Dynamic Refinement Research Articles

ADAPTIVE PHASE-FIELD CONCURRENT MULTISCALE METHOD FOR EFFICIENT SIMULATION OF QUASI-BRITTLE FRACTURE

An adaptive phase-field concurrent multiscale method for efficient simulation of quasi-brittle fracture is presented. In this method, the analysis model is first subjected to coarse mesh discretization and the corresponding damage phase field calculation analysis. Then, adaptive dynamic local mesh refinement is performed for the coarse scale elements exceeding the given damage threshold during the iterative process. The locally refined mesh is defined as the local subdomain, the outermost coarse elements of the refined mesh, and the coarse elements without refinement are defined as the global subdomain. The variant s-version method is used to realize the direct coupling connection of mismatched meshes in different subdomains and the application of the continuity condition of field variables on the global-local subdomain interface. The division of the local subdomain, the global subdomain, and their overlapping domain are dynamically updated with the crack propagation path in the proposed method. The generation of the global-local computing mesh has great flexibility without the need for scale separation, which provides a more concise and flexible implementation for multiscale phase field adaptive simulation. The proposed method overcomes the extra burden and complexity of field variable conversion between coarse and fine scales, imposition of continuity conditions, and program implementation in existing phase field multiscale methods, which can be easily applied to the analysis on damage-fracture behavior of quasi-brittle structures. Typical examples verify the correctness, robustness, and advantages of the method.

Efficient Dynamic Mesh Refinement Technique for Simulation of HPM Breakdown-Induced Plasma Pattern Formation

Numerical simulation of the complex plasma dynamics associated with high power, high-frequency microwave breakdown at high pressures, leading to the formation of filamentary plasma structures such as self-organized plasma arrays, is a computationally challenging problem. The widely used 2-D electromagnetic (EM)–plasma fluid model, which accurately captures the experimental observations, requires a runtime of several days to months to simulate standard problems due to stringent numerical requirements in terms of cell size and time step. This article presents a self-aware mesh refinement (MR) algorithm that uses a coarse mesh and a fine mesh that dynamically expand based on the plasma profile topology to resolve the sharp gradients in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$E$ </tex-math></inline-formula> -fields and plasma density in the breakdown region. The dynamic MR (DMR) technique is explained in detail, and its performance has been evaluated using a standard benchmark microwave breakdown problem. We observe a speedup of 8 (of the order of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(r^{3})$ </tex-math></inline-formula> , when the refinement factor ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula> ) is 2) compared with a traditional single uniform fine-mesh-based simulation. The technique is scalable and performs better when the problem size increases. We also present a comprehensive spatio-temporal visual analysis to explain the complex physics of high-power microwave (HPM) breakdown, leading to self-organized plasma filaments as an application of the DMR technique.

An adaptive numerical method for simulating diffusion flame jets

In this paper, we present an adaptive numerical methodology for a reacting three-dimensional low-Mach number flow. This computational strategy combines an adaptive mesh refinement (AMR), an implicit–explicit time stepping strategy (IMEX), an extension of increment-pressure projection method, and a mixture fraction to model the chemistry combustion dynamics. To accurately resolve sharp gradients, vorticity shedding, and localized small length scale flow features, dynamic adaptive mesh refinement (given by hierarchical nested Cartesian grid patches) is employed. That spatial dynamic adaptation is used in conjunction with a variable time step, second-order, linearly implicit time integration scheme. The capabilities of the present numerical method are demonstrated by numerical verification and simulation of two classical diffusion flame examples from literature.

Design high-performance AZ31 ultrathin strip through multi-pass electroplastic rolling without off-line annealing

The influence of the electropulsing parameters including the current density and the frequency, on the rolling force, the microstructure and the mechanical properties of AZ31 strips processed by electroplastic rolling (EPR) were investigated in this study. On the basis, the double grain refinement mechanism, combing the rapid completed static recrystallization refinement (SRX) of AZ31 strip before the roll with the subsequent dynamic recrystallization refinement (DRX) of AZ31 strips at the deformed zone, was put forward in the whole process of EPR. According to the mechanism of double grain refinement, an innovative method of the production of AZ31 ultrathin strip with excellent comprehensive properties is established and verified. The AZ31 ultrathin strip with the thickness of 0.35 mm was obtained at the optimal electropulsing parameters, and the total reduction of 69% can be obtained though only 2 continuous passes without any off-line intermediate heat treatment in the process of EPR; besides, the maximum rolling temperature does not exceed 483 K. It is indicated that the technology of EPR with the high current density of the electropulsing is one of the most potential method to improve the plastic formability of hardly-deformed metals.

Simultaneously enhancing strength-ductility synergy and strain hardenability via Si-alloying in medium-Al FeMnAlC lightweight steels

We studied the initial microstructures, mechanical responses and deformation-induced microstructures of the medium-Al Fe-21Mn-6Al-1C-xSi (x = 0, 1.5, 3 wt.%) lightweight steels both in their solution-treated and aged states. Our results reveal that nano-sized long-range ordered domains exist in the solution-treated steels, which feature L12 type ordering in the 0Si and 1.5Si steels and L′12 type ordering in the 3Si steel. Aging at 550 °C for 20 h has little effect on the microstructures of the 0Si steel, but leads to κ′-carbide precipitation in the 1.5Si steel. For the 3Si steel, aging at 550 °C for 1 h already results in the precipitation of uniformly-distributed nano-sized κ′-carbides (4.2 nm). The strength, ductility and strain hardenability of the solution-treated steels all enhance with increasing Si content. The yield strength (YS) of the aged steels with κ′-carbides enhances with increasing aging time, accompanied by the reduction of ductility. The short-time (1 h) aged 3Si steel exhibits excellent strength-ductility synergy, with YS > 900 MPa and total elongation > 50%. The increase in YS with Si addition originates from the grain boundary, solid-solution and order strengthening. For the 0Si steel, the strain hardening is governed by the evolution of high-density dislocation walls and microbands. The occurrence of both dynamic slip band refinement (DSBR) and twinning-induced plasticity effects in the 3Si steel accounts for the increase of strain hardenability with Si-alloying. The DSBR effect still exists and the progressively-formed slip bands are homogeneously distributed in the short-time aged 3Si steel, explaining its high ductility.

Achieving ultra-high elongation of 1401% in a warm-rolled medium Mn lightweight steel with dual-phase lamellar structure

The present work reports a dual-phase lamellar structure to combine ultra-high superplastic elongation and relatively low deformation temperature in a novel Al-added medium Mn lightweight steel. The specimens were controlled rolling in a two-phase zone; Hence the microstructure contained a high-volume fraction of residual austenite in the ferrite matrix. The ultra-high elongation of 1401% was obtained at the deformation temperature of 775 °C, which is more than 50 °C lower than others reported of the cold-rolled sheets. Interestingly, near 800 °C, due to the enhanced DIFT effect, the ductility was reduced by temperature rise, which is opposite to the condition of the cold-rolled sheets. The ultrahigh elongation at 775 °C was ascribed to the continued recovery and recrystallization of the deformation-induced ferrite, which not only achieves dynamic grain refinement but also maintains the balance of stress distribution between the two phases.

Effect of cold rolling and subsequent heat treatment on microstructural evolution and mechanical properties of Fe-Mn-Al-C-(Ni) based austenitic low-density steels

Thermo-mechanical processing in a two-phase domain of low-density steel (LDS) has the potential of enhancing strength-ductility combination. In the present study, the effects of alloy composition, cold rolling and heat treatment temperature (973–1173 K) on concurrent precipitation of κ-carbide/B2 particles and recrystallization and subsequently, mechanical properties include hardness variation and tensile response are evaluated. In order to understand the synergistic effect of Mn/Ni ratio towards selecting the two-phase processing window, three LDS alloy compositions, namely Fe–28Mn–9Al-0.9C, Fe–28Mn–9Al-0.9C–5Ni and Fe–15Mn–9Al-0.9C–5Ni (in weight percent) are vacuum induction melted, hot rolled and then cold rolled to 50% reduction in thickness at room temperature. The LDS alloys containing Ni showed much delayed recrystallization as compared to Ni-free LDS. The Mn/Ni ratio played a vital role towards controlling precipitation and recrystallization and accordingly, the mechanical properties. All the three alloys exhibited similar hardness, strength and ductility levels after 50% cold reduction. Upon heat treatment, there was precipitation of intergranular and intragranular B2 phase particles along with κ-carbides, whose fraction decreased with increasing the temperature. The tensile response of LDS alloys was influenced primarily by the volume fraction of these precipitates as well as the recrystallized austenite grains. Planar slip activity, dynamic slip band refinement in conjunction with dislocation-twin interaction mechanisms were noticed in fully recrystallized austenite and thereby leading to enhanced strain hardening and ductility. Furthermore, lowering Mn in Ni containing LDS reduced the processing temperature window of the alloy in two-phase region.

Ultra-strong heavy-drawn eutectic high entropy alloy wire

Metallic wires with high strength-ductility at both room and cryogenic temperatures are always pursued for engineering applications. However, traditional metallic wires are tortured inevitably by strength-ductility trade-off dilemma. In this work, a gradient heterogeneous lamella structure, characterized with hard gradient-distributed B2 lamellae embedded in soft FCC lamellae matrix, is introduced into AlCoCrFeNi2.1 eutectic high entropy alloy (EHEA) wire by well-designed multiple-stage heavy-drawn and heat treatment processes, which achieves an outstanding strength-ductility synergy. This EHEA wire exhibits not only high tensile strength of 1.85 GPa and sufficient uniform elongation of ∼12% at room temperature, but also ultra-high tensile strength of 2.52 GPa and even slightly elevated uniform elongation of ∼14% at cryogenic temperature. In-depth microstructure characterization indicates that the gradient heterogeneous lamella structure facilitates a radial gradient distribution of geometrically necessary dislocation (GND) during tension, i.e., the GND density decreases gradually from the surface region to the central region of EHEA wire, which induces pronounced strain gradient strengthening effect and thus greatly benefits the mechanical properties. Intriguingly, at cryogenic temperature, dense cross-slip which gives rise to intensively dynamic microstructure refinement is firstly observed in the B2 phase of EHEA wire. The activation of cross-slip provides sufficient ductility while inducing evidently dynamic Hall-Petch effect, becoming the most effective deformation mechanism contributing to the unprecedented cryogenic tension properties. This work sheds light on designing ultra-strong EHEA wire and other advanced metallic wires.

Ultrahigh strength and high ductility lightweight steel achieved by dual nanoprecipitate strengthening and dynamic slip refinement

In the present study, the microstructure and tensile properties of a newly prepared Fe–25Mn–10Al–1.2C–0.4 V (wt.%) lightweight steel subjected to a two-step thermomechanical treatment, annealing, and subsequent aging were investigated. The aged steel contains nanosized VC particles, κ-carbide, and a small number of ferrites. As a result, it exhibited ultrahigh yield strength of 1216 MPa due to multiple strengthening mechanisms, where the nanosized carbides and second phase strengthening process contributed 635 MPa. Additionally, the steel showed to have good ductility (28 % total elongation) even under aged conditions, which is mainly due to the refinement of its slip bands.

Efficient multi-level hp-finite elements in arbitrary dimensions

We present an efficient algorithmic framework for constructing multi-level hp-bases that uses a data-oriented approach that easily extends to any number of dimensions and provides a natural framework for performance-optimized implementations. We only operate on the bounding faces of finite elements without considering their lower-dimensional topological features and demonstrate the potential of the presented methods using a newly written open-source library. First, we analyze a Fichera corner and show that the framework does not increase runtime and memory consumption when compared against the classical p-version of the finite element method. Then, we compute a transient example with dynamic refinement and derefinement, where we also obtain the expected convergence rates and excellent performance in computing time and memory usage.

Local mesh refinement sensor for the lattice Boltzmann method

A novel mesh refinement sensor is proposed for lattice Boltzmann methods (LBMs) applicable to either static or dynamic mesh refinement algorithms. The sensor exploits the kinetic nature of LBMs by evaluating the departure of distribution functions from their local equilibrium state. This sensor is first compared, in a qualitative manner, to three state-of-the-art sensors: (1) the vorticity norm, (2) the Q-criterion, and (3) spatial derivatives of the vorticity. This comparison shows that our kinetic sensor is the most adequate candidate to propose tailored mesh structures across a wide range of physical phenomena: incompressible, compressible subsonic/supersonic single phase, and weakly compressible multiphase flows. As a more quantitative validation, the sensor is then used to produce the computational mesh for two existing open-source LB solvers based on inhomogeneous, block-structured meshes with static and dynamic refinement algorithms, implemented in the Palabos and AMROC-LBM software, respectively. The sensor is first used to generate a static mesh to simulate the turbulent 3D lid-driven cavity flow using Palabos. AMROC-LBM is then adopted to confirm the ability of our sensor to dynamically adapt the mesh to reach the steady state of the 2D lid-driven cavity flow. Both configurations show that our sensor successfully produces meshes of high quality and allows to save computational time.

A mass-conserving and volume-preserving lattice Boltzmann method with dynamic grid refinement for immiscible ternary flows

In this paper, a lattice Boltzmann model with dynamic grid refinement is proposed for immiscible ternary flows, which is capable of conserving the total mass and preserving the volume of each phase. The application of interpolation schemes in adaptive mesh refinement (AMR) techniques results in the violation of the total mass of the fluids system within the lattice Boltzmann method (LBM) framework. In the present model, a source term with two free parameters is introduced into the interface capturing equation, which can be determined by the mass conservation and the volume preservation properties. A piecewise constant function has been deliberately incorporated into the source term in order to avoid the appearance of an unphysical fluid at the interface of other two fluids. Based on a block-structured AMR method, the governing equations for phase-field variables and flow hydrodynamic properties are solved by the finite-difference multiple-relaxation-time (MRT) LBM. Simulations of several typical problems are performed in order to evaluate the accuracy and applicability of the proposed model. The numerical results demonstrate that the present model can conserve both mass and volume at the same time as well as reduce numerical dispersion in the bulk region.

CFD model of slot die coating for lithium-ion battery electrodes in 2D and 3D with load balanced dynamic mesh refinement enabled with a local-slip boundary condition in OpenFOAM

Slot die coating is a state-of-the-art process to manufacture lithium-ion battery electrodes with high accuracy and reproducibility, covering a wide range of process conditions and material systems. Common approaches to predict process windows are one-dimensional calculations with a limited expressiveness. A more detailed analysis can be performed using CFD simulations, which are often based on in-house code or closed-source software. In this study, a two-phase CFD model in two and three dimensions was created in OpenFOAM with the intent to provide a method for more detailed investigations of the slot die coating process with open access to source code and files. A custom boundary condition enables the proper description of the wetting behavior in the two-dimensional model. The combination of standard no-slip boundary conditions at the substrate boundary with the volume-of-fluid solution algorithm leads to a method-related air entrainment, which was prevented by allowing local slip at the dynamic wetting line at the upstream meniscus in the two-dimensional model. Additionally, a load-balancing dynamic refinement algorithm was implemented to minimize the computational effort and increase the ease of use of the simulation environment. The simulation was validated by comparing the simulated process limits to experimental observations, showing good agreement. As a result, this model enables detailed analyses regarding the influences of slot die geometries, material properties, and process parameters on the coating stability and wet-film profile.

Hot deformation behavior and microstructure evolution of the spray deposited and secondary hot extruded 2195 Al–Li alloy

This work aims to investigate the influence of hot deformation parameters on the microstructure evolution and deformation behavior of the extruded 2195 Al–Li alloy, as well as to explore its optimized hot deformation windows based on the hot compression tests carried out on a Gleeble-1500 thermo-mechanical simulator in the temperature range 370–520 °C and with the strain rate of 0.001–10 s−1. The results revealed that the extruded 2195 Al–Li alloy plate with a large aspect ratio had a lower deformation activation energy with respect to the spray deposited and as-cast 2195 Al–Li alloys owing to the existence of a large number of coarse second phases and LAGBs in the extruded plate. The optimized hot deformation temperature of the alloy ranged from 405 °C to 490 °C with a strain rate from 0.001 to 0.1 s−1. Hot deformation under the optimized conditions led to the occurrence of continuous dynamic recrystallization and resultant microstructure refinement. Although the occurrence of continuous dynamic recrystallization weakened the <101> deformation texture, but triggered another texture component with <001>//ND. Deformation at low temperature and high strain rate induced flow instability due to insufficient dynamic softening. In addition, the flow instability at a temperature higher than 490 °C arose from partial remelting of Al2Cu phase along grain boundaries. The work can provide an effective guidance for the designation of secondary hot processing of the extruded 2195 Al–Li alloy.

Wake modeling and simulation of an experimental wind turbine using large eddy simulation coupled with immersed boundary method alongside a dynamic adaptive mesh refinement

Accurate numerical models of the flow around wind turbines is highly relevant for optimizing the energy efficiency of wind farms. The main goal of this work is to apply large eddy simulation (LES) along with an immersed boundary (IB) method to generate spatial and temporal information of the velocity field and forces acting on a fully-resolved NREL S809 airfoil and NREL Phase VI wind turbine. The numerical framework used in the simulations performs LES under a Cartesian block-structured mesh that is dynamically refined via adaptive mesh refinement (AMR) to increase accuracy and reduce computational costs. The mesh refinement criteria is based on Lagrangian points and vorticity. Solid surfaces of the wind turbine are captured using the Lagrangian formulation of the IB method. The simulations are based on the NREL Phase VI wind turbine, where blade analysis of lift and drag coefficients were performed, followed by time-averaged streamwise velocity and vorticity evaluations. For different angles of attack, the wake centerline velocity analysis demonstrates high energy extraction in the near wake of the wind turbine blade. In terms of validation, the drag coefficient of the NREL S809 airfoil achieves better agreement with the experimental data than the lift coefficient. Validation from the NREL Phase VI shows that the power performance difference between the simulation and experiment is lower than 6%. Wake analysis of the wind turbine scenario are based on downstream profiles of the time-averaged streamwise velocity. The numerical simulation shows a higher loss of kinetic energy in the near wake region, mainly in the centerline, compared to benchmark data, but achieves very similar results to literature in the far-wake region.

Local Similarity Pattern and Cost Self-Reassembling for Deep Stereo Matching Networks

Although convolutional neural network based stereo matching architectures have made impressive achievements, there are still some limitations: 1) Convolutional Feature (CF) tends to capture appearance information, which is inadequate for accurate matching. 2) Due to the static filters, current convolution based disparity refinement modules often produce over-smooth results. In this paper, we present two schemes to address these issues, where some traditional wisdoms are integrated. Firstly, we introduce a pairwise feature for deep stereo matching networks, named LSP (Local Similarity Pattern). Through explicitly revealing the neighbor relationships, LSP contains rich structural information, which can be leveraged to aid CF for more discriminative feature description. Secondly, we design a dynamic self-reassembling refinement strategy and apply it to the cost distribution and the disparity map respectively. The former could be equipped with the unimodal distribution constraint to alleviate the over-smoothing problem, and the latter is more practical. The effectiveness of the proposed methods is demonstrated via incorporating them into two well-known basic architectures, GwcNet and GANet-deep. Experimental results on the SceneFlow and KITTI benchmarks show that our modules significantly improve the performance of the model. Code is available at https://github.com/SpadeLiu/Lac-GwcNet.

Study of novel steam assisted gravity drainage multilateral wells with dynamic gridding

SAGD (steam assisted gravity drainage) performance and its stream chamber growth are primarily determined by the vertical permeability of a reservoir. To deal with inter-bedded shale (IBS)-isolated intervals in bitumen reservoirs and improve steam chamber conformance, novel multilateral (MLT) wells with laterals and/or vertical legs in their trajectories are drilled to penetrate IBS. PetroChina Canada LTD. (PCC) has implemented MLT wells as a technology trial to evaluate potential mitigation to the presence of IBS in its MacKay River SAGD Project. Taking into account both accuracy and efficiency, dynamic local grid refinement (DLGR) is incorporated into the description of the mass and heat transfer phenomena in the vicinities of MLT wells. Also, to represent MLT injection and production wells as open hole branches, their lateral properties are adjusted by considering pore-scale mechanisms of fluid flow and heat transfer. With all these novel features established, the impacts of MLT wells on steam chamber growth and oil recovery are evaluated. It is discovered that MLT wells are conducive to increasing both injectivity and productivity due to the improvement of contact and drainage areas. Besides, how MLT wells perform with various steam operation strategies, geological parameters, injection pressure and NCG (non-condensable gas) wind-down scenarios is assessed.

Three-dimensional features of the lateral thermal plume discharge in the deep cross-flow using dynamic adaptive mesh refinement

Three-dimensional features of the lateral thermal plume discharge in the deep cross-flow using dynamic adaptive mesh refinement

Modeling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods

A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial discretization, which enables boundary and interface conditions to be enforced with high-order accuracy on curved embedded geometries. High-order accuracy is achieved via high-order quadrature rules for implicitly-defined domains and boundaries, whilst a cell-merging strategy addresses the presence of small cut cells. The framework is used to discretize the governing equations of elastodynamics, written using a first-order hyperbolic momentum-strain formulation, and an exact Riemann solver is employed to compute the numerical flux at the interface between dissimilar materials with general anisotropic properties. The space-discretized equations are then advanced in time using explicit high-order Runge–Kutta algorithms. Several two- and three-dimensional numerical tests including dynamic adaptive mesh refinement are presented to demonstrate the high-order accuracy and the capability of the method in the elastodynamic analysis of single- and bi-phases solids containing complex geometries.

A geometrical optimization and comparison study on the charging and discharging performance of shell-and-tube thermal energy storage systems

Shell-and-tube latent heat thermal energy storage (ST-LHTES) systems have been extensively studied due to their high thermal/cold storage capacity during the charging/discharging process and their wide range of applications. The thermal performance of these systems is heavily dependent on the shape and geometry of the shell part. This research aims to investigate the transient heat transfer of phase change material (PCM) in the vertical ST-LHTES systems during charging (melting) and discharging (solidification) and the impact of geometric design on the heat transfer characteristics and consequently the thermal performance of the system in both processes. For this purpose, phase change heat transfer in a conventional cylindrical shell is compared with conical configurations with arbitrary inclination angles. The different heat transfer characteristics, e.g., the rate of phase change fraction and the energy stored/released, are determined and compared for all systems to evaluate their thermal performance and find the optimal design. The phase change process is also numerically visualized to track the phase change interface during both charging and discharging processes. A dynamic adaptive mesh refinement technique is implemented to capture gradients and simulate phase change front accurately. Depending upon the inclination angle, a favorable result can be achieved for the charging process in conical shape compared with a cylindrical geometry, while inverse results are obtained for the discharging process. In other words, increasing the lateral slope of the shell from a vertical to tilted state enhances the melting process resulting in a faster energy storage rate during the charging process, whereas decreasing this slope leads to better thermal performance for discharging process. The optimum designs can improve the system performance by 52% and 56% for the charging and discharging processes, respectively. A comprehensive experimental setup is developed for the cylindrical case to visualize and compare the charging and discharging process experimentally as well. Results obtained from numerical simulations exhibit similar patterns to experimental visualizations.