Convective Domain Research Articles

Generalized particle domain method: An extension of material point method generates particles from the CAD files

SummaryIn this paper, a generalized particle domain method (GPDM) is proposed and developed within the framework of the convected particle domain interpolation method. This new method generates particles directly from non‐uniform rational B‐spline (NURBS)‐based CAD file of a continuum body. The particle domain corresponds to a NURBS element even for trimmed elements of solids with complex geometries. The shape functions and the gradient of shape functions are evaluated using NURBS basis functions to map material properties between particles and grid nodes. It approves that this proposed GPDM can track the domain of particles accurately and avoid the issue of cell‐crossing instability. Several numerical examples are presented to demonstrate the high performance of this proposed new particle domain method. It is shown that the results obtained using the proposed GPDM are consistent with the experimental data reported in the literature. Further development of the generalized particle domain method can provide a link to the material point method and isogeometric analysis.

Multiple discrete crack initiation and propagation in Material Point Method

Cracks in MPM (CRAMP) is one of the most prominent discrete crack simulation methods in the Material Point Method (MPM) due to its simplicity and versatility. However, CRAMP is yet to include the capability to simulate concurrent crack initiations and propagations, as well as propagation to the edge of the material domain. The method proposed in this paper enables the simulation of multiple crack paths with CRAMP via the dynamic assignment of particles to separate grids while minimizing the number of necessary grids. It also proposes methods of evaluating crack initiation and propagation via the Rankine criterion. The proposed methods are then implemented in an in-house Convected Particle Domain Interpolation (CPDI) MPM developed at Aalto University.To verify the integrity of the CPDI algorithm, our CPDI code with the proposed method implemented simulated a CPDI vortex. Furthermore, six fracture-simulation verification test cases were carried out: (1) through-crack in an infinite plate; (2) mode-I propagation; (3) initiation; (4) initiation with large deformations; (5) merging; (6) multiple initial cracks; and (7) radially-cracked thick ring. All these verification tests show successful initiation, propagation, merging, crack opening, and agreement with the results from the literature, as well as the convergence of various parameters with the expected rates.

Nonsimilar mixed convection analysis of ternary hybrid nanofluid flow near stagnation point over vertical Riga plate

PurposeThis work aims to concentrate on the mixed convection of the stagnation point flow of ternary hybrid nanofluids towards vertical Riga plate. Aluminum trioxide (Al2O3), silicon dioxide (SiO2) and titanium dioxide (TiO2) are regarded as nanoparticles, with water serving as the base fluid. The mathematical model incorporates momentum boundary layer and energy equations. The Grinberg term for the viscous dissipation and the wall parallel Lorentz force coming from the Riga plate are taken into consideration in the context of the energy equation.Design/methodology/approachThrough the use of appropriate nonsimilar transformations, the governing system is transformed into nonlinear nondimensional partial differential equations (PDEs). The numerical method bvp4c (built-in package for MATLAB) is used in this study to simulate governing equations using the local non-similarity (LNS) approach up to the second truncation level.FindingsNumerous graphs and numerical tables expound on the physical properties of the nanofluid temperature and velocity profiles. The local Nusselt correlations and the drag coefficient for pertinent parameters have been computed in tabular form. Additionally, the temperature profile drops while the velocity profile increases when the mixed convection parameter is included to oppose the flow.Originality/valueThe fundamental goal of this work is to comprehend how ternary nanofluids move towards a vertical Riga plate in a mixed convective domain with stagnation point flow.

B-spline convected particle domain interpolation method

The B-spline material point method (BSMPM) has been shown to be a promising approach to effectively mitigate the cell-crossing instability by using high-order B-spline basis functions. However, the BSMPM still suffers from the quadrature error, another well-known source of inaccuracy in the material point methods. On the other hand, the convected particle domain interpolation (CPDI) method effectively reduces the quadrature error by using alternative basis functions. The B-spline basis functions can be naturally used within the CPDI formulation, here called the BSCPDI method. The BSCPDI may be prone to the cell-crossing instability since the alternative basis functions in the BSCPDI are always C0-continuous despite the high-continuity of the B-spline basis functions used as the original grid basis functions. In this paper, the reproducibility of the BSCPDI effective basis function gradients and the susceptibility of the method to the cell-crossing instability are investigated analytically and numerically. The effectiveness of the BSCPDI in mitigating the quadrature error is also investigated through numerical simulations.

Shell Structure Analysis Based on the Convected Particle Domain Interpolation

Shell Structure Analysis Based on the Convected Particle Domain Interpolation

An improved convected particle domain interpolation material point method for large deformation geotechnical problems

AbstractA novel material point method called the improved convected particle domain interpolation (ICPDI) is proposed in this paper to simulate large‐deformation problems in geotechnical engineering. The ICPDI framework is based on the existing convected particle domain interpolation (CPDI) and employs an adaptive orthogonal improved interpolating moving least square (AOIIMLS) shape functions. The AOIIMLS shape functions prevent computational instability problems caused by singular or ill‐conditioned matrices through avoiding the direct solving of inverse matrices. Additionally, ICPDI adopts the velocity gradient to calculate the velocity field in particle domains and reduces cell‐crossing errors by using AOIIMLS shape functions. To reconstruct the velocity function in the background grid, the velocities of the material points and four related corner points are employed through AOIIMLS shape functions. The bar axis‐aligned vibration, ring radial expansion, slope elasto‐plastic slumping, and post‐failure tunnel collapse behavior examples are used to verify the accuracy and effectiveness of ICPDI by comparing the results with other numerical methods and experiments. Numerical simulation results show that ICPDI outperforms the material point method (MPM) and CPDI in terms of computational accuracy and convergence while reducing cell‐crossing errors. Consequently, this study demonstrates the capability of ICPDI in simulations of large‐deformation geotechnical problems.

Heat transfer in a quasi-one-dimensional Rayleigh–Bénard convection cell

We report an experimental and numerical study on Rayleigh–Bénard convection in a slender rectangular geometry with the aspect ratio $\varGamma$ varying from 0.05 to 0.3 and a Rayleigh number range of $10^5\leqslant Ra\leqslant 3\times 10^9$ . The Prandtl number is fixed at $Pr=4.38$ . It is found that the onset of convection is postponed when the convection domain approaches the quasi-one-dimensional limit. The onset Rayleigh number shows a $Ra_c=328\varGamma ^{-4.18}$ scaling for the experiment and a $Ra_c=810\varGamma ^{-3.95}$ scaling for the simulation, both consistent with a theoretical prediction of $Ra_c\sim \varGamma ^{-4}$ . Moreover, the effective Nusselt–Rayleigh scaling exponent $\beta =\partial (\log Nu)/\partial (\log Ra)$ near the onset of convection also shows a rapid increase with decreasing $\varGamma$ . Power-law fits to the experimental and numerical data yield $\beta =0.290\varGamma ^{-0.90}$ and $\beta =0.564\varGamma ^{-0.92}$ , respectively. Near onset, the flow shows a stretched cell structure. In this regime, the velocity and temperature variations in a horizontal cross-section are found to be almost invariant with height in the core region of a slender domain. As the Rayleigh number increases, the system evolves from the viscous dominant regime to a plume-controlled one, a feature of which is enhancement in the heat transport efficiency. Upon further increase of $Ra$ , the flow comes back to the classical boundary-layer-controlled regime, in which the quasi-one-dimensional geometry has no apparent effect on the global heat transfer.

Frequency suppression of director oscillations in AC-driven liquid-crystal-based terahertz phase shifters.

Frequency-induced instability is widely present in nematic liquid crystals (LCs), which poses a problem in improving liquid-crystal-based phase-shift devices driven by alternating currents. Herein, the Fréedericksz transition of thick nematic LCs was investigated under alternating electric fields to reveal the suppression of frequency-induced instability in the low frequency range. By extending the Frank-Leslie equation to the AC-driven case, the response of the LC was numerically calculated, and the frequency threshold for suppressing the driven instability was estimated in conjunction with the perturbation method. Experimentally, the frequency suppression of LC fluctuations was verified by using applied electric fields. In addition, the root-mean-square-error of the refractive index was measured to be less than 2 × 10-5, which excludes the convective instability-generating domains in devices. It was revealed that the fabricated thick LC phase shifters provided a phase shift of more than 360° at 2 THz and can be used in the terahertz band. It was observed that the electrically driven phase-shift characteristics were in accordance with the theoretical results as the threshold frequency condition was satisfied. This work provides an experimental and theoretical reference for improving modulation performance and enhancing the characterization of AC-driven LC-based phase-shift devices.

Estimation of the low-wavenumber component of turbulent boundary layer pressure field using vibration data

In structures subjected to a high-speed flow, the convective region of the wall pressure field (WPF) beneath a turbulent boundary layer (TBL) plays a crucial role in their vibration behaviour. However, when it comes to underwater structures experiencing low-speed flow, they effectively filter out the convective domain of WPF and the bending wavenumber of structures align with the low-wavenumber domain of the WPF. As a result, the primary cause of vibration in this case is the low-wavenumber components of the WPF. Thus, accurate estimation of the WPF at low-wavenumber domain is crucial for predicting vibration responses of these structures. Existing models for WPF accurately predict the convective region but differ significantly in predicting the low-wavenumber levels. This numerical study aims to investigate the feasibility of estimating the low-wavenumber WPF by analysing measured vibration data from a flat plate excited by a TBL. The WPF's cross spectrum in the wavenumber domain can be linked to the cross spectrum of the plate's acceleration. By employing regularization techniques and solving an inverse problem, the low-wavenumber components of the WPF can be then estimated. Virtual experiments are performed to evaluate the accuracy of the studied process by comparing its prediction to the input WPF model.

Coupling Explicit Phase-field MPM for Two-Dimensional Hydromechanical Fracture in Poro-elastoplastic Media

In this paper, a novel coupling explicit phase-field material point method with the convected particle domain interpolation (ePF-CCPDI) is proposed to predict the large deformation elastoplastic failure behavior in two-dimensional fully saturated porous media. This method provides a new thermodynamic derivation for the explicit phase-field modeling of multi-physical fracture problems. To account for the coupling effect of pore fluid flow on fractured porous solids, the pressure energy is included in the coupled system energy balance equation. The constitutive relationship of saturated porous media indicates that the pore pressure has a direct effect on the deformation of the solid skeleton. For achieving the fluid pressure smoothly distributed in damaged porous media under large deformation, exponential indicator functions are constructed to interpolate the fluid properties from the intact medium to the fully broken one. Meanwhile, the crack-opening-dependent permeability is introduced to estimate fluid flow inside the crack. The coupled explicit phase-field plasticity model is adopted to characterize the elastoplastic failure behavior of the solid skeleton. Moreover, a mixed explicit-implicit staggered solution scheme is developed to effectively solve the governing equations of the coupled system. To eliminate the numerical noises while material points cross the cell boundaries in large deformation simulation, the improved convected particle domain interpolation technique (CPDI) is adopted to enhance the computational accuracy. Two solution schemes are also proposed based on the extended material point penalty method to handle the specified pressure boundary condition. Finally, several representative two-dimensional numerical examples are conducted to validate the accuracy and capability of the proposed method.

Explicit phase-field material point method with the convected particle domain interpolation for impact/contact fracture in elastoplastic geomaterials

A novel explicit phase-field material point method with the convected particle domain interpolation (ePF-CPDI) is proposed for solving large deformation dynamic impact/contact fracture problems in elastoplastic geomaterials. In this method, we derive an explicit rate-dependent phase-field fracture model relying on the microforce balance law and the second law of thermodynamics. A coupled explicit phase-field plasticity model is then developed to describe dynamic elastoplastic fracture responses of geomaterials. Here the explicit time integration strategy and the staggered solution scheme are utilized in this work to solve the coupled-field governing equations based on the material point method. To eliminate the numerical noises caused by material points crossing cell boundaries, the convected particle domain interpolation technique is adopted to improve the computational accuracy in large deformation simulation. Furthermore, the proposed approach combining with the particle to particle contact algorithm is extended to deal with more complicated high-velocity impact and multi-body contact elastoplastic fracture problems. Numerical experiments are employed to validate the high accuracy and excellent capability of the proposed method and discuss the influences of main parameters on the phase-field fracture modeling.

Generalizability of reservoir computing for flux-driven two-dimensional convection.

We explore the generalization properties of an echo state network applied as a reduced-order model to predict flux-driven two-dimensional turbulent convection. To this end, we consider a convection domain with constant height with a variable ratio of buoyancy fluxes at the top and bottom boundaries, which break the top-down symmetry in comparison to the standard Rayleigh-Bénard case, thus leading to highly asymmetric mean and fluctuation profiles across the layer. Our direct numerical simulation model describes a convective boundary layer in a simple way. The data are used to train and test a recurrent neural network in the form of an echo state network. The input of the echo state network is obtained in two different ways, either by a proper orthogonal decomposition or by a convolutional autoencoder. In both cases, the echo state network reproduces the turbulence dynamics and the statistical properties of the buoyancy flux, and is able to model unseen data records with different flux ratios.

Deep convection in the Subpolar Gyre: Do we have enough data to estimate its intensity?

Deep convection in the Subpolar Gyre (SPG) forms a link between the upper and lower limbs of the Atlantic Meridional Overturning Circulation (AMOC). The intensity of convection in ocean studies is usually estimated using mixed layer depth (MLD). Here MLD is derived using vertical profiles of potential density from the gridded ARMOR3D dataset and from in situ observations of the EN4 dataset. Given limited areas of convective chimneys, the robustness of the estimates from an available set of vertical profiles needs to be verified before accessing mechanisms of interannual variability of deep convection. For reaching this goal, we first outlined three convection domains in the SPG with a high frequency of deep convection events: the southwestern Labrador Sea (L-DC), the central Irminger Sea (I-DC), and the area south of Cape Farewell (F-DC). The minimum number of randomly scattered casts, required to be executed from January to April for a robust estimate of the maximum MLD, depends on the typical area of the convective regions within the domain and forms 50 casts for L-DC, 40 casts for I-DC and 10 casts for F-DC. For the investigated convection domains, a sufficient number of casts were collected for several standalone winters of the late 1990s, while continuous time series of the convection intensity can be obtained only since the mid-2000s.

Coupled GIMP and CPDI material point method in modelling blast-induced three-dimensional rock fracture

Three-dimensional rock fracture induced by blasting is a highly complex problem and has received considerable attention in geotechnical engineering. The material point method is firstly applied to treat this challenging task. Some inherent weaknesses can be overcome by coupling the generalized interpolation material point (GIMP) and the convected particle domain interpolation technique (CPDI). For the media in the borehole, unchanged GIMP-type particles are used to guarantee a homogenous blast pressure. CPDI-Tetrahedron type particles are employed to avoid the fake numerical fracture near the borehole for the rock material. A blasting experiment using three-dimensional single-borehole rock was simulated to examine the applicability of the coupled model under realistic loading and boundary conditions. A good agreement was achieved between the simulation and experimental results. Moreover, the mechanism of three-dimensional rock fracture was analyzed. It was concluded that rock particle size and material parameters play an important role in rock damage. The reflected tensile waves cause severe damage in the lower part of the model. Rayleigh waves occur on the top face of the rock model to induce a hoop failure band.

An adaptive interpolation material point method and its application on large-deformation geotechnical problems

A novel Material Point Method (MPM) called the Adaptive Interpolation Material Point Method (AIMPM) is proposed to simulate large deformation problems in this work. The proposed method combines the domain interpolation proposed by the Convected Particle Domain Interpolation (CPDI) with the particle interpolation from the original MPM to address large deformation problems of geotechnical materials. The novelty of the model is twofold. First, the 3D domain interpolation formula is extended, and the volume term in the shape function is calculated from the corner points characterizing the material configuration. Second, the particle interpolation and the domain interpolation are coupled to accurately reflect the stress-strain behavior of geotechnical materials under large deformation. The two interpolation methods can be transformed adaptively through the criterion of Jacobian determinant or equivalent plastic strain. The performance of the AIMPM is verified by axial vibration, generalized vortex, rectangular collision, and column collapse cases. The simulation results show that the AIMPM significantly reduces the cell crossing error by domain interpolation compared to the MPM. More importantly, AIMPM is more accurate in capturing the exact location of geotechnical material flow. The work described in this study demonstrates the capability of the AIMPM in simulations of large-deformation geotechnical problems.

Phase-field implicit material point method with the convected particle domain interpolation for brittle–ductile failure transition in geomaterials involving finite deformation

A phase-field implicit material point method with the convected particle domain interpolation (PF-ICPDI) is proposed to model the brittle–ductile failure transition in pressure-sensitive geomaterials involving finite deformation. In this method, the phase-field fracture formulation relying on the microforce balance law and the second law of thermodynamics is adopted as a nonlocal damage function for the elastoplastic fracture analysis. A smooth two-yield-surface plasticity constitutive model is utilized to evaluate the brittle–ductile failure transition behavior of pressure-sensitive geomaterials. The coupling effect of phase-field fracture model and cap plasticity model is established by introducing an effective phase-field stress and splitting the total stored energy into elastic and plastic parts. The implicit material point method that can avoid severe mesh distortion and improve numerical stability is then developed to solve the quasi-static elastoplastic fracture finite deformation problem. Furthermore, the convected particle domain interpolation technique is adopted to eliminate numerical noises and improve computational accuracy while material points crossing cell boundaries in modeling the large deformation brittle–ductile failure transition process. The staggered incremental iterative scheme is carried out to solve the coupled discrete governing equations. The accuracy and capability of the proposed PF-ICPDI method are demonstrated through several representative numerical examples, as well as the effects of main material parameters on the phase-field brittle–ductile failure transition modeling of geomaterials are discussed.

Multi-surfaced elasto-plastic wood material model in material point method

Wood is a naturally occurring material widely used for construction. Due to its natural origin, wood properties vary and its behaviour is complex. This paper shows an implementation of a multi-surface elasto-plastic constitutive material model for wood into a custom explicit material point method code. The constitutive model chosen is one proposed by Schmidt & Kaliske with minor modifications to ensure better internal consistency. The model parameters are chosen based on literature data for spruce. The paper presents two Convected Particle Domain Interpolation Material Point Method simulations of experiments, both performed with the previously established model parameters. The first simulation replicates a compression test of a spruce specimen perpendicular to grain direction, carried out at the Department of Civil Engineering, Aalto University. The second simulation replicates an experiment from literature, in which a spruce specimen with knots is tensioned until failure. The numerical simulations successfully replicate the experimental outcomes qualitatively in terms of the deformation and load-displacement curves. Simulations of the three knotted specimens under tension, with introduced slight variation in wood grain direction, replicate different failure patterns with a similar failure load, resembling the behaviour of natural wooden structural elements. Additionally, one of the obtained failure patterns replicates that of the experiment well.

CFD simulation of laminar free convection flows of nanofluids in a cubical enclosure

Understanding the physics behind heat transfer within an enclosure especially in the natural convection domain has many important applications. The heat transfer performance of nanofluids inside a cubical enclosure with an internal heat source fixed on the side-wall of the enclosure will be investigated under natural convection flow condition in this paper. A three-dimensional two-phase mixture model will be developed and validated for this investigation. Computational fluid dynamic (CFD) simulations will be undergone using an in-house solver developed on simplified marker and cell (SMAC) algorithm within a collocated grid by finite difference method. The time dependent flow and characteristics of heat transfer for nanofluids will be investigated with pure water as the base fluid dispersed with different nanoparticles. In addition, parametric studies will also be performed by varying the particle volume concentrations (0%≤Φ ≤ 3%), particle diameters (25 nm ≤ Dp ≤ 50 nm) and Grashof numbers (103 ≤ Gr ≤ 106). The particle volume concentration when increased in a nanofluid gives more affinity to heat absorption. Velocity increase of particles leads to the efficient mixing of nanofluid and so an increase in Grashof number also leads to heat transfer enhancement. Decrease in particle diameter is the final parameter which shows a heat transfer increase.

A multi-physics ensemble approach for short-term precipitation forecasts at convective permitting scales based on sensitivity experiments over southern parts of peninsular India

The southern peninsular India is characterized by unique climatology with rainfall processes throughout the year from land–ocean contrasts. In addition, the complex terrain induces localized effects causing huge spatial and temporal variability in the observed precipitation. This study aims at evaluating the sensitivity of the high-resolution Weather Research and Forecasting (WRF) model (4 km) to multi-physics parameterizations, 3D variational data assimilation, and domain configuration, in the study domain covering southern peninsular India. Furthermore, the study focusses on the formulation of an ensemble method to improve the simulation of precipitation across seasons. A total of 120 experiments were set up across four crucial rainfall events, of varying spatial extent and duration, dominated by different rainfall generation mechanisms. The assessment of the experiments shows that the model’s cumulus and microphysics schemes have the highest impact on the location, intensity, and spread of the simulated 4-day long Quantitative Precipitation Forecasts (QPFs). Applying cumulus schemes at all domains represented the variability in the QPFs, across space and time, for the precipitation events dominated by convective activity. The cases without cumulus schemes at the convective scale domain (4 km), captured the higher intensity rains during organized cyclonic circulations in the north-east monsoon period. Hence, a 10-member multi-physics ensemble approach including members with and without cumulus parameterization at the fine resolution domain was adopted. The preliminary results demonstrate that the mean from the suggested ensemble approach (n-MPP) performed well in capturing the dynamics of QPFs across the rainfall events, as opposed to a single-member deterministic simulation and mean from larger member conventional multi-physics ensemble approach (c-MPP) without cumulus parameterization at the convective scale. The rank histogram, delta semi-variance plots, and outlier statistics at various lead times clearly showed that the suggested n-MPP was able to capture the high-intensity rainfall, increasing the spread of precipitation forecasts and consequently reducing the occurrence of outliers.

Non-Boussinesq Low-Prandtl-number Convection with a Temperature-dependent Thermal Diffusivity

Abstract In an attempt to understand the role of the strong radial dependence of thermal diffusivity on the properties of convection in Sun-like stars, we mimic that effect in non-Oberbeck–Boussinesq convection in a horizontally extended rectangular domain (aspect ratio 16) by allowing the thermal diffusivity κ to increase with the temperature (as in the case of stars). Direct numerical simulations (i.e., numerical solutions of the governing equations by resolving up to the smallest scales without requiring any modeling) show that, in comparison with Oberbeck–Boussinesq simulations (two of which we perform for comparison purposes), the symmetry of the temperature field about the mid-horizontal plane is broken, whereas the velocity and heat flux profiles remain essentially symmetric. Our choice of κ(T), which resembles the variation in stars, results in a temperature field that loses its fine structures toward the hotter part of the computational domain, but the characteristic large scale of the turbulent thermal “superstructures,” which are structures whose size is typically larger than the depth of the convection domain, continues to be largely independent of the depth.