Numerical Grid Research Articles

Detached-Eddy Simulation of Supersonic Turbulent Flow over a Cylinder/Skewed Flare Configuration

The computational campaign reported in this article focuses on a series of experiments at Mach 2.85 carried out in the 1980s at NASA Ames Research Center on a set of cylinder/skewed flare configurations designed to produce highly three-dimensional shock-wave/boundary-layer interactions in the absence of end-wall effects. Computations carried out in that era were unable to match the experimental results using the numerical techniques, turbulence models, and grid resolution available at the time. In the present work, newer Reynolds-averaged Navier–Stokes and detached-eddy simulation methods have been applied to these flows, and relatively good agreement has been obtained with the experimental data. Difficulty in capturing the correct separation-bubble size was encountered with initial detached- eddy simulations, but the introduction of resolved turbulence via a boundary-layer trip produced much better results. The present paper reports on results obtained for four inclination angles (0, 5, 10, and 23 deg) of the skewed 30-deg flare. Detached-eddy simulation is seen to be an economical alternative to large-eddy simulation for capturing many features of large-scale separation unsteadiness over long time intervals at true Reynolds number.

A data-driven strategy for phase field nucleation modeling

We propose a data-driven strategy for parameter selection in phase field nucleation models using machine learning and apply it to oxide nucleation in Fe-Cr alloys. A grand potential-based phase field model, incorporating Langevin noise, is employed to simulate oxide nucleation and benchmarked against the Johnson-Mehl-Avrami-Kolmogorov model. Three independent parameters in the phase field simulations (Langevin noise strength, numerical grid discretization and critical nucleation radius) are identified as essential for accurately modeling the nucleation behavior. These parameters serve as input features for machine learning classification and regression models. The classification model categorizes nucleation behavior into three nucleation density regimes, preventing invalid nucleation attempts in simulations, while the regression model estimates the appropriate Langevin noise strength, significantly reducing the need for time-consuming trial-and-error simulations. This data-driven approach improves the efficiency of parameter selection in phase field models and provides a generalizable method for simulating nucleation-driven microstructural evolution processes in various materials.

Minimizing ice contamination during specimen preparation for cryo-soft X-ray tomography and cryo-electron tomography

Cryo-soft X-ray tomography (cryo-SXT) is a newly developed technique for imaging 3D whole cells in nearly native states. Cryo-SXT users require the preparation of numerous cryo-sample grids to use the allocated beamtime to study cellular phenomena under various conditions. Therefore, it is important to promptly prepare cryo-sample grids as efficiently and carefully as possible to minimize ice contamination on the frozen sample grid. In this study, we designed a cryo-multi-grid-box storage system, which includes a shell, funnel holder, and multi-grid-box container. Our system not only increases the number of cryo-sample grids that can be temporarily stored but also reduces the frequency of cryo grid-box container transfers, thus decreasing the probability of forming ice on the grid. We have also applied this system to A549 cryo cell grid preparation. The correlative images from cryo light microscopy and cryo-SXT showed that limited ice had formed on the grid when preparation was performed using our system. Additionally, 3D images of mitochondria with the lamellar shape of the cristae could be observed in our cryo-SXT results. Our cryo-multi-grid-box storage system can be used for cryo-SXT and cryo-electron tomography (cryo-ET) applications.

Interface and mixing zone between soil waters arising from upward and downward seepage - Part II: Heterogeneous total density.

Freshwater lenses in otherwise saline environments contain an important source of fresh water for natural vegetation and agricultural crops. Such lenses are regularly found in areas where both upward seeping saline groundwater and downward infiltrating fresh recharge water occur simultaneously during part of the year, resulting in shallow freshwater lenses which are highly susceptible to changes in recharge or seepage. In a series of two papers, we consider the water – and solute transport in a 2D cross-section between two parallel outflow faces. In this second part of the series, we build upon expressions presented in the first part to consider a situation where the density of seepage water exceeds that of recharge water, as typical for many deltaic areas around the world. Analytical expressions and approximations are given to obtain the steady state position of the interface between the two types of water using a sharp interface approximation, with a focus on the position midway between two outflow faces. Results show that the effect of a heterogeneous density distribution is limited when the seepage flux exceeds the density difference induced flux, but increases rapidly for ratios of the seepage flux over the density flux falling below 1. The heterogeneous density distribution then results in a decrease in freshwater lens thickness and, correspondingly, a decrease in fresh water availability. We also consider time-variant, oscillatory boundary conditions, and show that for heterogeneous density distributions the interface approaches its equilibrium position faster than for a corresponding situation with a homogeneous density distribution, indicating a higher vulnerability for changing boundary conditions. We also demonstrate that heterogeneous density distributions have limited effect on the amplitude of the interface oscillations. Analytical results obtained with the simplified model are validated using the numerical code SUTRA, which solves the full model for a numerical grid.

Particle trajectories in the KP-II equation

In the current work, we consider particle trajectories beneath traveling soliton solutions described by the Kadomtsev–Petiviashvili-II (KP-II) equation, which is a model for small-amplitude water waves in shallow water. The KP-II equation has a large number of exact solutions describing crossing line solitons. Here, we describe the particle drift induced by the single line soliton and various two- and three-soliton solutions on a two-dimensional horizontal domain.First, the derivation of the KP-II equation is used to exhibit expressions for the three components of the fluid velocity vector induced by a surface wave profile given by the KP-II equation. These velocity components can be used to specify a coupled system of ordinary differential equations (ODEs) which describe the motion of a fluid particle. Given an initial position inside the fluid for a specific particle, as well as continuously providing time-dependent values for the surface deflection, the ODE system can be solved numerically to find the particle path induced by the passage of a wave. A special numerical integration grid tracking the particle is used to handle integral terms occurring in the fluid velocity expressions.

Two-loop mixed QCD-EW corrections to charged current Drell-Yan

We present the two-loop mixed strong-electroweak virtual corrections to the charged current Drell-Yan process. The final-state collinear singularities are regularised by the lepton mass. The evaluation of all the relevant Feynman integrals, including those with up to two different internal massive lines, has been worked out relying on semi-analytical techniques, using complex-valued masses. We can provide, at any arbitrary phase-space point, the solution as a power series in the W-boson mass, around a reference value. Starting from these expansions, we can prepare a numerical grid for any value of the W-boson mass within their radius of convergence in a negligible amount of time.

Using the Multiple-Sensor-Based Frost Observation System (MFOS) for Image Object Analysis and Model Prediction Evaluation in an Orchard

Accurate frost observations are crucial for developing and validating frost prediction models. In 2022, the multi-sensor-based automatic frost observation system (MFOS), including an RGB camera, a thermal infrared camera, a leaf wetness sensor (LWS), LED lighting, and three glass plates, was developed to replace the naked-eye observation of frost. The MFOS, herein installed and operated in an apple orchard, provides temporally high-resolution frost observations that show the onset, end, duration, persistence, and discontinuity of frost more clearly than conventional naked-eye observations. This study introduces recent additions to the MFOS and presents the results of its application to frost weather analysis and forecast evaluation in an orchard in South Korea. The NCAM’s Weather Research and Forecasting (WRF) model was employed as a weather forecast model. The main findings of this study are as follows: (1) The newly added image-based object detection capabilities of the MFOS helped with the extraction and quantitative comparison of surface temperature data for apples, leaves, and the LWS. (2) The resolution matching of the RGB and thermal infrared images was made successful by resizing the images, matching them according to horizontal movement, and conducting apple-centered averaging. (3) When applied to evaluate the frost-point predictions of the numerical weather model at one-hour intervals, the results showed that the MFOS could be used as a much more objective tool to verify the accuracy and characteristics of frost predictions compared to the naked-eye view. (4) Higher-resolution and realistic land-cover and vegetation representation are necessary to improve frost forecasts using numerical grid models based on land–atmosphere physics.

Reactive transport modeling of the Aquifer Thermal Energy Storage (ATES) system at Stockton University, New Jersey during seasonal operations

Hydrogeochemical processes associated with Aquifer Thermal Energy Storage (ATES) operations can often impact the system performance owing to mineral precipitation either at the wellbore or in the aquifer owing to changes in temperature and fluid disequilibria. Although failure of ATES systems due to mineral precipitation ("fouling") is common, predictive reactive-transport models have rarely been applied to plan their design and operation. The objective of this study is to develop a reactive-transport model by coupling thermal, hydrological, and chemical (THC) processes to evaluate effects of introduced atmospheric oxygen on water chemistry, mineral precipitation/dissolution, porosity, and permeability changes associated with an ATES system at Stockton University (New Jersey, USA). The THC model builds on a Thermal-Hydrological-Mechanical (THM) model of the site (Smith et al., 2021) that evaluated system failure owing to possible fracturing in the caprock or around the wellbore. The causes of the system failure are not known – potential causes include hydraulic fracturing owing to elevated pump pressures that took place, a flow pathway created by one of the boreholes, or a pre-existing natural hydrologic connection between the upper unconfined aquifer and the ATES aquifer, any of which could have led to oxygenated water entering the reservoir and causing the observed Fe-oxide fouling on well screens. The THC model is used to evaluate some of the hypotheses and observations regarding system failure owing to geochemical processes.The reactive-transport code TOUGHREACT V4 (Sonnenthal et al., 2021) was used to model the THC processes during seasonal heating and cooling operations at the Stockton ATES site over 6 years of operation. In the THC simulations, the primary effects on geochemistry were observed when the injection water is saturated with atmospheric oxygen. Simulations show greater precipitation of goethite near the cold wells as compared to the warm wells. Although volume fractions of Fe-hydroxides were relatively small, the model was aimed at processes in the aquifer at the scale of meters and larger rather than at the scale of mm or cm (i.e., a well screen). Kaolinite is the dominant precipitating phase, also around the cold wells. Illite dissolves near the cold wells and precipitates near the warm wells. There is a net decrease in the porosity near the cold wells and increase near the warm wells, although a slight amount of thermal contraction near the cold wells and expansion near the warm wells is responsible for a significant proportion of the porosity change. Owing to the coarse discretization of the numerical grid near the wells (compared to the screen thickness) the magnitude of permeability changes at the wellbore are likely underestimated. The reactive transport model in this study can be used for characterization of aquifers, optimizing the operational parameters (temperature, pressure, pH etc.), and planning of mitigation strategies for ATES systems.

Numerical parametrization of stationary axisymmetric black holes in a theory agnostic framework

The pursuit of a comprehensive theory of gravity has led to the exploration of various alternative models, necessitating a model-independent framework. The Konoplya-Rezzolla-Zhidenko (KRZ) parametrization offers a robust method for approximating stationary axisymmetric black hole spacetimes, characterized by a rapidly converging continued-fraction expansion. However, while analytical metrics benefit from this approach, numerical metrics derived from complex gravitational theories remain presenting computational challenges. Bridging this gap, we propose a method for a numerical KRZ parametrization, tested and demonstrated on pseudonumerical Kerr and Kerr-Sen spacetimes. Our approach involves constructing numerical grids to represent metric coefficients and using the grids for fitting the parameters up to an arbitrary order. We analyze the accuracy of our method across different orders of approximation, considering deviations in the metric functions and shadow images. In both Kerr and Kerr-Sen cases, we observe rapid convergence of errors with increasing orders of continued fractions, albeit with variations influenced by spin and charge. Our results underscore the potential of the proposed algorithm for parametrizing numerical metrics, offering a pathway for further investigations across diverse gravity theories. Published by the American Physical Society 2024

Double emulsion generation in shear-thinning fluids under electric field effects

Double emulsions are encapsulated microstructures with medical, food, and cosmetics applications. Precise control over their parameters, such as volume, thickness, and size distribution, is crucial. This study numerically investigates, for the first time, the generation of double emulsions in a shear-thinning outer fluid under the influence of an external DC electric field. A dual co-flowing microfluidic device is chosen as the flow domain, and the shear-thinning behavior of the outer fluid is approximated by the Carreau–Yasuda rheological model. The governing equations are discretized on structured numerical grids using the VOF-CSF model and the finite volume method. The combined effects of the shear-thinning behavior and electric forces on compound droplet formation parameters, including volume, eccentricity, maximum thickness, and jet length, are studied carefully. Results show that for highly shear-thinning fluids, the application of electric forces can ensure the generation of desired compound droplets, which is not feasible without electric field effects. However, excessive electric forces can disrupt the droplet generation process, especially for moderate to low shear-thinning fluids. These findings provide new insights into the role of external electric fields in double emulsion generation and highlight their potential to optimize the production process.

Impacts of Moisture Advection Scheme on Precipitation in the Steep Topography Region between the Tibetan Plateau and the Sichuan Basin

Abstract Water vapor transport is a crucial process in modeling and can contribute to errors in precipitation forecasts. To investigate the sensitivity of precipitation to the moisture advection scheme, this study introduced the two-step shape-preserving advection scheme (TSPAS), which has been proven to improve precipitation simulation over steep topography at lower resolutions, into the Southwest Center Weather Research and Forecast (WRF)-based Intelligent Numerical Grid Forecast System (SWC-WINGS) at a convection-permitting resolution. According to experiments conducted throughout the summer of 2021, the precipitation over the eastern slope of the Tibetan Plateau (TP) is highly sensitive to the moisture advection scheme. TSPAS successfully improved precipitation over the eastern slope of the TP, especially for torrential rainfall. The fractions skill score (FSS) is improved by 0.075 (27.78%) for daily precipitation with a threshold of 100 mm. Compared with the experiment with the original WRF advection scheme, the TSPAS reduced the overestimation of precipitation in the topographic region and excessive water vapor transport in a low-level atmosphere. To understand the precipitation improvement contributed by the advection scheme, additional experiments were conducted for a particular precipitation process from two approaches: switching advection schemes during the rainfall evolution and updating the variables related to moisture advection individually. Results demonstrate that the precipitation improvement is mainly contributed by the moisture advection scheme before the precipitation. Among the different variables, the combination of wind and water vapor was the most influential factor causing the precipitation improvement under the TSPAS.

Benchmarking Correlation-Consistent Basis Sets for Frequency-Dependent Polarizabilities with Multiresolution Analysis.

This paper presents the first converged frequency-dependent HF polarizability results for general molecules, on a set of 89 closed-shell atoms and molecules. The solver employs multiresolution analysis (MRA) in a multiwavelet basis to compute both ground and response states to a guaranteed precision, which are validated against independent numerical grid calculations on atoms and linear molecules. The MRA ground-state energies and response properties are used to evaluate results in correlation-consistent basis sets up to 5Z augmented with either single or double diffuse functions and core-polarization functions. Systematic trends are revealed through consideration of chemical composition as well as the use of machine learning to cluster convergence trends, the latter suggesting the possibility of learning and correcting basis-set error.

Ground state properties of the screened helium atom under harmonic confinement

In this contribution, we show electronic property results for the ground state of the helium atom screened by a Debye plasma under an isotropic harmonic confinement as a function of the screening length (λD) and the angular frequency (ω0). The associate Hamiltonian is solved by expanding the wave function in the Hylleraas basis to incorporate the electron correlation in a simple manner. Furthermore, in order to compare with other findings the Hartree–Fock approach is implemented using a numerical grid method. The main results show that the total energy reaches the ionization threshold by the action of the electron coupling with the plasma medium and the strength of the harmonic confinement. The electron–electron average distance shows the compression of the system as the Debye plasma and the harmonic interactions become strongest (low λD and large ω0 values). We found acceptable results for the electron correlation energy when separate interactions are considered. In the absence of both interactions, the findings are in excellent agreement with other theoretical results.

Influence of alloy solidification path on melt pool behavior in additive manufacturing

Numerical models used to study transport phenomena in laser-powder bed fusion processes often rely on assumptions and simplifications to reduce their computational expense. One common simplification is in the description of latent heat evolution during the solid-liquid phase change (i.e., the solidification pathway), justified by the fact that the mushy zone thickness is similar to the numerical grid spacing used for continuum transport models. The lack of resolution of transport phenomena in the mushy zone motivates the use of computationally convenient solidification paths such as linear or sigmoidal relationships over pathways derived from fundamental solidification theory such as equilibrium or Scheil models. In the present work, an uncertainty quantification (UQ) framework is used to analyze the influence of solidification pathway selection on the solidification dynamics and melt pool geometries in laser based additive manufacturing (AM) of IN625. Results show the solidification pathway has a quantifiable influence on the cooling rate at the liquidus isotherm, mushy zone thickness, and solidification time. Due to similarities in the latent heat evolution at the beginning of solidification, the equilibrium and Scheil models predict similar cooling rates near the liquidus isotherm, however the wider freezing range of Scheil leads to a wider mushy zone compared to equilibrium. The non-physical latent heat release profiles of sigmoidal and linear paths lead to significant overpredictions of cooling rates at the liquidus isotherm compared to equilibrium and Scheil. These results indicate that careful consideration should be given to the choice of solidification pathway to ensure reliable model predictions.

Comparative analysis of CFD models to simulate temperature non-uniformity during hydrogen tank refuelling

This study compares four computational fluid dynamics (CFD) models, i.e. k-ε, RSM, SAS, and LES, to simulate temperature non-uniformity during hydrogen tank refuelling. Three grids with a total number of control volumes of 64k, 363k, and 2.9 M were used. The maximum dimensionless wall distances, y+, were 80, 5 and 2.5, respectively. The predictive capability of the models was assessed by recommended statistical indicators using ten thermocouple locations during 620 s of the experiment. The comparative analysis demonstrated a better predictive capability of temperature non-uniformity and stratification by the LES model and a shorter simulation time. It is concluded that meshes with y+ larger than 80 would overpredict the average hydrogen temperature while meshes with y+<5 provide a good simulation accuracy. The results underline the importance of the turbulence model choice and the numerical grid resolution for proper prediction of temperature non-uniformity during hydrogen tank refuelling.

A fully automated tool for constructing multiphysics model and performing simulations of kW-scale solid oxide cell stacks

Multiphysics simulations of solid oxide cell (SOC) require extensive experience and can be labor intensive. This paper reports the first successful implementation of automated multiphysics simulation process for industrial-scale planar SOC stacks. The automation is realized through Python based Ansys SpaceClaim scripting for building geometric model, Python based Ansys Workbench Meshing scripting for setting numerical grids, and Scheme based Ansys Fluent TUI commands for performing multiphysics simulations. The model building process allows for customized dimensions of all stack components and the corresponding edge grid counts. The automation of simulations streamlines all the computational steps in multiphysics modeling. The multiphysics model is shown to agree well with the experimental data. The automated tool is illustrated in a parametric analysis of SOC operations, illuminating the influences of size, shape and thermal boundary on the stack performance. The automation makes the simulations simple and efficient, invaluable for the SOC design and operation analysis.

Grid: A Python library for molecular integration, interpolation, differentiation, and more.

Grid is a free and open-source Python library for constructing numerical grids to integrate, interpolate, and differentiate functions (e.g., molecular properties), with a strong emphasis on facilitating these operations in computational chemistry and conceptual density functional theory. Although designed, maintained, and released as a stand-alone Python library, Grid was originally developed for molecular integration, interpolation, and solving the Poisson equation in the HORTON and ChemTools packages. Grid is designed to be easy to use, extend, and maintain; this is why we use Python and adopt many principles of modern software development, including comprehensive documentation, extensive testing, continuous integration/delivery protocols, and package management. We leverage popular scientific packages, such as NumPy and SciPy, to ensure high efficiency and optimized performance in grid development. This article is the official release note of the Grid library showcasing its unique functionality and scope.

Blood flow in deforming vessels

Blood flow is most often modeled in vessels whose shape does not change over time. This approach significantly simplifies the calculations and reduces their time. Temporal vascular deformations affect blood flow patterns, the deposition of atherosclerotic plaques, the formation of aneurysms, and many other phenomena. There are two methods to consider blood vessel deformations: registration of vascular geometry by diagnostic imaging such as CT, MRI, ultrasound or the use of the fluid-structure interaction (FSI) models. The first method requires additional procedures for processing image data, and the second requires knowledge of the material properties of the vessel walls, which is a very challenging task for in vivo experiments. The article will show the method to obtain a time-varying geometry of the coronary artery based on images obtained by angioCT. Emerging difficulties arise from the use of images of different resolutions and the need to generate numerical grids of the same topology at every time step. This problem was solved by using image segmentation, smoothing the resulting 3D geometry, and projecting the numerical grid on subsequent shapes of the vessel using diffeomorphism. The simulations have been validated using measurements on a phantom. The resulting velocity fields show the locations of intense oscillations of the shear stress of the wall where the atherosclerotic plaque is deposited.

A hybrid one‐step leapfrog ADI‐FDTD and subgridding approach based on a heterogeneous computing platform

AbstractThe finite‐difference time‐domain (FDTD) method often demands numerous grids for fine structure analysis, leading to high computational costs. To address this challenge, a subgridding scheme emerges as an attractive solution. However, the explicit nature of the FDTD subgrid method, constrained by Courant–Friedrichs–Lewy (CFL) conditions, can lead to inefficiencies with complex structures. In response, the leapfrog alternating‐direction implicit (ADI)‐FDTD method, exhibiting unconditional stability, has been developed to overcome CFL limitations. This paper presents a hybrid approach merging the one‐step leapfrog ADI‐FDTD method with a subgridding scheme using heterogeneous computing. By optimizing hardware usage and leveraging different device performances, this approach maximizes throughput in heterogeneous systems. Central processing units and graphics processing units handle workloads to minimize system latency. Simulation results on heterogeneous platforms demonstrate superior efficiency over single processor setups while maintaining simulation accuracy, especially in analyzing electromagnetic scattering from multiscale structures.

An Update of the NeQuick-Corr Topside Ionosphere Modeling Based on New Datasets

A new analytical formula for H0, one of the three parameters (H0, g, and r) on which the NeQuick model is based to describe the altitude profile of the electron density above the F2-layer peak height hmF2, has recently been proposed. This new analytical representation of H0, called H0,corr, relies on numerical grids based on two different types of datasets. On one side, electron density observations by the Swarm satellites over Europe from December 2013 to September 2018, and on the other side, IRI UP (International Reference Ionosphere UPdate) maps over Europe of the critical frequency of the ordinary mode of propagation associated with the F2 layer, foF2, and hmF2, at 15 min cadence for the same period. The new NeQuick topside representation based on H0,corr, hereafter referred to as NeQuick-corr, improved the original NeQuick topside representation. This work updates the numerical grids of H0,corr by extending the underlying Swarm and IRI UP datasets until December 2021, thus allowing coverage of low solar activity levels, as well. Moreover, concerning Swarm, besides the original dataset, the calibrated one is considered, and corresponding grids of H0,corr calculated. At the same time, the role of g is investigated, by considering values different from the reference one, equal to 0.125, currently adopted. To understand what are the best H0,corr grids to be considered for the NeQuick-corr topside representation, vertical total electron content data for low, middle, and high latitudes, recorded from five low-Earth-orbit satellite missions (COSMIC/FORMOSAT-3, GRACE, METOP, TerraSAR-X, and Swarm) have been analyzed. The updated H0,corr grids based on the original Swarm dataset with a value for g = 0.15, and the updated H0,corr grids based on the calibrated Swarm dataset with a value for g = 0.14, are those for which the best results are obtained. The results show that the performance of the different NeQuick-corr models is reliable also for low latitudes, even though these are outside the spatial domain for which the H0,corr grids were obtained, and are dependent on solar activity.