Fine Grid Research Articles

Meshfree multiscale method for the infiltration problem in permafrost

This study introduces a multiscale simulation approach, employing the Meshfree Generalized Multiscale Finite Element Method (GMsFEM), to numerically model fluid seepage in permafrost soil conditions. Combining Meshfree and Finite Element Methods, the coarse-grid system is addressed, while the standard Finite Element Method operates on the fine grid. For representing fractures at the fine grid level, the Discrete Fracture Model (DFM) is utilized. The findings demonstrate the method’s efficacy in accurately depicting soil heterogeneity and the impact of fractures on soil temperature.

A dual-grid approach to speed up large-scale CFD-DEM simulations

With the development of heterogeneous computing, the discrete element method (DEM) and computational fluid dynamics (CFD) coupling has become an effective approach to simulate large-scale particle–fluid systems. With various models and algorithms accelerating the DEM part significantly, the CFD part becomes an efficiency bottleneck, especially for large-scale simulations. A dual-grid approach is proposed to address this issue. On the fine grid, the fluid velocity and particle–fluid interaction are solved without compromising accuracy in capturing flow details, and the pressure is solved on the coarse grid to ensure mass conservation to boost the CFD part. This approach is validated by simulating several gas–solid fluidized beds, a performance demonstrating speedup of 2.6 for low workload and 10.1 for high workload.

Modeling Lobe‐And‐Cleft Instabilities on a River Plume

AbstractThe lobe‐and‐cleft instability is a widely recognized mechanism leading to along‐front structure on density current fronts. Early studies based on laboratory and numerical simulations suggested that the lobe‐and‐cleft instability is due to convective instability in the nose of gravity currents traveling over a nonslip boundary. Horner‐Devine and Chickadel (2017, https://doi.org/10.1002/2017gl072997) reported the presence of lobe‐and‐cleft instabilities at the Merrimack River, which are generated at the river front in the absence of a no‐slip boundary. Hence, the observed lobe‐and‐cleft instabilities must be due to other mechanisms. In this study, we carried out non‐hydrostatic large eddy simulations of a riverine outflow into an idealized 3D domain. With a fine grid resolution of 0.15 × 0.31 m in two horizontal directions and about 0.125 m in the vertical direction, the model reproduced the lobe‐and‐cleft feature, with the magnitude and size of lobes consistent with the field observation. The model results revealed that instabilities start from the primary Kelvin‐Helmholtz instability, followed by the secondary instability through stretching and tilting, generating counter‐rotating streamwise vortices in the plume and at the plume head. The upwelling associated with streamwise vortex cells brings a slower flow to the plume surface, resulting in lobe‐and‐cleft patterns at the front and positive and negative vertical vorticity at the plume surface. The model also predicted a lobe width of about two to three times the plume thickness, consistent with the field observation and the lobe/cleft spacing associated with pairs of counter‐rotating streamwise vortices. Modeled turbulent dissipation rate shows a trend of exponential decay from 10−4 to 10−3 m2/s3 at the frontal head to 10−7 to 10−6 m2/s3 behind the front, similar to the findings in the previous field studies.

Towards a cutting‐edge metallization process for silicon heterojunction solar cells with very low silver laydown

AbstractWithin this work, we investigate the potential to optimize the screen‐printed front side metallization of silicon heterojunction (SHJ) solar cells. Three iterative experiments are conducted to evaluate the impact of the utilized fine mesh screen configurations and grid layout adaption (finger pitch) for the front side metallization on silver laydown and electrical performance of the solar cells. With respect to the screen configuration, we compare the performance of a fine‐mesh knotless screen to a conventionally angled screen demonstrating an additional gain of Δη = +0.1%abs due to reduced shading losses. Additionally, a grid layout is improved by increasing the number of contact fingers from 120 to 156. Furthermore, the current possibility to push the fine‐line printing process for low‐temperature pastes to the limit is investigated by reducing the nominal finger width wn to 20, 18, and 15 μm. It is shown that even the smallest nominal width of wn = 15 μm can be printed with high quality, leading to an additional efficiency gain of Δη = +0.15%abs as well as a reduction of silver paste laydown by −5 mg. Finally, a batch of champion cells is fabricated by applying the findings of the previous experiments, which results in a maximum efficiency of ηmax = 23.2%. Compared to the reference group without optimization, this corresponds to a gain of Δη = +0.17%abs, which comes along with an additional decrease of the silver paste laydown by approximately −2 mg. This emphasizes the significance of consistent optimization of the screen‐printing process in terms of cell performance and resource utilization for SHJ solar cells.

Lattice Boltzmann simulation of dissolution patterns in porous media: Single porosity versus dual porosity media

Understanding the influence of porous media structure, particularly dual porosity, on solvent transport and pore geometry evolution during chemical reactions is a complex and critical area of study. This research leverages the lattice Boltzmann method to investigate how the presence of aggregates in a medium affects solvent transport and pore space development, focusing on distinct dissolution regimes: face and wormhole dissolution. The study addresses the challenge of managing variable pore sizes in dual porosity media by developing specialized GPU algorithms, which efficiently handle fine grids and complex pore spaces. The findings reveal that dual porosity significantly enhances dissolution rates in both the face and wormhole dissolution regimes. Intriguingly, while the pattern of face dissolution remains largely unchanged, dual porosity markedly alters the pattern of wormhole dissolution. In dual-porosity media, the wormholes tend to be narrower and more elongated compared to the wider wormholes observed in single-porosity media. This variation is attributed to the reaction area dynamics, where the reduced reactive surface area along the main wormhole path in dual-porosity media results in less solvent engagement in the reaction processes. Moreover, the research provides insights into the microscale interactions in porous media, emphasizing how variations in microscale porosity can have substantial impacts on the overall dissolution dynamics. The study results are not only significant for understanding the fundamental aspects of chemical dissolution in porous media but also have practical implications in fields such as geo-energy and groundwater remediation. These findings help optimizing reaction processes in complex and heterogeneous porous systems, highlighting the need for detailed consideration of microstructural characteristics in modeling and industrial applications.

A dual grid-based deep reinforcement learning and computational fluid dynamics method for flow control and its application to nucleate pool boiling

This paper presents a proposition of a dual grid (DG)-based coupled deep reinforcement learning (DRL) and computational fluid dynamics (CFD) method for active flow control. The DG-DRL-CFD method uses a dual-resolution grid, with a coarser grid for the training phase and a finer grid for the testing phase of the DRL-CFD method. Further, after a validation study for our DRL-CFD-based parallelized in-house solvers, this paper presents a performance study for a periodic suction/ejection-based drag reduction for a cylinder in a channel-confined flow. Using an immersed boundary method for CFD on a Cartesian grid, this novel DG-DRL-CFD method is shown to result in almost same accuracy (within 1%) in a substantially reduced computational time as compared to the traditional DRL-CFD method (on the finer uniform grid). Finally, using a sharp interface level set method for an axisymmetric two-phase flow, this paper presents an application of the DR-DRL-CFD method for an oscillating base plate-based enhancement of heat transfer during nucleate pool boiling. As compared to our recent CFD study-based parametric study for the nucleate pool boiling problem, the present DG-DRL-CFD method leads to a profile and frequency of plate-oscillation that results in a larger value of average Nusselt number Nuavg for the plate. The coupled DRL-CFD method leads to plate oscillation profile giving higher enhancement in Nuavg, compared to an open-loop control strategy that involves a parametric sweep involving multiple simulations.

Fast Two-Grid Finite Element Algorithm for a Fractional Klein- Gordon Equation

In this article, we propose a spatial two-grid finite element algorithm combined with a shifted convolution quadrature (SCQ) formula for solving the fractional Klein-Gordon equation. The time direction at tn − θ is approximated utilizing a second-order SCQ formula, where θ is an arbitrary constant. The spatial discretization is performed using a two-grid finite element method involving three steps: calculating the numerical solution by solving a nonlinear system iteratively on the coarse grid, obtaining the interpolation solution based on the computed solutions in the first step, and solving a linear finite element system on the fine grid. We present a numerical algorithm, validate the two-grid finite element method’s effectiveness, and demonstrate the computational efficiency for our method by the comparison of the computing results between the two-grid finite element method and the standard finite element method.

Computable turbulence modeling of laminar-turbulent transition characterized boundary layer flows with the aid of artificial neural network

The continuous development of machine learning algorithms has stimulated the technological revolution on turbulence modeling for Reynolds-averaged Navier–Stokes (RANS) simulations. In this paper, a computable transition-enabled turbulence model is developed with the aid of an artificial neural network (ANN), which maps the relation between the mean flow variables from the shear stress transport (SST) model on coarse grid and the turbulent viscosity from SST-γ model on fine grid. It turns out that the ANN model can predict the aerodynamic integral quantities, transition onset location, laminar separation bubble structure, streamwise velocity distribution, etc. with superior accuracy and robustness for subsonic and moderate transonic airfoil flows. Meanwhile, the ANN model can significantly improve the convergence property with a much higher convergence speed of the model equation in comparison with traditional transition-enabled RANS model. Moreover, due to the lack of solving RANS model equations and use of grid interpolation technology, the computation speed of this ANN model is improved by a factor of about six over the conventional benchmark model. Therefore, the present computable ANN model provides a new perspective for high-efficiency simulation of transition-characterized flows in engineering applications.

Hyper-local source strength retrieval and apportionment of black carbon in an urban area

Neighborhood-scale air pollution hotspots have recently been identified through detailed field campaigns, including the 100x100 Black Carbon Experiment which took place in West Oakland, CA, in 2017. Here, high-resolution nested atmospheric simulations are used together with a Bayesian inversion framework to estimate source apportionment at the hyper-local scale for a neighborhood in West Oakland. Forward simulations are performed with the Weather Research and Forecasting (WRF) model using 6 grid nests from 11.25 km to 2 m horizontal resolution. On the finest grid, building geometries are resolved using the immersed boundary method. Seven point sources and four line sources at known locations are included in the forward simulation for two 1-h periods during the 2017 field campaign. Data from 12 black carbon sensors are used to perform source inversion using a Markov Chain Monte Carlo approach, which provides a probability distribution for each of the 11 source strengths. From this, a most-likely plume can be created using the peaks of the distributions, and source apportionment can be estimated for each sensor. In addition, a composite plume can be constructed to indicate 90% confidence that concentrations are above or below a specified value. With this probabilistic analysis, it is possible to determine that more than half of the neighborhood has black carbon concentrations of higher than 0.4 μg/m3, with some areas higher than 3 μg/m3 during the time periods studied.

Addressing equifinality in agent-based modeling: a sequential parameter space search method based on sensitivity analysis

This study addresses the challenge of equifinality in agent-based modeling (ABM) by introducing a novel sequential calibration approach. Equifinality arises when multiple models equally fit observed data, risking the selection of an inaccurate model. In the context of ABM, such a situation might arise due to limitations in data, such as aggregating observations into coarse spatial units. It can lead to situations where successfully calibrated model parameters may still result in reliability issues due to uncertainties in accurately calibrating the inner mechanisms. To tackle this, we propose a method that sequentially calibrates model parameters using diverse outcomes from multiple datasets. The method aims to identify optimal parameter combinations while mitigating computational intensity. We validate our approach through indoor pedestrian movement simulation, utilizing three distinct outcomes: (1) the count of grid cells crossed by individuals, (2) the number of people in each grid cell over time (fine grid) and (3) the number of people in each grid cell over time (coarse grid). As a result, the optimal calibrated parameter combinations were selected based on high test accuracy to avoid overfitting. This method addresses equifinality while reducing computational intensity of parameter calibration for spatially explicit models, as well as ABM in general.

A time two-grid algorithm for two-dimensional nonlinear time-fractional partial integro-differential equations

In this paper, a temporal second order two-grid difference scheme is proposed for the two-dimensional nonlinear time-fractional partial integro-differential equations with a weakly singular kernel. The first-order backward difference and L1 formula are used in the temporal direction to estimate the first level of time, the L2−1σ formula and L1-type formula are used in the temporal direction for later time steps, and the central difference formula is used in the spatial directions. To improve the computational efficiency of nonlinear system, an efficient time two-grid algorithm is proposed. This algorithm firstly solves a nonlinear system on the coarse grid, and then the Lagrangian linear interpolation is applied on the coarse grid to estimate the function values on the fine grid. The stability and convergence of the two-grid difference scheme are analyzed by the energy method. The convergence order of the two-grid difference scheme is O(τF2+τC4+hx2+hy2), where τF and τC are the time step sizes of fine grid and coarse grid respectively, while hx and hy are the space step sizes. Numerical experiments show that the accuracy of the theoretical analysis and the efficiency of the two-grid algorithm.

The Hertzsprung progression of classical Cepheids in the Gaia era

ABSTRACT A new fine grid of non-linear convective pulsation models for the so-called ‘bump Cepheids’ is presented to investigate the Hertzprung progression (HP) phenomenon shown by their light and radial pulsation velocity curves. The period corresponding to the centre of the HP is investigated as a function of various model assumptions, such as the efficiency of superadiabatic convection, the mass–luminosity relation, and the metal and helium abundances. The assumed mass–luminosity relation is found to significantly affect the phenomenon but variations in the chemical composition as well as in the stellar mass (at fixed mass–luminosity relation) also play a key role in determining the value of the HP centre period. Finally, the predictive capability of the presented theoretical scenario is tested against observed light curves of bump Cepheids in the ESA Gaia data base, also considering the variation of the pulsation amplitudes and of the Fourier parameters R21 and Φ21 with the pulsation period. A qualitative agreement between theory and observations is found for what concerns the evolution of the light curve morphology as the period moves across the HP centre, as well for the pattern in period–amplitude, period–R21, and period–Φ21 planes. A larger sample of observed Cepheids with accurate light curves and metallicities is required in order to derive more quantitative conclusions.

A two-level finite element method with grad-div stabilizations for the incompressible Navier–Stokes equations

This article presents and studies a two-level grad-div stabilized finite element discretization method for solving numerically the steady incompressible Navier–Stokes equations. The method consists of two steps. In the first step, we compute a rough solution by solving a nonlinear Navier–Stokes system on a coarse grid. And then, in the second step, we pass the coarse grid solution to a fine grid to linearize the nonlinear term, update the solution by solving a linearized problem based on Newton iterations. In both steps, a grad-div stabilization term is incorporated into the system to reduce the influence of pressure on the approximate velocity. We analyze stability and asymptotic convergence of the approximate solutions, derive explicit dependence of the solution errors on the grad-div stabilization parameter and viscosity. We perform also some numerical tests to validate the theoretical analysis and illustrate the efficiency of the proposed method. Compared with the standard two-level method without stabilizations, the grad-div stabilization term added in present method improves the accuracy of the approximate velocity, accelerates the convergence of the nonlinear iterations for the coarse mesh nonlinear system, and reduces the computational time.

An efficient two-grid high-order compact difference scheme with variable-step BDF2 method for the semilinear parabolic equation

Due to the lack of corresponding analysis on appropriate mapping operator between two grids, high-order two-grid difference algorithms are rarely studied. In this paper, we firstly discuss the boundedness of a local bi-cubic Lagrange interpolation operator. And then, taking the semilinear parabolic equation as an example, we first construct a variable-step high-order nonlinear difference algorithm using compact difference technique in space and the second-order backward differentiation formula with variable temporal stepsize in time. With the help of discrete orthogonal convolution kernels, temporal-spatial error splitting idea and a cut-off numerical technique, the unique solvability, maximum-norm stability and corresponding error estimate of the high-order nonlinear difference scheme are established under assumption that the temporal stepsize ratio satisfies rk := τk/τk−1 < 4.8645. Then, an efficient two-grid high-order difference algorithm is developed by combining a small-scale variable-step high-order nonlinear difference algorithm on the coarse grid and a large-scale variable-step high-order linearized difference algorithm on the fine grid, in which the constructed piecewise bi-cubic Lagrange interpolation mapping operator is adopted to project the coarse-grid solution to the fine grid. Under the same temporal stepsize ratio restriction rk < 4.8645 on the variable temporal stepsize, unconditional and optimal fourth-order in space and second-order in time maximum-norm error estimates of the two-grid difference scheme is established. Finally, several numerical experiments are carried out to demonstrate the effectiveness and efficiency of the proposed scheme.

Multi-head neural networks for simulating particle breakage dynamics

The breakage of brittle particulate materials into smaller particles under compressive or impact loads can be modelled as an instantiation of the population balance integro-differential equation. In this paper, the emerging computational science paradigm of physics-informed neural networks is studied for the first time for solving both linear and nonlinear variants of the governing dynamics. Unlike conventional methods, the proposed neural network provides rapid simulations of arbitrarily high resolution in particle size, predicting values on arbitrarily fine grids without the need for model retraining. The network is assigned a simple multi-head architecture tailored to uphold monotonicity of the modelled cumulative distribution function over particle sizes. The method is theoretically analyzed and validated against analytical results before being applied to real-world data of a batch grinding mill. The agreement between laboratory data and numerical simulation encourages the use of physics-informed neural nets for optimal planning and control of industrial comminution processes.

A Two-Grid Algorithm of the Finite Element Method for the Two-Dimensional Time-Dependent Schrödinger Equation

In this paper, we construct a new two-grid algorithm of the finite element method for the Schrödinger equation in backward Euler and Crank–Nicolson fully discrete schemes. On the coarser grid, we solve coupled real and imaginary parts of the Schrödinger equation. On the fine grid, real and imaginary parts of the Schrödinger equation are decoupled, and we solve the elliptic equation about real and imaginary parts, respectively. Then, we obtain error estimates of the exact solution with the two-grid solution in the H1-norm and carry out two numerical experiments.

TWO-GRID VIRTUAL ELEMENT DISCRETIZATION OF QUASILINEAR ELLIPTIC PROBLEM

In this paper a two grid algorithm for quasilinear elliptic problem based on virtual element method (VEM) discretization is proposed. With this new algorithm the solution of a quasilinear elliptic problem on a fine grid is reduced to the solution of a quasilinear elliptic problem on a much coarser grid, and the solution of a linear system on the fine grid. A priori error estimate in H1 norm is derived. Numerical experiments are carried out to illustrate the theoretical findings.

Sea Ice Extent Retrieval Using CSCAT 12.5 km Sampling Data

Polar sea ice extent exhibits a highly dynamic nature. This paper investigates the sea ice extent retrieval on a fine (6.25 km) grid based on the 12.5 km sampling data from the China France Ocean Satellite Scatterometer (CSCAT), which is generated by an adapted Bayesian sea ice detection algorithm. The CSCAT 12.5 km sampling data are analyzed, a corresponding sea ice GMF model is established, and the important calculation procedures and parameter settings of the adapted Bayesian algorithm for CSCAT 12.5 km sampling data are elaborated on. The evolution of the sea ice edge and extent based on CSCAT 12.5 km sampling data from 2020 to 2022 is introduced and quantitatively compared with sea ice extent products of Advanced Microwave Scanning Radiometer 2 (AMSR2) and the Advanced Scatterometer onboard MetOp-C (ASCAT-C). The results suggest the sea ice extent of CSCAT 12.5 km sampling data has good consistency with AMSR2 at 15% sea ice concentration. The sea ice edge accuracy between them is about 7 km and 10 km for the Arctic and Antarctic regions, and their sea ice extent difference is 0.25 million km2 in 2020 and 0.5 million km2 in 2021 and 2022. Compared to ASCAT-C 12.5 km sampling data, the sea ice edge Euclidean distance (ED) of CSCAT 12.5 km data is 14 km (2020 and 2021) and 12.5 km (2022) for the Arctic region and 14 km for the Antarctic region. The sea ice extent difference between them is small except for January to May 2020 and 2021 for the Arctic region. There are significant deviations in the sea ice extents of CSCAT 12.5 km and 25 km sampling data, and their sea ice extent difference is 0.3–1.0 million km2.

An adaptive mesh refinement method based on a characteristic‐compression embedded shock wave indicator for high‐speed flows

AbstractNumerical simulation of high‐speed flows often needs a fine grid for capturing detailed structures of shock or contact wave, which makes high‐order discontinuous Galerkin methods (DGMs) extremely costly. In this work, a characteristic‐compression based adaptive mesh refinement (AMR, h‐adaptive) method is proposed for efficiently improving resolution of the high‐speed flows. In order to allocate computational resources to needed regions, a characteristic‐compression embedded shock wave indicator is developed on incompatible grids and employed as the criterion for AMR. This indicator applies the admissible jumps of eigenvalues to measure the local compression of homogeneous characteristic curves, and theoretically can capture regions of characteristic‐compression which contain structures of shock, contact waves and vortices. Numerical results show that the proposed h‐adaptive DGM is robust, efficient and high‐resolution, it can capture dissipative shock, contact waves of different strengths and vortices with low noise on a rather coarse grid, and can significantly improve resolution of these structures through mild increase of computational resources as compared with the residual‐based h‐adaptive method.

A theoretical framework for BL Her stars. II. New period-luminosity relations in Gaia passbands

In the era of the Hubble tension, it is crucial to obtain a precise calibration of the period-luminosity ($PL$) relations of classical pulsators. Type II Cepheids (T2Cs; often exhibiting negligible or weak metallicity dependence on $PL$ relations) used in combination with RR Lyraes and the tip of the red giant branch may prove useful as an alternative to classical Cepheids for the determination of extragalactic distances. We present new theoretical $PL$ and period-Wesenheit ($PW$) relations for a fine grid of convective BL Her (the shortest period T2Cs) models computed using mesa-rsp in the $Gaia$ passbands and we compare our results with the empirical relations from $Gaia$ DR3. Our goal is to study the effect of metallicity and convection parameters on the theoretical $PL$ and $PW$ relations. We used the state-of-the-art 1D non-linear radial stellar pulsation tool mesa-rsp to compute models of BL Her stars over a wide range of input parameters:\ metallicity ($-2.0\; dex Fe/H dex $), stellar mass ($0.5M_ odot -0.8M_ odot $), stellar luminosity ($50L_ odot -300L_ odot $), and effective temperature (across the full extent of the instability strip; in steps of 50K). We used the Fourier decomposition technique to analyse the light curves obtained from mesa-rsp and $Gaia$ DR3 and then compared the theoretical and empirical $PL$ and $PW$ relations in the $Gaia$ passbands. The BL Her stars in the All Sky region exhibit statistically different $PL$ slopes compared to the theoretical $PL$ slopes computed using the four sets of convection parameters. We find the empirical $PL$ and $PW$ slopes from BL Her stars in the Magellanic Clouds to be statistically consistent with theoretical relations computed using the different convection parameter sets in the $Gaia$ passbands. There is a negligible effect coming from the metallicity on the $PL$ relations in the individual $Gaia$ passbands. However, there is a small but significant negative coefficient of metallicity in the $PWZ$ relations for the BL Her models using the four sets of convection parameters. This could be attributed to the increased sensitivity of bolometric corrections to metallicities at wavelengths shorter than the $V$ band. Our BL Her models also suggest a dependence of the mass-luminosity relation on metallicity. We found the observed Fourier parameter space to be covered well by our models. Higher mass models ($> 0.6\ odot $) may be needed to reliably model the observed light curves of BL Her stars in the All-Sky region. We also found the theoretical light curve structures (especially the Fourier amplitude parameters) to be affected by the choice of convection parameters.