residual error norms of the difference between successive iterations to affirm convergence to the expected solution. To illustrate the application and check the solution accuracy, we conduct systematic analyses of the effect of model parameters on distribution profiles. Findings are in good agreement with theory and literature, thereby revealing suitability of the MV-SLQLM to solve coupled nonlinear PDEs with environmental fluid dynamics applications.