3D Problems Research Articles

Numerical simulations of underwater explosions using a compressible multi-fluid model

We present a novel solver for simulating compressible multi-fluid multiphase flow in underwater explosions (UNDEXs). The developed solver uses a modified version of Saurel's six-equation model, which includes an additional total mixture energy equation to resolve discrepancies in the thermodynamic states predicted under shock conditions. Additionally, we integrate a more precise stiffened gas equation of state (SG-EOS) that is determined using a novel method to enhance the accuracy of predicting experimental data based on a shock Hugoniot curve. We also propose a solution procedure using the modified Saurel's six-equation model on a three-dimensional (3D) structured Cartesian grid system. This involves discretizing the equation system using a Godunov scheme with a two-fluid Harten-Lax-van Leer-Contact approximate Riemann solver and a MUSCL-Hancock primitive scheme with total-variation-diminishing limiters, achieving a second-order extension. Both the dimensional splitting and fractional-step methods are utilized to model one-dimensional (1D) operators, splitting them into sequential operators. The modified model is validated for 1D and 3D problems, including the water–air shock tube, cavitation, shock–bubble interaction, and UNDEX problems in a free field, near a free surface, and near a rigid dam. Our simulations accurately predict the shockwave propagation, shock and free-surface interactions, cavitation evolution, and water jetting impact characteristics, exhibiting satisfactory agreement with those of previous studies. The proposed solver provides insight into the effects of UNDEXs on rigid structures, with potential applications in engineering and defense. The proposed method for determining the SG-EOS parameters can be applied to other areas of research involving high-pressure multi-phase flows.

Three-temperature radiation hydrodynamics with PLUTO

In circumstellar disks around T Tauri stars, visible and near-infrared stellar irradiation is intercepted by dust at the disk’s optical surface and reprocessed into thermal infrared. It subsequently undergoes radiative diffusion through the optically thick bulk of the disk. The gas component, overwhelmingly dominated by mass but contributing little to the opacity, is heated primarily by gas-grain collisions. However, in hydrodynamical simulations, typical models for this heating process (local isothermality, β-cooling, and two-temperature radiation hydrodynamics) incorporate simplifying assumptions that limit their ranges of validity. To build on these methods, we developed a “three-temperature” numerical scheme, which self-consistently models energy exchange between gas, dust, and radiation, as a part of the PLUTO radiation-hydrodynamics code. With a range of test problems in 0D, 1D, 2D, and 3D, we demonstrate the efficacy of our method and make the case for its applicability across a wide range of problems in disk physics, including hydrodynamic instabilities and disk-planet interactions.

Structure learning for 3D Point Cloud Generation from Single RGB Images

Abstract3D point clouds can represent complex 3D objects of arbitrary topologies and with fine‐grained details. They are, however, hard to regress from images using convolutional neural networks, making tasks such as 3D reconstruction from monocular RGB images challenging. In fact, unlike images and volumetric grids, point clouds are unstructured and thus lack proper parameterization, which makes them difficult to process using convolutional operations. Existing point‐based 3D reconstruction methods that tried to address this problem rely on complex end‐to‐end architectures with high computational costs. Instead, we propose in this paper a novel mechanism that decouples the 3D reconstruction problem from the structure (or parameterization) learning task, making the 3D reconstruction of objects of arbitrary topologies tractable and thus easier to learn. We achieve this using a novel Teacher‐Student network where the Teacher learns to structure the point clouds. The Student then harnesses the knowledge learned by the Teacher to efficiently regress accurate 3D point clouds. We train the Teacher network using 3D ground‐truth supervision and the Student network using the Teacher's annotations. Finally, we employ a novel refinement network to overcome the upper‐bound performance that is set by the Teacher network. Our extensive experiments on ShapeNet and Pix3D benchmarks, and on in‐the‐wild images demonstrate that the proposed approach outperforms previous methods in terms of reconstruction accuracy and visual quality.

HAP-assisted multi-aerial base station deployment for capacity enhancement via federated deep reinforcement learning

Aerial base stations (AeBSs), as crucial components of air-ground integrated networks, are widely employed in cloud computing, disaster relief, and various applications. How to quickly and efficiently deploy multi-AeBSs for higher capacity gain has become a key research issue. In this paper, we address the 3D deployment optimization problem of multi-AeBSs with the objective of maximizing system capacity. To overcome communication overhead and privacy challenges in multi-agent deep reinforcement learning (MADRL), we propose a federated deep deterministic policy gradient (Fed-DDPG) algorithm for the multi-AeBS deployment decision. Specifically, a high-altitude platform (HAP)-assisted multi-AeBS deployment architecture is designed, in which low-altitude AeBS act as the local nodes to train its own deployment decision model, while the HAP acts as the global node to aggregate the weights of local models. In this architecture, AeBSs do not exchange raw data, addressing data privacy concerns and reducing communication overhead. Simulation results show that the proposed algorithm outperforms fully distributed MADRL algorithms and closely approximates the performance of multi-agent deep deterministic policy gradient (MADDPG), which requires global information during training, but with less training time.

Deep Learning Method Based on Physics-Informed Neural Network for 3D Anisotropic Steady-State Heat Conduction Problems

This paper uses the physical information neural network (PINN) model to solve a 3D anisotropic steady-state heat conduction problem based on deep learning techniques. The model embeds the problem’s governing equations and boundary conditions into the neural network and treats the neural network’s output as the numerical solution of the partial differential equation. Then, the network is trained using the Adam optimizer on the training set. The output progressively converges toward the accurate solution of the equation. In the first numerical example, we demonstrate the convergence of the PINN by discussing the effect of the neural network’s number of layers, each hidden layer’s number of neurons, the initial learning rate and decay rate, the size of the training set, the mini-batch size, the amount of training points on the boundary, and the training steps on the relative error of the numerical solution, respectively. The numerical solutions are presented for three different examples. Thus, the effectiveness of the method is verified.

Prevention of enclosed voids in topology optimization using a cumulative sum flood fill algorithm

Topology optimization has seen increased interest with the rise of additive manufacturing (AM) as a fabrication method, because of its ability to exploit the geometric complexity that AM offers. However, AM still imposes some geometric restrictions on the design, most notably on minimum feature size, overhang angles, and enclosed voids. Enclosed voids are problematic because for many AM methods it is impossible to remove supports, unmelted powder or uncured liquid from them. This paper introduces a filter based on a cumulative sum flood fill algorithm to alleviate this issue in a flexible manner. This filter produces a density field where every enclosed void element is rendered solid. It successfully eliminates enclosed voids in both 2D and 3D problems, with low computational cost due to its geometric nature. In addition we demonstrate direct control over the location, amount, and size of powder removal features by varying boundary conditions for the filter, running additional flood fills, and adding morphology operators, respectively.

Implementation of Chemistry in the Athena++ Code

Chemistry plays a key role in many aspects of astrophysical fluids. Atoms and molecules are agents for heating and cooling, determine the ionization fraction, serve as observational tracers, and build the molecular foundation of life. We present the implementation of a chemistry module in the publicly available magnetohydrodynamic code Athena++. We implement several chemical networks and heating and cooling processes suitable for simulating the interstellar medium (ISM). A general chemical network framework in the KIDA format is also included, allowing users to easily implement their own chemistry. Radiation transfer and cosmic-ray ionization are coupled with chemistry and solved with the simple six-ray approximation. The chemical and thermal processes are evolved as a system of coupled ordinary differential equations with an implicit solver from the CVODE library. We perform and present a series of tests to ensure the numerical accuracy and convergence of the code. Many tests combine chemistry with gas dynamics, including comparisons with analytic solutions, 1D problems of the photodissociation regions and shocks, and realistic 3D simulations of the turbulent ISM. We release the code with the new public version of Athena++, aiming to provide a robust and flexible code for the astrochemical simulation community.

Two-dimensional filtering in the Fourier domain of transient grating coherent artifacts in time-resolved spectroscopy

Removal of coherent artifacts is important in the analysis of time and wavelength resolved spectroscopy data. By taking advantage of the strong correlation between spectra acquired sequentially in time, artifact removal can be formulated as a 2D problem for improved effectiveness. This paper proposes a 2D method to remove transient grating coherent artifacts from femtosecond time-resolved spectroscopy data based on filtering in the Fourier domain, leading to better estimation of the material parameters from the measured data. The method is simple, intuitive, and light on computation resources. The effectiveness of the method is demonstrated with experimental data acquired from a bare gold film with and without coherent artifacts using mutually parallel and perpendicular pump/probe polarizations, as well as with more complex samples (nanostructured gold film on a glass substrate and rhodamine fluorophores in solution). The proposed method is expected to be applicable to coherent artifact removal in other types of time and wavelength-resolved spectroscopy data.

An accurate, robust and efficient convection-pressure flux splitting scheme for compressible Euler flows

The popular Roe's flux difference splitting scheme has high resolution for various types of discontinuities but it fails to satisfy the entropy condition and will encounter different forms of instability while calculating shock waves, such as the post-shock oscillation of the slowly moving shock waves and the carbuncle phenomenon of the multidimensional strong shock waves. In the present work, a simple flux difference splitting scheme based on the idea of convection-pressure splitting is proposed. With application of the Toro-Vázquez splitting procedure, the flux of the 3D Euler equations is split into the convection part and the pressure part. Due to having a complete set of linearly independent eigenvectors, the pressure subsystem can be solved by the conventional flux difference splitting method. The weakly hyperbolic convection subsystem, however, does not have a complete set of linearly independent eigenvectors and thus is solved by the flux difference splitting scheme based on the generalized eigenvectors [1]. In addition, a strategy that combines the THINC reconstruction with the BVD algorithm is employed on the numerical dissipation term of the convection flux to further improve the resolution for contact discontinuities. A comprehensive range of numerical simulations for classical 1D, 2D and 3D benchmark test problems demonstrate the good performance of the proposed scheme.

Topology optimization for material extrusion-based additive manufacturing processes with weak bead bonding

Topology optimization (TO) is a powerful design tool that has been used to design lightweight high-performing structures. Additive manufacturing (AM) is a favoured fabrication method for TO designs because of its high precision and flexibility to realize complex optimized structures. This paper describes a new TO approach that can account for fabrication characteristics and constraints of extrusion-based AM. The fabrication process is mimicked as the design is generated by enforcing a fixed radius feature size in design outputs, and introducing a secondary material between adjacent beads. Lowering the stiffness of this additional material allows for consideration of the weak bead bonds in extrusion-printed materials and promotes continuity of design features. The user can control the radius of the discrete feature size and the relative stiffness of the weak bond. The algorithm is demonstrated on benchmark TO problems in 2D. The design results contain both a description of the physical layout of the structure and a design variable distribution that can be used as a trace for the raster path. The design results are found to respond to user specifications on bead size and relative bond weakening. Continuity of the raster path increases as the stiffness of the bead bonding decreases.

Top-down metacomputing with algebraic dimensionality raising for automating theory-building to enable directly computable multiphysics models

The need to address the fundamental issues associated with the computational model generation process in the context of multiphysics theories that observe conservation laws and relevant assumptions motivates the present work. Accordingly, the goal of this paper is to describe, discuss, and demonstrate the benefits and implications of using metacomputing (i.e., the utilization of computational technologies for computing or generating programs that, in turn, compute the desired results) for theory or model generation, further assisted by metacomputing for raising the semantic and syntactic dimensionality of physics models for continua. The issues associated with the model generation process are identified at the outset. Then, a top-down approach that contains three distinct metacomputing activities is described. First, a meta-theoretical description of generating continuum multiphysics models defined in terms of quantities instantiated from the field of real numbers is described, along with its computational implementation. Then, a computational framework for raising the semantic dimensionality from the reals to the hypercomplex numbers is presented for both 2D and 3D continuum multiphysics problems. The semantic dimensionality is expressed in terms of the order of the algebra used to define the tensorial quantities of interest and their associated operations, as they participate in representing physics models expressed initially as systems of partial differential equations. The utilization of hypercomplex algebras, such as those for complex numbers and quaternions, is demonstrated for representative applications of models. Subsequently, syntactic dimensionality is defined in terms of the basis of the space utilized to write equational systems. Finally, a prototype of a computational system for converting equational systems to directed graphs termed “Algebraic Solution Graphs” is described. Examples of how to utilize these technologies are also presented to convey the efficacy and efficiency of the proposed approach.

Heterogeneous parallel computing method for 3D transient nonlinear thermomechanical problems on CPU-GPU platforms

A heterogeneous parallel computing method for 3D transient nonlinear thermomechanical problems is proposed based on CPU-GPU platforms. The method is developed based on the stable node-based smoothed finite element method (SNS-FEM) and element-by-element (EBE) strategy. The SNS-FEM method ensures the accuracy of temperature and displacement solution. To obtain higher computational efficiency, a series of parallel computing strategies are proposed in this paper. A one-to-one mapping relationship is established between smoothing domains calculation and threads in GPU. To improve the efficiency of constructing the smoothing domain, a semi-parallel construction method is developed. And a preindexing method is proposed to improve the computational efficiency of solving linear equations by the parallel preconditioned conjugate gradient (PCG) method. The developed heterogeneous parallel computing method is quite accurate and efficient in computing the model composed of tetrahedral elements, obtaining a speedup ratio of 52.31 when the model contains 67,204 degrees of freedom.

Multigrid multilevel Monte Carlo for a lattice with a displacement

AbstractThe Hutchinson method can be used to estimate the trace of a function of a matrix A, that is, , stochastically. With the variance of the Hutchinson estimator decreasing as , techniques to reduce the variance of this estimator become necessary due to the high accuracy required by some calculations in scientific computing. In lattice QCD, where A is the Dirac operator D stemming from a discretization of the Dirac equation, the accuracy of some calculations involving renders them practically unfeasible if one uses the Hutchinson estimator to approximate the trace. One such variance reduction technique, known as multigrid multilevel Monte Carlo, has been introduced recently to deal with for the Laplace 2D, Gauge Laplacian, and Schwinger problems. We use it here in the context of lattice QCD, and moreover, we analyze its impact when dealing with , where is the matrix that emerges when a displacement in one of the four spacetime dimensions of the lattice is introduced. This latter trace is of importance when computing generalized parton distributions in lattice QCD.

QoS-aware UAV mounted base station deployment in a disaster scenario with user position estimation

The base station installed on the unmanned aerial vehicle, referred to as the UAV-mounted base station (UBS), is considered an innovative paradigm for restoring cellular connectivity in areas where a terrestrial network does not exist, has been demolished, or is overcrowded. The challenging issue in this context is how to acquire the position information of user equipment (UE), characterize the air-to-ground (A2G) channel, and identify the optimal locations for quality-of-service (QoS)-aware 3D UBS deployment. To tackle these issues, we proposed a framework for 3D UBS deployment with the goal of maximizing the number of UEs covered. First, unlike the existing UBS deployment schemes, which ignore the UEs' localization, we propose a received signal strength indicator (RSSI)-based localization (RBL) approach to localize the randomly distributed UEs. Then, the 3D UBS deployment problem is divided into horizontal position optimization to meet the QoS requirements of individual UEs’ and vertical position optimization for path loss minimization. We propose a K-means initialized grey wolf optimization (KIGWO) approach in which UBSs are deployed to maximize the covered UEs percentage while taking the QoS requirements of individual UEs’ and UBS’ total capacity into account. Finally, the effectiveness of the proposed approach is demonstrated through Monte Carlo simulations conducted in four different environmental scenarios.

An efficient accurate scheme for solving the three-dimensional Bratu-type problem

In this manuscript, we present an innovative discretization algorithm designed to address the challenges posed by the three-dimensional (3D) Bratu problem, a well-known problem characterized by non-unique solutions. Our algorithm aims to achieve exceptional precision and accuracy in determining all potential solutions, as previous studies in the literature have only managed to produce limited accurate results. Additionally, our computational scheme approximates the critical values of the transition parameter. Moreover, we establish a rigorous proof demonstrating the uniform convergence of the approximation sequence to the exact solution of the original problem, under the condition that the initial guess is sufficiently close to the true solution. This theoretical result further establishes the reliability of our algorithm. To evaluate the effectiveness of our proposed approach, we conduct extensive numerical simulations, which convincingly demonstrate its capability to accurately solve the 3D Bratu problem while effectively determining the critical values of the transition parameter. Furthermore, we investigate the bifurcated behavior of the solution by analyzing the infinity norm for various values of the transition parameter. The outcomes of our study offer a robust and efficient method for tackling the 3D Bratu problem, making a significant contribution to the field of numerical analysis of partial differential equations (PDEs) where non-unique solutions are commonly encountered. Our algorithm's ability to produce accurate results for this challenging problem showcases its potential for broader applications in diverse scientific and engineering domains.

A Hybrid Reproducing Kernel Particle Method for Three-Dimensional Elasticity Problems

This study presents a fast meshless method called the hybrid reproducing kernel particle method (HRKPM) for the solution of three-dimensional (3D) elasticity problems. The equilibrium equations of 3D elasticity are divided into three groups of equations, and two equilibrium equations are contained in each group. By coupling the discrete equations for solving two arbitrary groups of equations, the complete solution of 3D elasticity can be obtained. For an arbitrary group of equations, the 3D elasticity problem is transformed into a series of associated two-dimensional (2D) ones, which is solved by the RKPM to derive the discrete formulae. The discrete equations of 2D problems are combined using the difference method in dimension splitting direction. Then, arbitrarily choosing another group of equilibrium equations, the discrete equation of another group of 2D problems can be obtained similarly. By combining the discrete equations for these two groups of 2D problems, the solution to an original 3D problem will be reached. The numerical results show that the HRKPM performs better than RKPM in solution efficiency.

THE OCCURRENCE OF EXTREME WAVE HEIGHT IN A TWO-DIMENSIONAL RANDOM WAVEFIELD IN COASTAL AREA

As the water waves come to the coastal area, the variation in dispersion relation due to the spatial inhomogeneity brings about the deformation of the wave shape. With the local bathymetry effect, the propagation of the wave experiences a complicated evolution process, including the reflection, wave shoaling and breaking, etc. Considering the directional spreading effect and wave refraction becomes indispensable when it comes to a two-dimensional (2D) problem in the random wavefield. Mori et al. (2011) indicated that the distribution of maximum wave height in deep-water is decided by the directional dispersion. In this research, we aim to discuss the occurrence of maximum wave height in the 2D wave evolution in the coastal area. It helps to estimate better extreme events in the prevention work of coastal hazards. To simulate the 2D propagation, we develop a nonlinear model as an extension work of Lyu et al. (2021), which considers the high order harmonic interactions of irregular waves before the breaking in surf zone.

3D reconstruction based on hierarchical reinforcement learning with transferability

3D reconstruction is extremely important in CAD (computer-aided design)/CAE (computer-aided Engineering)/CAM (computer-aided manufacturing). For interpretability, reinforcement learning (RL) is used to reconstruct 3D shapes from images by a series of editing actions. However, typical applications of RL for 3D reconstruction face problems. The search space will increase exponentially with the action space due to the curse of dimensionality, which leads to low performance, especially for complex action spaces in 3D reconstruction. Additionally, most works involve training a specific agent for each shape class without learning related experiences from others. Therefore, we present a hierarchical RL approach with transferability to reconstruct 3D shapes (HRLT3D). First, actions are grouped into macro actions that can be chosen by the top-agent. Second, the task is accordingly decomposed into hierarchically simplified sub-tasks solved by sub-agents. Different from classical hierarchical RL (HRL), we propose a sub-agent based on augmented state space (ASS-Sub-Agent) to replace a set of sub-agents, which can speed up the training process due to shared learning and having fewer parameters. Furthermore, the ASS-Sub-Agent is more easily transferred to data of other classes due to the augmented diverse states and the simplified tasks. The experimental results on typical public dataset show that the proposed HRLT3D performs overwhelmingly better than recent baselines. More impressingly, the experiments also demonstrate the extreme transferability of our approach among data of different classes.

Stochastic virtual element methods for uncertainty propagation of stochastic linear elasticity

This paper presents stochastic virtual element methods for propagating uncertainty in linear elastic stochastic problems. We first derive stochastic virtual element equations for 2D and 3D linear elastic problems that may involve uncertainties in material properties, external forces, boundary conditions, etc. A stochastic virtual element space that couples the deterministic virtual element space and the stochastic space is constructed for this purpose and used to approximate the unknown stochastic solution. Two numerical frameworks are then developed to solve the derived stochastic virtual element equations, including a Polynomial Chaos approximation based approach and a weakly intrusive approximation based approach. In the Polynomial Chaos based framework, the stochastic solution is approximated using the Polynomial Chaos basis and solved via an augmented deterministic virtual element equation that is generated by applying the stochastic Galerkin procedure to the original stochastic virtual element equation. In the weakly intrusive approximation based framework, the stochastic solution is approximated by a summation of a set of products of random variables and deterministic vectors, where the deterministic vectors are solved via converting the original stochastic problem to deterministic virtual element equations by the stochastic Galerkin approach, and the random variables are solved via converting the original stochastic problem to one-dimensional stochastic algebraic equations by the classical Galerkin procedure. This method avoids the curse of dimensionality in high-dimensional stochastic problems successfully since all random inputs are embedded into one-dimensional stochastic algebraic equations whose computational effort weakly depends on the stochastic dimension. Numerical results on 2D and 3D problems with low- and high-dimensional random inputs demonstrate the good performance of the proposed methods.

Analyzing Three-Dimensional Laplace Equations Using the Dimension Coupling Method

Due to the low computational efficiency of the Improved Element-Free Galerkin (IEFG) method, efficiently solving three-dimensional (3D) Laplace problems using meshless methods has been a longstanding research direction. In this study, we propose the Dimension Coupling Method (DCM) as a promising alternative approach to address this challenge. Based on the Dimensional Splitting Method (DSM), the DCM divides the 3D problem domain into a coupling of multiple two-dimensional (2D) problems which are handled via the IEFG method. We use the Finite Element Method (FEM) in the third direction to combine the 2D discretized equations, which has advantages over the Finite Difference Method (FDM) used in traditional methods. Our numerical verification demonstrates the DCM’s convergence and enhancement of computational speed without losing computational accuracy compared to the IEFG method. Therefore, this proposed method significantly reduces computational time and costs when solving 3D Laplace equations with natural or mixed boundary conditions in a dimensional splitting direction, and expands the applicability of the dimension splitting EFG method.