Adaptive Meshing Technique Research Articles

An ALE residual distribution scheme for the unsteady Euler equations over triangular grids with local mesh adaptation

This work presents a novel interpolation-free mesh adaptation technique for the Euler equations within the arbitrary Lagrangian–Eulerian framework. For the spatial discretization, we consider a residual distribution scheme, which provides a pretty simple way to achieve high order accuracy on unstructured grids. Thanks to a special interpretation of the mesh connectivity changes as a series of fictitious continuous deformations, we can enforce by construction the so-called geometric conservation law, which helps to avoid spurious oscillations while solving the governing equations over dynamic domains. This strategy preserves the numerical properties of the underlying, fixed-connectivity scheme, such as conservativeness and stability, as it avoids an explicit interpolation of the solution between different grids. The proposed approach is validated through the two-dimensional simulations of steady and unsteady flow problems over unstructured grids.

Seismic Stability of Dual Tunnels in Cohesive–Frictional Soil Subjected to Surcharge Loading

In this study, a self-developed adaptive finite element limit analysis (AFELA) code was adopted to explore the stability of dual tunnels in cohesive–frictional soil subjected to surcharge loading and seismic action. Parametric studies of different influential factors, including the depth of tunnels, horizontal distance between tunnels, seismic acceleration coefficient, unit weight, cohesion and internal friction angle of soils, were conducted using the AFELA code. An adaptive meshing technique was adopted for optimal accuracy and efficiency, and a pseudostatic method was used to simulate the seismic action. Strict upper bound (UB) and lower bound (LB) results with relative errors of less than 7% were acquired. Detailed design tables were presented to facilitate the engineering design, and three typical failure patterns, including single side-wall failure, half-cross-shaped failure and cross-shaped failure, corresponding to different stable levels, were summarized for a deeper insight into how the failure mechanism evolved under different conditions. The results indicated that the variations in soil unit weight and void depth affected the seismic bearing capacity almost linearly. Furthermore, the dual tunnel system is vulnerable to seismic actions, and the stability of tunnels was further undermined by the adverse effects of additional seismic-caused interactions between two adjacent tunnels.

Predicting the Instability Trajectory of an Obliquely Loaded Pipeline on a Clayey Seabed

Predicting the instability trajectory of an obliquely loaded pipeline on the seabed is vital for the global buckling assessment. To numerically investigate the obliquely loaded pipe–soil interactions, a plane strain elastoplastic finite element model incorporating the adaptive meshing technique and the contact-pair algorithm is employed and verified with the existing experimental data and the analytical predictions. The evolution of slip mechanisms within the underlying soil is simulated, indicating the instability direction of the pipe, and the corresponding ultimate soil resistance is closely correlated. It is also indicated that the ultimate load angle is in the positive correlation with the movement angle, the dimensionless embedment of the pipe and the roughness coefficient of the pipe–soil interface. On the basis of numerous simulations, a force-resultant plasticity model including the bearing capacity envelope and the flow rule is proposed for predicting the behavior of a partially embedded pipeline on the clayey seabed. Finally, an explicit expression with respect to the critical submerged weight of the pipe is derived for distinguishing the lateral instability of a pipe between the ‘light’ and the ‘heavy’ mode.

Optimum configuration of a metal foam layer for a fast thermal charging energy storage unit: A numerical study

The melting heat transfer of capric acid Phase Change Material (PCM) was numerically addressed in a channel shape Thermal Energy Storage (TES) unit. A combination of Cu nanoparticles and copper foam was used to improve the charging time of TES. A fixed amount of copper foam was applied to improve the heat transfer rate. The enthalpy-porosity approach, along with the finite element method, was used to simulate the free-convection melting heat transfer of composite PCM in the TES unit. Automatic time-step control and mesh adaptation technique were used to ensure the accuracy and convergence of the numerical solution. The porosity and the shape of the copper foam layer and volume fraction of nanoparticles were systematically optimized for minimum charging time using the Taguchi optimization approach. The results showed that a left right-hand triangle porous zone could lead to minimal charging time. The higher the porosity and volume fraction of nanoparticles, the lower the charging time. The combination of copper-foam, Cu nanoparticles, and optimum design of the porous layer reduced the melting time by three times. The optimal total charging time is reduced by 12.8% and 21.96% while changing the porous zone configuration from the RHT to REC and LHT.

A mesh adaptation algorithm using new monitor and estimator function for discontinuous and layered solution

<p style='text-indent:20px;'>In this work a novel mesh adaptation technique is proposed to approximate discontinuous or boundary layer solution of partial differential equations. We introduce new estimator and monitor function to detect solution region containing discontinuity and layered region. Subsequently, this information is utilized along with equi-distribution principle to adapt the mesh locally. Numerical tests for numerous scalar problems are presented. These results clearly demonstrate the robustness of this method and non-oscillatory nature of the computed solutions.</p>

Seismic Stability of the Slope Containing a Laterally Loaded Pile by Finite-Element Limit Analysis

In this study, the seismic stability of a slope containing a laterally loaded pile under seismic conditions is evaluated by the finite-element limit analysis (FELA) approach. The seismic action is idealized as a horizontal seismic coefficient, ranging from 0 to 0.3, within the framework of the pseudo-static approach, and applied as an accelerogram of earthquakes to the numerical model in the seismic analysis. By means of the adaptive meshing technique, the finite-element method, and limit theorem of plasticity, the slope failure mechanism need not be presumed in advance. The feasibility of the FELA is validated by comparing the obtained factors of safety and critical sliding surfaces with those provided by published literature. Based on this, the effects of various factors (e.g., horizontal seismic coefficient, internal friction angle, cohesion, slope angle, slope height, and lateral load atop the pile) on the factor of safety and failure mechanism, with a normalized parameter (seismic-multiplier) is proposed. Furthermore, some detailed design tables and four representative slope failure patterns are presented to estimate the seismic stability of the slope containing a laterally loaded pile.

Periodic adjoints and anisotropic mesh adaptation in rotating frame for high-fidelity RANS turbomachinery applications

The scope of this paper is to demonstrate the viability and efficiency of metric-based unstructured anisotropic mesh adaptation techniques to turbomachinery applications. The main difficulty in turbomachinery is the periodicity of the domain that must be taken into account in the mesh-adaptive solution process. The periodicity is strongly enforced in the flow solver using ghost entities to minimize the impact on the source code. For the mesh adaptation, the local remeshing is done in two steps. First, the inner domain is remeshed with frozen periodic frontiers, and, second, the periodic surfaces are remeshed after moving geometric entities from one side of the domain to the other. One of the main goal of this work is to demonstrate that mesh-independent certified numerical solutions can be obtained thanks to anisotropic mesh adaptation and that it is possible to run high-fidelity CFD on unstructured adapted meshes composed only of tetrahedra. This paper demonstrates how mesh adaptation, thanks to its automation, is able to generate meshes that are extremely difficult to envision and almost impossible to generate manually, leading to highly accurate numerical solutions. This study considers feature-based error estimate based on the standard multi-scale Lp interpolation error estimate and goal-oriented error estimate using an adjoint state to control the error on turbomachinery output functionals. A description of the flow solver and the adjoint solver is given in this work, as they are very different from what is encountered in the turbomachinery community. We also present all the specific modifications that have been introduced in the adaptive process to deal with periodic simulations used for turbomachinery applications. The periodic mesh adaptation strategy is then tested and validated on the LS89 high pressure axial turbine vane and the NASA Rotor 37 test cases.

An improved CIP-based numerical model for simulating free-surface flow with adaptive mesh

In this paper, an improved CIP (constrained interpolation profile)-based numerical model, which combines with Afivo (Adaptive Finite Volume quadtree/Octree mesh, an adaptive mesh framework), has been presented to simulate free-surface flow. In the CIP-based model, the constrained interpolation profile (CIP) method, a high-order finite difference method, is employed as the base flow solver and THINC/SW (Tangent of Hyperbola for Interface Capturing with Slope Weighting) method, a volume of fluid method, is applied to capture the flow interface. In this present model, an adaptive mesh technique is introduced to reduce the computational cost and multigrid technique is used to improve the solution efficiency. In the adaptive mesh system, new spatial interpolation schemes are provided, which have better performance in mass conservation compared with schemes provided in Afivo. Lid-driven cavity flow test was carried out to validate the accuracy of the flow solver with adaptive mesh and two/three-dimensional interface benchmark tests were performed to test the reliability of the interface capturing scheme and spatial interpolation schemes. Then two/three-dimensional applications (dam-break flow case, tank sloshing case and dam-break flow over a rectangular obstacle case) were investigated to demonstrate the model accuracy. The numerical results were compared with the previous experimental and numerical results, and good agreements were observed. It is demonstrated that the present numerical model has good applicability in modeling the free-surface flow.

Demonstration of a three-dimensional dynamically adaptive atmospheric dynamic framework for the simulation of mountain waves

In this paper, Fluidity-Atmosphere, representative of a three-dimensional (3D) non-hydrostatic Galerkin compressible atmospheric dynamic framework, is generated to resolve large-scale and small-scale phenomena simultaneously. This achievement is facilitated by the use of non-hydrostatic equations and the adoption of a flexible 3D dynamically adaptive mesh where the mesh is denser in areas with higher gradients of variable solutions and relatively sparser in the rest of the domain while maintaining promising accuracy and reducing computational resource requirements. The dynamic core is formulated based on anisotropic tetrahedral meshes in both the horizontal and vertical directions. The performance of the adaptive mesh techniques in Fluidity-Atmosphere is evaluated by simulating the formation and propagation of a non-hydrostatic mountain wave. The 2D anisotropic adaptive mesh shows that the numerical solution is in good agreement with the analytic solution. The variation in the horizontal and vertical resolutions has a strong impact on the smoothness of the results and maintains convergence even at high resolutions. When the simulation is extended to 3D, Fluidity-Atmosphere shows stable and symmetric results in the benchmark test cases. The flows over a bell-shaped mountain are resolved quite smoothly. For steep mountains, Fluidity-Atmosphere performs very well, which shows the potential of using 3D adaptive meshes in atmospheric modeling. Finally, as an alternative cut-cell mesh in Fluidity-Atmosphere, the anisotropic adaptive mesh coupled with the Galerkin method provides an alternative accurate representation of terrain-induced flow.

Analysis of multi-crack propagation by using the extended boundary element method

A new way is proposed to simulate the crack propagation paths of the multi-cracked structure. Firstly, the complete displacement and stress fields of the multi-cracked structure are calculated by the extended boundary element method (XBEM) coupled with characteristic analysis of the crack tip. Secondly, based on the maximum circumferential stress criterion by considering the contribution of the non-singular stress terms, the crack initiation angles are obtained. Thirdly, the cracks propagate forward along the crack initiation angles to form a new multi-cracked structure. During this process, boundary element adaptive mesh technique is established and the XBEM is used to analyze the newly formed multi-cracked structure repeatedly. Finally, the crack propagation paths of the multi-cracked structure are obtained. Numerical examples show that the results obtained by the XBEM are in good agreement with the experimental results.

Adaptive Semi-Structured Mesh Refinement Techniques for the Finite Element Method

The adaptive mesh techniques applied to the Finite Element Method have continuously been an active research line. However, these techniques are usually applied to tetrahedra. Here, we use the triangular prismatic element as the discretization shape for a Finite Element Method code with adaptivity. The adaptive process consists of three steps: error estimation, marking, and refinement. We adapt techniques already applied for other shapes to the triangular prisms, showing the differences here in detail. We use five different marking strategies, comparing the results obtained with different parameters. We adapt these strategies to a conformation process necessary to avoid hanging nodes in the resulting mesh. We have also applied two special rules to ensure the quality of the refined mesh. We show the effect of these rules with the Method of Manufactured Solutions and numerical results to validate the implementation introduced.

Design of Single Cell Membrane Shape and Array Configuration for MEMS Based Micromachined Ultrasonic Sensor to Improve the Performance: A Three Dimensional Model Characterization

The output acoustic energy of a capacitive micromachined ultrasonic transducer (CMUT) can be enhanced by adjusting its membrane structure. In this paper three dissimilar membranes shapes of CMUT: circular, rectangular and hexagonal, were aimed and 3D finite element method simulated using adaptive meshing technique. The displacement as well as strain and stress outputs for a single membrane and an array of four membranes on a single substrate were obtained. The simulated results are supported by analytical modeling. A static bias of 40 V and a signal of amplitude 100 mV are employed. A pressure of 8603.98 N/m2 resulting in a force of 16.894 µN was applied at the membrane. Fixtures were provided on every possible face of the structure except the face 1 (membrane). The outcomes showed that the membrane displacement is highest for a circular geometry under same uniform pressure and area of vibration. Moreover as the distance between the elemental membranes increases the displacement decreases for circular and hexagonal membranes while the reverse behavior is observed for rectangular membranes.

Simulation of welding to study residual stress and distortions

Abstract The welding process has a major role in industrial production, especially in the automotive, marine, and aerospace industries. As the simulation is less expensive, the welding process simulation for a lap joint using finite element analysis can be done. In this paper, the aluminum material of the 2400 series is selected, because of its physical and thermal properties. An aluminum plate of 460*310 mm with a thickness of 3 mm lap Joint. Two stage modeling and analysis is performed. The first stage includes the design of the arc welding process for Aluminum Lap Joint. Thermal analysis of the three-dimensional moving heat source by considering the Gaussian distribution method and temperature-dependent properties comparing the actual weld pool. The adaptive Mesh technique is used in second–stage in the sequential analysis. And to determine material distortion and residual stress, the thermal analysis are imported. Proper loads and boundary conditions are applied. Experimental results are obtained through the neutron diffraction technique. Different simulation results are recorded using various types of elements. The final results are successfully validated with the experimental results with the optimum percentage error of 1.5 to 2%.

Study of accuracy of a non-conformal finite element domain decomposition method

Domain Decomposition Methods (DDM) have been widely used in the Computational Electromagnetics (CEM) community in the last years to tackle large-scale problems with Finite Element Methods (FEM). Non-conformal DDM is more flexible (e.g., independently created meshes for different parts of the problem under analysis are supported) but may introduce an approximation error. In this communication, a thorough study of the accuracy of the solutions when using non-conformal DDM is presented. Three experiments are analyzed showing the verification of the implementation and that the accuracy is acceptable with different numbers of discontinuities in the propagation direction and various aspect ratios of the mesh on the interface. The numerical results use three different shapes (tetrahedra, prisms, and hexahedra) and up to order three in the basis functions that approximate the field. These studies are relevant for the introduction of non-conformal DDM with real problems or scalable (in the parallel sense) implementation of adaptive mesh techniques.

Hydrodynamic and heat transfer characteristics of droplet train spreading-splashing transition on heated surface

Heat transfer and hydrodynamic characteristics of droplet-induced spreading-splashing transition have been investigated experimentally and numerically. Specifically, the study involved the characterization of a train of monodispersed micron-sized droplets impinging on a heated surface covered by a thin liquid film at different droplet Weber number values. A single stream of mono-dispersed droplets was generated using a piezo-electric droplet generator with the ability to adjust parameters such as droplet impingement frequency, droplet diameter and droplet impingement velocity. A thin layer of Indium Tin Oxide was coated on a translucent sapphire substrate, which was used as a heating element. High-speed optical imaging and infrared thermal imaging techniques were used to characterize the hydrodynamics and heat transfer of droplet train impingement, respectively. It was observed that at low Weber number (We = 280), droplet impingements resulted in smooth spreading of the droplet-induced crown while splashing was observed at high Weber number (We > 489) cases. The effect of spreading-splashing transition on surface heat transfer has also been investigated at fixed flow rate conditions. Time-averaged temperature measurements indicate that the heat flux-surface temperature curves are linear at low surface temperature and before the onset of dry-out. However, a sharp increase in surface temperature was observed when dry-out appeared on the heater surface due to phase change. It was also found that strong splashing is unfavorable for heat transfer at high surface temperatures due to the instabilities seen in the liquid film, which leads to the onset of dry-out. Numerically, the Coupled Level Set-Volume of Fluid approach was used successfully to capture the hydrodynamic and thermal aspects of droplet train impingement on a heated surface. Furthermore, the dynamic mesh adaption technique was used in all simulations, which is capable of capturing the propagation of droplet-induced crown with high spatial and temporal resolutions. A good agreement was reached between experimental and numerical data in terms of droplet-induced crown morphology and surface temperatures. Thermal boundary layer displacement thickness profiles from numerical analysis were used to understand the coupled nature of hydrodynamics and heat transfer within the thin liquid film. In summary, the results indicate that droplet Weber number is a significant factor in spreading-splashing transition and droplet-induced liquid film heat transfer.

An experimental and numerical investigation of propeller-rudder-hull interaction in the presence of tip vortex cavitation (TVC)

This paper presents the investigation of propeller-rudder-hull interaction by using Computational Fluid Dynamics (CFD), and Experimental Fluid Dynamics (EFD) approaches including the propeller's performance in cavitating conditions, particularly the effect of the tip vortex cavitation on the interaction phenomenon. The investigation was focused on the recently generated benchmark test data for the research catamaran, The Princess Royal, and its scaled model which was tested for cavitation and noise investigations in the large circulating water channel of CNR-INM, Italy within the scope of the European collaborative project. The propeller-rudder-hull interaction of a 1/3.4 scaled model of this vessel was simulated by using the commercial CFD software, STAR-CCM+, which implemented the Schnerr–Sauer cavitation model for the cavitation effect. Large Eddy Simulations (LES) was used for a better resolution of high velocity and pressure gradients to model the tip vortex cavitation. A new adaptive meshing technique using a Mesh Adoption Refinement Approach for Cavitation Simulations (MARCS) was applied for more effective modelling of the tip vortex cavitation during the propeller-rudder-hull interaction. The results of the CFD simulations were compared with the EFD data, particularly for the cavitation dynamics.

An alternative phase-field interfacial tension force representation for binary fluid systems

The Navier–Stokes/Cahn–Hilliard (NSCH) system of equations has been extensively used for investigating the dynamics of two-phase flows of Newtonian fluids. However, the accurate calculation of interfacial tension via NSCH has been perceptibly doubted, and thus, a successive solution of NSCH equations is rarely not accompanied by mesh adaptation techniques and complex numerical schemes. In this work, it is demonstrated that the cause of such a miscalculation of the interfacial tension is inherent when following the conventional way of coupling the Navier–Stokes with the Cahn–Hilliard equation in their dimensionless form, where the capillary number is defined by assuming that the fluid/fluid interface is flat and at equilibrium. Hence, an alternative NSCH model was developed for the more accurate computation of interfacial tension that does not rely on any such a priori assumptions, and it uses a more abstract coupling by accounting for the distribution of the binary system’s energy on the interfacial region. This model was implemented on two different cases: (i) an investigation of the effects of inertia and capillarity on the deformation of liquid drops in simple shear flow and (ii) a study of an interfacial instability due to viscosity stratification. To solve the set of governing equations, implicit time integration schemes based on finite differences were further developed and implemented. The results regarding the topological evolution of the fluid/fluid interface from both cases were additionally cross-validated with other methods from the literature as well as with the conventional NSCH model. The comparison suggests that our NSCH model indeed remedies the standard NSCH model, without the need of mesh adaptation or any complex numerical scheme, by more accurately computing the interfacial tension for binary systems consisting of incompressible, immiscible, and Newtonian fluids.

Undrained seismic bearing capacity of strip footings horizontally embedded in two-layered slopes

This study investigated the undrained seismic bearing capacity of strip footings embedded in two-layered slopes by finite element limit analysis (FELA); in particular, a pseudostatic method was specified to seismic loads. Lower bound theory (LB), upper bound theory (UB), and adaptive meshing technique are employed for exploring the effect of the shear strength ratio of top layer and bottom layer, cu1/ cu2; the horizontal embedment depth of footings, b/ B; the footing locations (in bottom layer or top layer); seismic coefficient kh; and the slope gradient β on seismic bearing capacity. Results indicated that the seismic bearing capacity would increase with the growth of horizontal embedment depth of footings. The comparison between the predictions obtained from the proposed method and the existing method was presented, and the failure mechanisms are further summarized.

Pre-drilling Effect on Thermal Friction Drilling of Cast Aluminum Alloy Using Thermo-mechanical Finite Element Analysis

Thermal friction drilling is a non-conventional hole making process, which uses a rotating tool to penetrate the workpiece and create a bushing. Friction drilling of brittle cast alloys is likely to result in severe petal forming and radial fracturing. This research investigates the effect of pre-drilling diameter and depth on the produced bushing cracks and petal formations while drilling cast aluminum alloy (A380). A three-dimensional finite element model of high-temperature deformation and large plastic strain is performed by using ABAQUS software. Modeling by using dynamic, temperature-displacement, explicit, as well as the adaptive meshing, element deletion, interior contact, and mass scaling techniques, is necessary to enable the convergence of the solution. The finite element analysis results predict that the pre-drilling has a significant effect on the produced bushing shape. The effect of initial deformation decreases with pre-drilling, leading to fewer cracks and petal formations. Hence, the obtained bushing length increases, so providing a more load-bearing surface that leads to a stiffer joint. Additionally, the effect of pre-drilling on the produced temperature is studied, and the results reveal that by increasing the pre-drilling diameter or depth the temperature decreases. Therefore, less workpiece material melting occurs, which leads to less adhering on the tool surface, so fewer cracks and petal formations.

Evaluation of different models for turbulent combustion of hydrogen-air mixtures. Large Eddy Simulation of a LOVA sequence with hydrogen deflagration in ITER Vacuum Vessel

• LES with TFM model was validated vs H2 experiments. • Validated model was used to simulate ITER VV LOVA sequence with H2 combustion. • In LOVA sequence burning speed increased 1–3.5 times due to flame acceleration. • Maximum average VV pressure was 4–5.5 times to the initial one. The modelling of premixed combustion in the presence of a turbulent field in three-dimensional (3-D) confined scenarios was studied in this work, and applied to hydrogen combustion within ITER vacuum vessel (VV). Two different combustion approaches were tested with Large Eddy Simulation: a Flamelet Progress Variable (LES-FPV) and a Thickened Flame Model (LES-TFM). For the case of LES-TFM modelling, Dynamic Adaptive Chemistry (DAC) with a detailed kinetic mechanism for hydrogen combustion and in-situ adaptive tabulation (ISAT) methods were employed. Moreover, an adaptive meshing technique was used with the aim of tracking the flame front to ensure an adequate spatial resolution in this region. Experimental validation was performed to assess the ability of the different studied approaches to predict the flame burning speed, flame acceleration, and pressure evolution for lean H 2 -Air volume percent mixtures from 16 to 28 % propagating within a turbulent field. Results revealed that both approaches led to accurate predictions in terms of flame burning speed. When considering DAC and ISAT methods with detailed chemistry, LES-TFM model was found to be a cost-efficient solution. This model was used to analyse two loss of vacuum accident (LOVA) sequences within ITER VV. Results showed that turbulence might increase the flame burning speed by a factor of up to 3.5 for the case of big breaches (0.15 m 2 ) but it would not affect in case of breaches of 0.02 m 2 . Besides, results showed that autoignition with 2 kg of H 2 within the VV at 13.35 kPa might degenerate in detonation with average wall pressure levels ∼70 kPa.