Adaptive Meshing Technique Research Articles

An adaptive level-set/square-root-conformation representation/discontinuous Galerkin method for simulating viscoelastic two-phase flow systems

A new numerical method, which is based on the coupling of adaptive mesh technique, level set (LS) method, square-root-conformation representation (SRCR) approach, and discontinuous Galerkin (DG) method within the dual splitting framework, is developed for viscoelastic two-phase flow problems. This combination has been more effective than expected. The LS method is performed to capture the moving interface due to its efficiency and simplicity when dealing with the significant interface deformations. The dual splitting scheme is applied to decouple the whole system into subequations, which circumvent the limitation of the Ladyzhenskaya-Babuška-Brezzi condition. The SRCR approach is employed to reconstruct the Oldroyd-B constitutive equation to solve the high Weissenberg number problem. The high-order DG method is performed for the spatial discretizations of equations to deal with the convection-dominated problems. In addition, the reinitialization method of the LS function and a simple mass correction technique are applied to guarantee the mass conservation in calculation. In this coupled method, there is no need to require reinitialization within every time step but after suitable time steps. Meanwhile, the adaptive mesh technique is implemented in the coupling procedure, which greatly improves the computational efficiency. The coupled algorithm is performed to simulate the swirling deformation flow, Rayleigh–Taylor instability and bubble rising problems. And the influences of the parameters on the rising speed and shape of bubble in viscoelastic liquid are analyzed in detail. The numerical results indicate that the coupled algorithm is effective and accurate for simulating the interface evolution problems with complex topological structure changes, and can guarantee the mass conservation property.

Seismic performance of inclined discontinuous broken-back block-type gravity quay walls: Numerical investigation and GEP-based modeling

This study explores the seismic performance of discontinuous broken-back block-type gravity quay walls with varying configurations using the finite element method (FEM). For this purpose, plane strain FE meshes are constructed by integrating adaptive meshing and error-based adaptivity techniques. To simulate discontinuities along the wall height and the interaction between the wall and the neighboring medium, interface elements are comprehensively applied between the concrete blocks and between the wall and the surrounding soils. The developed FE models are initially validated against observations from corresponding 1g shaking table tests available in the literature. The primary objective is to evaluate the effectiveness of different inclination angles of the wall body, its base block, and the underlying seabed soil layer in mitigating seismic deformations and lateral earth pressures. FE results reveal that simultaneously inclining the wall body, base block, and seabed layer by 9° significantly reduces permanent horizontal displacement, base sliding, and settlement of the wall. Under a worst-case seismic scenario with a PGA of 0.9g and a frequency of 3 Hz, these deformation parameters decrease by 37.26%, 14.47%, and 48.88%, respectively, compared to the non-inclined quay wall. The suggested mitigation approach improves the overall stability and serviceability of ports and their inland infrastructures during seismic and post-seismic events. This study also develops a predictive polynomial model utilizing Gene Expression Programming (GEP) based on 630 data points derived from validated FE models. The GEP model aims to predict the horizontal displacement of both inclined and non-inclined broken-back block-type quay walls. The novelty of the current research lies in the investigation of inclined configurations as a remediation technique to mitigate deformations and enhance the seismic resilience and performance of broken-back block-type quay walls, utilizing an advanced FE modeling approach. Additionally, a practical machine learning-based model is proposed to estimate the wall's seismic deformations.

A novel numerical method for mixed-frame multigroup radiation-hydrodynamics with GPU acceleration implemented in the quokka code

Abstract Mixed-frame formulations of radiation-hydrodynamics (RHD), where the radiation quantities are computed in an inertial frame but matter quantities are in a comoving frame, are advantageous because they admit algorithms that conserve energy and momentum to machine precision and combine more naturally with adaptive mesh techniques, since unlike pure comoving-frame methods they do not face the problem that radiation quantities must change frame every time a cell is refined or coarsened. However, implementing multigroup RHD in a mixed-frame formulation presents challenges due to the complexity of handling frequency-dependent interactions and the Doppler shift of radiation boundaries. In this paper, we introduce a novel method for multigroup RHD that integrates a mixed-frame formulation with a piecewise powerlaw approximation for frequency dependence within groups. This approach ensures the exact conservation of total energy and momentum while effectively managing the Lorentz transformation of group boundaries and evaluation of group-averaged opacities. Our method takes advantage of the locality of matter-radiation coupling, allowing the source term for Ng frequency groups to be handled with simple equations with a sparse Jacobian matrix of size Ng + 1, which can be inverted with O(Ng) complexity. This results in a computational complexity that scales linearly with Ng and requires no more communication than a pure hydrodynamics update, making it highly efficient for massively parallel and GPU-based systems. We implement our method in the GPU-accelerated RHD code quokka and demonstrate that it passes a wide range of numerical tests, including preserving the asymptotic diffusion limit. We demonstrate that the piecewise powerlaw method shows significant advantages over traditional opacity averaging methods for handling rapidly variable opacities with modest frequency resolution.

Effect of hot rolling process parameters on surface wear of descaling rolls

PurposeThe purpose of this study is to explain the effect of slab and roll initial temperatures on the wear characteristics of the surface of hot roll descaling rolls.Design/methodology/approachThe UMESHMOTION subroutine and the Arbitrary Lagrangian-Eulerian adaptive mesh technique are used to investigate the wear profile of the descale roll surface and to evaluate the effect of the slab and roll’s initial temperature on the wear depth.FindingsWear is more pronounced at the edges of the roll-slab contact area and less severe in the roll-body’s central region. A rise in the initial slab temperature from 1,337 K to 1,429 K results in a 67% rise in maximum wear depth and 52% in frictional stress. The peak wear region progressively shifted toward the center of the roll body. A rise in the initial roll temperature from 308.15 K to 673.15 K caused a 46% reduction in maximum wear depth and 73% in frictional stress. The location of the peak wear region remained primarily unchanged.Originality/valueThis study used the UMESHMOTIONI subroutine and the Arbitrary Lagrangian-Eulerian adaptive mesh technique in ABAQUS® to evaluate the quantitative correlation between the wear depth of the descaling roll surfaces and the initial temperatures of the slab and rolls. This study offers valuable insights into improving the wear of descaling roll surfaces.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-06-2024-0231/

Numerical evaluation of wear parameters using meta-models

AbstractWear parameters identified by linear friction tester (LFT) experiments overestimate the wear mass loss when applied on a laboratory abrasion & skid tester 100 (LAT100) simulation. On the other hand, the identification of wear parameters directly from the LAT100 experiment can be challenging since variables such as the contact area and the slip velocity are not measured experimentally and need to be assumed. To improve the identification process, numerical calibration is used as a more suitable approach. This approach relies on meta-models as a target function for minimization. The meta-models are generated using a sample of wear parameters applied to an LAT100 finite element modeling (FEM) to calculate the corresponding wear mass.. In this model, a transport velocity is defined for the rolling simulation, and an arbitrary lagrangian–eulerian (ALE) adaptive meshing approach is adopted for the wear modeling. For the wear model, a combination of archard’s wear model and schallamach’s abrasion law is used. This model contains a pair of wear parameters to be identified. The ALE adaptive meshing technique moves the nodes independently of the material. Since the mesh topology remains the same, failure of the simulation occurs if the wear volume loss exceeds that of the element. Meta-models are created to extend wear modeling beyond this failure. Once the meta-models are created, they are used as a target function for the minimization algorithm. The minimization algorithm aims to find the optimal wear parameters by minimizing the difference between experimentally observed and numerically produced wear mass loss. The minimization algorithm inputs a set of wear parameters into the meta-models which in turn yield a prediction of the wear mass loss. The process is carried out until an optimum parameter set is identified. Such an approach has a lower accuracy if the parameters are identified directly from the experiment using assumptions regarding the contact shear stress and the sliding velocity. Nonetheless, the main advantage of parameters identified using the meta-model approach is the usability of these parameters in an LAT100 model.

Dynamic thermal shock resilience of functionally graded materials: An adaptive phase-field approach

This work presents a phase field model for dynamic fracture under thermo-mechanical loads to analyze functionally graded material (FGM). Coupled governing equations are derived by minimizing the total energy consisting of kinetic energy and elastic strain energy, along with the energy due to the external heat source. To overcome the computational expense associated with the standard finite element analysis for implementing the phase field model, an adaptive approach based on the quadtree algorithm is employed that enhances computational efficiency while preserving accuracy. The hanging nodes within the element are treated as polygonal elements. The governing equations are solved using a staggered solution algorithm, following a hybrid phase field implementation strategy. The notch location, temperature variation, and gradation profile of FGM are carefully examined and investigated using numerous examples. It is observed that these parameters significantly influence the behavior of FGM. The results align well with the existing literature, validating our methodology within the examples explored. Additionally, the computational efficiency of adaptive meshing techniques is assessed, demonstrating the significant reductions in computational overhead while preserving accuracy and versatility in handling multi-physics fracture scenarios.

Combined Reynolds-averaged Navier-Stokes/Large-Eddy Simulations for an aircraft wake until dissipation regime

A new methodology has been devised to simulate the aerodynamic wake of an airliner during cruise flight using Reynolds-averaged Navier-Stokes (RANS) and Large Eddy Simulations (LES). The wake evolution is simulated considering the full geometry of the aircraft and spans from the jet regime to the dissipation regime. First, the jet regime is computed using RANS modeling and state-of-the-art anisotropic mesh adaptation techniques. Second, the vortex and dissipation regimes are solved using temporal LES with flow field initialization from the previous RANS calculation. RANS information on turbulent quantities is transferred to the LES domain using synthetic turbulence methods. The methodology is first tested on a NACA-0012 wing. It is then applied to the NASA Common Research Model (CRM) geometry on cruise flight conditions. Jet/vortex interaction is studied during the jet regime up to twenty wingspans behind the aircraft. The influences of atmospheric turbulence, jet turbulence, and stable atmospheric stratification are investigated for the vortex and dissipation regimes. It is observed that atmospheric turbulence intensity and stratification both accelerate the vortex decay. Moreover, the secondary wake structure is found to be much more turbulent for numerical RANS initialization than for classical analytic initialization, showcasing the importance of early aerodynamics on wake evolution.

Parametric study of the laser energy absorption in high-power laser beam welding

Laser energy absorption on the keyhole wall is decisive for the thermodynamic behavior and the resultant weld properties in the high-power laser beam welding process. However, its highly transient nature on a microsecond scale makes the quantitative analysis challenging. In this paper, the influence of the relevant welding parameters on laser energy absorption is studied statistically by utilizing multiphysical modeling, in which the three-dimensional transient keyhole dynamics and thermo-fluid flow are calculated. A dynamic mesh adaption technique and a localized level-set-based ray-tracing method are employed to improve the model accuracy further. The results show that the focus position has a remarkable effect on the time-averaged laser absorption, and in contrast, the laser energy distribution regime is only slightly influenced by the welding speed in the studied parameter range (1.5–3.0 m/min). The absorption ratio of the laser energy on the keyhole front wall decreases with increasing welding speed and increases with upward-moving focus positions. The comparison between the calculated results and the experimental measurements ensures the validity of the proposed model.

Experimental investigations and finite element simulation for predicting wear life of overrunning clutches

An overrunning clutch, generally known as a freewheel clutch, is a direction dependent torque transmitting device that works on the principle of wedge friction. The overrunning wear characteristics of freewheels are studied using pin-on-disc tribometry. The wear experiments for freewheels are performed at accelerated loads to promote wear in a short period. The overrunning wear life of the clutch under operating conditions is predicted using an appropriate load-life relationship. A finite element-based Archard’s wear model is implemented as a numerical strategy to evaluate the wear profile. The maximum local wear for various loads is computed using experimentally obtained wear and friction coefficients. The numerical simulation is performed with an adaptive mesh technique utilizing incremental nodal displacements to predict surface wear. The experimental and numerical results are compared in terms of wear characteristics. The numerical wear results are almost 11% higher than the experimental results. The wear life of an overrunning clutch is predicted in terms of overrunning speed based on the wear amount.

Topology and parameter optimization of IPM motor considering mechanical strength by stress and connection constraints

PurposeThe purpose of this study is to apply the topology and parameter optimization (TPO) to interior permanent magnet (IPM) motors to obtain the optimized shape with higher torque, lower ripple and sufficient mechanical strength.Design/methodology/approachThe constraints regarding the maximum stress, connectivity and mesh quality were considered to achieve not only high electrical performance but also high mechanical strength. To enhance the accuracy of the finite element analysis of the elastic analysis, this paper used body-fitted mesh adaptation technique to avoid the stress concentration.FindingsThe proposed method in this study resulted in feasible shapes with sufficiently high strength compared to previous studies. It is also shown that TPO yielded IPM motors with higher torque compared to topology optimization (TO) with fixed parameters.Practical implicationsDifferent from the existing studies on topology optimization of IPM motors, the mechanical strength is even considered by evaluating the stress values. Therefore, in the practical phase, geometries can be designed that are less likely to be damaged due to deformation, even in the high-speed rotation range.Originality/valueThis paper performed TO and parameter optimization (PO) simultaneously, considering not only the electrical performance but also the mechanical strength. Furthermore, the mechanical strength was evaluated more precisely by devising the elastic analysis conditions and mesh generation.

Predicting uplift capacity of group anchors in sand using 3D FELA and MARS

Similar to pile group, the process of designing an anchor group requires the determination of an efficiency factor that describes the overlapping effects of neighboring anchors. This research article introduces an efficiency factor denoted as ξ, which represents the ratio of the ultimate uplift pressure of a single anchor within a group to the ultimate uplift pressure of an isolated anchor. The primary approach employed involves advanced 3D finite element limit analysis with an adaptive meshing technique, which can be utilized to examine the uplift stability problem of 3D anchor groups. Numerical findings are compared with those obtained from previous research, incorporating both experimental and analytical results. This would ensure that our results are validated and provide valuable information into the performance of anchor groups. In addition to these findings, we introduce a MARS machine learning model, which has been trained using a dataset of 875 data points. This model is designed to establish an empirical equation that can be practically used for design purposes. To further enhance our understanding, we present the relative importance index (RII). This index allows us to identify which factors have the most significant impact on the behavior of anchor groups. In conclusion, the results presented in this article are of practical significance for the geotechnical engineering community.

Heat transfer treatment of system during freezing with implement of nanoparticles

The present attempt investigates solidification through a tank equipped with T-shaped fins, a crucial aspect of cold storage technology. Utilizing the Finite Element Method (FEM) for simulation, implementation of a mesh adaptation technique enhances the accuracy of modeling. Equations are derived based on the assumption of neglecting velocity effects during solidification, simplifying the mathematical framework for analysis. Validation of the numerical approach is conducted through comparisons with previously published works, affirming the reliability of the methodology. A notable aspect of the study is the utilization of nanosized powders dispersed within the water, serving to bolster system performance. This innovative approach enhances water conductivity, thereby augmenting the rate of cold storage. Employing powders with a greater shape factor yields promising results, leading to a discernible decrease in completion time by approximately 10.6 %, attributed to heightened conductivity facilitated by the nanomaterial. Furthermore, the investigation explores the impact of varying volume fractions of particles on solidification time, revealing a significant reduction of approximately 32.78 % with the implementation of higher particle volumes.

The Allen–Cahn model with a time-dependent parameter for motion by mean curvature up to the singularity

In this article, we investigate the temporal evolution of arbitrary, simple, closed two-dimensional (2D) and three-dimensional (3D) interfaces under motion driven by mean curvature up to a singularity. To facilitate this investigation, we propose a novel Allen–Cahn (AC) model with a time-dependent interfacial thickness parameter. The original AC equation was developed to model the phase separation of a binary mixture. It is well known that a level set or interface of the solution of the AC equation obeys the dynamics of motion by curvature as the interfacial thickness parameter approaches zero. Generally, it is difficult to find a closed-form analytic solution of the AC equation with any initial condition. Therefore, we need to estimate the solution of the AC equation through computational approaches such as finite difference method (FDM), finite element method (FEM), Fourier-spectral method (FSM), and finite volume method (FVM). Any simple, closed curves and convex surfaces eventually shrink to a point due to motion by mean curvature. Therefore, it becomes necessary to use adaptive mesh techniques to resolve this small size problem. However, even though we use adaptive mesh techniques, we still confront the relatively thick interfacial transition layer when the curves or interfaces become very small. To avoid this problem, we can start with a very small mesh size for a small value of the interfacial parameter, which results in an extremely high computational cost even when using adaptive mesh techniques. To resolve these issues, we present the AC equation with a time-dependent interfacial parameter and develop an adaptive mesh refinement system. To show the superior performance of the proposed mathematical equation and its computational algorithm, we present various numerical experiments and investigate the motion by mean curvature up to the singularity of curves in 2D space and interfaces in 3D space.

An adaptive finite element method for coupled fretting wear and fatigue crack propagation simulation

Fretting wear and fatigue crack propagation often occur at the same time in the service of mechanically connected structures. In order to analyze the effect of fretting wear on the process of fatigue crack propagation, a finite element simulation method for fatigue crack propagation considering fretting wear is proposed. In this method, the Archard model is used to predict the wear process, and the conventional Paris equation is modified based on the wear rate. In order to improve the accuracy of crack propagation prediction, a crack-tip super singular element (CSSE) is used to calculate the singular stress field and fracture control parameters of the crack tip. An adaptive meshing technique that automatically adjusts the mesh density according to the simulation process is designed to ensure the computational efficiency of the algorithm and the accuracy of the numerical results. The smoothing technique used in wear simulation can alleviate the influence of contact stress fluctuation on wear profile prediction. The usage of the new simulation method is introduced through benchmark examples. It is proved that the numerical results of crack propagation obtained by the adaptive finite element method (FEM) have high precision, good convergence and high computational efficiency. It is found that wear reduces the crack growth rate compared with the simulation results without considering wear. This method has a promising application in the coupling analysis of fretting wear and fatigue crack propagation of mechanically connected structures.

NUMERICAL INVESTIGATION OF OFF-CENTER COLLISION BETWEEN TWO EQUAL-SIZED WATER DROPLETS

Droplet collision is a basic phenomenon in numerous natural and industrial processes, while the understanding of collision dynamics is still lacking. In this work, a numerical investigation of the offcenter collision of two equal-sized water droplets is performed with the Weber number of 14 to 196 and impact parameter of 0 to 0.8. The incompressible Navier-Stokes equations are solved by the finite volume method. The volume of fluid (VOF) method and adaptive mesh technique are used to capture the gas-liquid interface. First, by comparing with reliable published experimental data, the reliability of the numerical results is verified. Then, the shape evolution for coalescence, reflexive separation, and stretching separation is described in detail. The effect of the Weber number and impact parameter on the collision of two equal-sized water droplets is analyzed. Moreover, the analysis of the surface energy and kinetic energy is conducted for the collision process. Furthermore, the dimensions of ligament and bridge for high-impact parameter stretching separation are presented quantitatively. Finally, the collision outcome for the simulation cases in this work is depicted and discussed. This work is helpful for fundamentally understanding the mechanism of collision dynamics of droplets, as well as applying the droplet collision model to related processes.

Registration-based model reduction of parameterized PDEs with spatio-parameter adaptivity

We propose an automated nonlinear model reduction and mesh adaptation framework for rapid and reliable solution of parameterized advection-dominated problems, with emphasis on compressible flows. The key features of our approach are threefold: (i) a metric-based mesh adaptation technique to generate an accurate mesh for a range of parameters, (ii) a general (i.e., independent of the underlying equations) registration procedure for the computation of a mapping Φ that tracks moving features of the solution field, and (iii) an hyper-reduced least-square Petrov-Galerkin reduced-order model for the rapid and reliable estimation of the mapped solution. We discuss a general paradigm — which mimics the refinement loop considered in mesh adaptation — to simultaneously construct the high-fidelity and the reduced-order approximations, and we discuss actionable strategies to accelerate the offline phase. We present extensive numerical investigations for a quasi-1D nozzle problem and for a two-dimensional inviscid flow past a Gaussian bump to display the many features of the methodology and to assess the performance for problems with discontinuous solutions.

Design and analysis of efficient computational techniques for solving a temporal‐fractional partial differential equation with the weakly singular solution

This work deals with the construction of robust numerical schemes for solving a time‐fractional convection‐diffusion (TFCD) equation with variable coefficients subject to weakly singular solution. The solution of the underlying problem exhibits a weak singularity at time . The methods are designed on both graded and adapted grids, in which the temporal derivative is approximated on the nonuniform grid, in order to tackle the singularity. In the case of adaptive mesh technique, the mesh is constructed adaptively via equidistribution of a positive monitor function. The resulting semi‐discretized equation is further discretized by a high‐order compact finite difference (CFD) scheme to obtain a fully discrete scheme. Stability and convergence of the method on graded mesh are analyzed. Numerical results for one test problem subjected to nonsmooth analytical solution are presented which shows the robustness and efficiency of the proposed numerical schemes. The elapsed computational time (CPU time) for the proposed methods are provided. Numerical results obtained from the methods on graded and adapted grids are compared with those from the scheme on uniform grid. Finally, as an application, the TFCD model and the suggested numerical techniques were employed to price options of a European butterfly spread. The effect of fractional order (FO) derivative on the option price profile is investigated.

Fast Physical Optics Method Based on Adaptive Mesh Technique

Fast Physical Optics Method Based on Adaptive Mesh Technique

Numerical simulation of abrasive cutoff operation based on ALE adaptive meshing technique

Metal cutting is one of the most important and commonly used manufacturing processes in industry and has been studied for years; however, accurate simulation of cutoff operation is still a big challenge because of the complexity of the material removal process. The main challenge for the classical simulation method is computational difficulties during the material removal process, and furthermore, the material deletion criterion has to be somehow empirical. To conquer these problems, a more robust and efficient simulation technique for the cutoff process is proposed herein, in which the material removal is achieved through continuously adjusting mesh nodes on contact surfaces based on ALE adaptive meshing technique, instead of deleting elements. Finally, this new simulation technique is used to predict the heat partition and temperature field evolution during the cutoff operation of the steel plate. It is found that the obtained simulation results agree well with those by the analytical approach, demonstrating its effectiveness.

Solver algorithm for stabilized space-time formulation of advection-dominated diffusion problem

This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution using higher-order continuous B-spline basis functions in both spatial and temporal dimensions. This problem is very difficult to solve numerically using the standard Galerkin finite element method due to artificial oscillations present when the advection term dominates the diffusion term. However, a first-order constraint least-square formulation allows us to obtain numerical solutions avoiding oscillations. The advantages of space-time formulations are the use of high-order methods and the feasibility of developing space-time mesh adaptive techniques on well-defined discrete problems. We develop a solver for a least-square formulation to obtain a stabilized and symmetric problem on finite element meshes. The computational cost of our solver is bounded by the cost of the inversion of the space-time mass and stiffness (with one value fixed at a point) matrices and the cost of the GMRES solver applied for the symmetric and positive definite problem. We illustrate our findings on an advection-dominated diffusion space-time model problem and present two numerical examples: one with isogeometric analysis discretizations and the second one with an adaptive space-time finite element method.