Large Grid Spacing Research Articles

Effect of surface texture spacing on interface heat transfer and tensile property of laser‐welded steel/CFRTP joint

AbstractMetal‐polymer hybrid joints can contribute to weight reduction and have potential use in transportation industries. In this work, laser texturing was used to enhance bonding strength of laser‐welded 304 stainless steel/carbon fiber reinforced thermoplastics (CFRTP) joint. The tight relationship between surface texture spacing and porosity characteristic as well as tensile property of joint was systematically investigated. The temperature field distribution during welding process was simulated and the mechanism of porosity suppression depending on grid spacing was discussed. The result showed that the number of pores at cross‐section decreased first and then rose with the increase of micro‐structure spacing, which corresponded to the variation trend of bonding strength and was inconsistent with the evolution of connecting area. The joint achieved the minimum porosity defect and reached maximum fracture load of 2594 N when the grid spacing was 1.2 mm, while the maximum joint width of 9.28 mm was obtained when 0.4 mm spacing was adopted, indicating that the joint quality rather than mechanical interlocking governed the mechanical property of joint. Appropriate interface contact conductance (TCC) related to texture spacing could optimize the interface heat dissipation rate, and was the key factor to efficiently control the shrinkage porosity. The TCC of small or large grid spacing was too high or too small, resulting in failure of the heat transfer path through the interface to metal during cooling process. Moreover, the proper texture spacing improved the uniformity of joint strain distribution in tensile‐shear testing, which benefited joint strength.Highlights Laser‐textured grid pattern spacing affected number and distribution of pores. Heat dissipation rate varied with various spacing at joint interface. 1.2 mm spacing texture reduced stress concentration during tensile process.

Design of proton deflectometry with in situ x-ray fiducial for magnetized high-energy-density systems.

We report a design and implementation of proton deflectometry with an in situ reference x-ray image of a mesh to precisely measure non-uniform magnetic fields in expanding plasmas at the OMEGA and OMEGA EP laser facilities. The technique has been developed with proton and x-ray sources generated from both directly driven capsule implosions and short pulse laser-solid interactions. The accuracy of the measurement depends on the contrast of both the proton and x-ray images. We present numerical and analytic studies to optimize the image contrast using a variety of mesh materials and grid spacings. Our results show clear enhancement of the image contrast by factors of four to six using a high Z mesh with large grid spacing. This leads to further improvement in the accuracy of the magnetic field measurement using this technique in comparison with its first demonstration at the OMEGA laser facility [Rev. Sci. Instrum.93, 023502 (2022)RSINAK0034-674810.1063/5.0064263].

Sub-grid Scale Modelling and a-Posteriori Tests with a Morphology Adaptive Multifield Two-Fluid Model Considering Rising Gas Bubbles

The predictive simulation of gas–liquid multiphase flows at industrial scales reveals the challenging task to consider turbulence and interfacial structures, which span a large range of length scales. For simulation of relevant applications, a hybrid model can be utilised, which combines the Euler–Euler model for the description of small interfacial structures with a volume-of-fluid model as a scale-resolving multiphase approach. Such a hybrid model needs to be able to simulate interfaces, which are hardly resolved on a coarse numerical grid. The goal of this work is to improve the prediction of interfacial gas–liquid flows on a numerical grid with comparably large grid spacing. From the low-pass filtering of the two-fluid model five unclosed sub-grid scale terms arise. The convective and the surface tension part of the aforementioned contributions are individually modelled with multiple closure formulations. Those models are a-posteriori assessed in cases of two- and three-dimensional gas bubbles rising in stagnant liquid. It is shown, that the chosen closure modelling approach is suitable to improve the predictive power of the numerical model utilised in this work. Hence, simulation results on comparably coarse grids are changed towards results obtained with higher spatial resolution.

TTI equivalent medium parametrization method for the seismic waveform modelling of heterogeneous media with coarse grids

SUMMARYIn recent years, many higher-order and optimized schemes have been developed to reduce the dispersion error with the use of large grid spacing in finite-difference seismic waveform simulations. However, there are two problems in the application of coarse grids for heterogeneous media: the generation of artefact diffraction from the stair-step representation of non-planar interfaces and the inaccuracy of the calculated waveforms due to the interface error. Several equivalent medium parametrization approaches have been proposed to reduce the interface error of the finite-difference method in heterogeneous media. However, these methods are specifically designed for the standard (2,4) staggered-grid scheme and may not be accurate enough for coarse grids when higher-order and optimized schemes are used. In this paper, we develop a tilted transversely isotropic equivalent medium parametrization method to suppress the interface error and the artefact diffraction caused by the staircase approximation under the application of coarse grids. We use four models to demonstrate the effectiveness of the proposed method, and analyse the accuracy of each seismic phase related to the interface. The results show that our method can be used with higher-order and optimized schemes at 3 points per wavelength and produce satisfactory results.

Large-Eddy Simulation with Modeled Wall Stress for Complex Aerodynamics and Stall Prediction

The aerodynamics of aircraft high-lift devices at near-stall conditions is particularly difficult to predict numerically. The computational requirements for accurate wall-resolved large-eddy simulations are currently prohibitive, whereas Reynolds-averaged Navier–Stokes (RANS) models are generally reliable only for low angles of attack with fully attached boundary layers. Methods such as detached-eddy simulation resolve unsteadiness of the outer boundary layer and can predict separation, but they rely upon a thick RANS layer and highly stretched cells that damp the resolved turbulent fluctuations near the wall. An alternative approach, adopted here, is to extend the LES down to the wall, employing a relatively large near-wall normal grid spacing and avoiding grid stretching and high aspect ratios near the wall. A boundary condition then applies the correct wall shear stress as provided by a semiempirical wall model. An adaptive formulation of this wall-modeled large-eddy simulation is presented here and validated using realistic test cases. Validation using a channel flow case at a range of Reynolds numbers demonstrates accurate results with a seamless transition between fully resolved () and wall resolved (). Predictions of the MD-30P/30N airfoil using a modest grid with give excellent agreement with experiments and correctly predict . Finally, the method is demonstrated for the NASA High-Lift Common Research Model providing surface pressure coefficients and velocity profiles. The predictions using a 50-million-cell mesh (for a full aircraft half-model) are in good agreement with considerably finer-grid RANS solutions. The presented method has considerable potential because it can produce accurate solutions to challenging engineering problems involving separation with modest grid and computational requirements while being robust to variations in near-wall grid spacing.

Real-space orthogonal projector-augmented-wave method

The projector augmented wave (PAW) method of Bl\"ochl makes smooth but non-orthogonal orbitals. Here we show how to make PAW orthogonal, using a cheap transformation of the wave-functions. We show that the resulting Orthogonal PAW (OPAW), applied for DFT, reproduces (for a large variety of solids) band gaps from the ABINIT package. OPAW combines the underlying orthogonality of norm-conserving potentials with the large grid spacings and small spectral range in PAW. The OPAW framework can also be combined with other electronic structure theory methods.

Analog IC Design Using Precomputed Lookup Tables: Challenges and Solutions

Design productivity remains an important aspect in the analog integrated circuit design industry, as growing competition and shorter design cycles pressure the traditional flow that involves time-consuming manual iterations in a circuit simulator. This paper describes innovations within an alternative framework that uses precomputed look-up tables (LUTs) to enable fast and accurate evaluation of circuit sizing scenarios without a simulator in the loop. It lets the designer explore and understand the design space boundaries in a systematic setting, thus supporting informed decision making and architectural innovation that is difficult to attain with fully automated, black-box sizing tools. Our discussion begins with an overview of the LUT-based design paradigm and its two primary variants: inverse design (finding design parameters that meet the specifications) and forward evaluation (sweeping design parameters to search the design space). In support of the latter, the core of our work focuses on improving the accuracy and speed of LUT access, enabling millions of queries within seconds on a standard computer. Large improvements over prior art are enabled using enhanced interpolation methods, which allow for a relatively large LUT grid spacing (hence small memory footprint) and yet accurate parameter lookup. We evaluate the efficacy of the proposed methods using two classical analog circuits, a bandgap reference and a folded cascode amplifier. In the bandgap example, we observe less than 1 ppm error between the LUT-predicted temperature coefficient and circuit simulation. In the folded-cascode example, one million design points are generated in only 4 seconds, providing the designer with useful maps that delineate the reachability of certain target specifications.

Analysis of Cloud-Resolving Model Simulations for Scale Dependence of Convective Momentum Transport.

We use 3-D cloud-resolving model (CRM) simulations of two mesoscale convective systems at mid-latitudes and a simple statistical ensemble method to diagnose the scale dependency of convective momentum transport (CMT) and CMT-related properties, and evaluate a parameterization scheme for convection-induced pressure gradient (CIPG) developed by Gregory et al. (GKI97). GKI97 relates CIPG to a constant coefficient multiplied by mass flux and vertical mean wind shear. CRM results show that mass fluxes and CMT exhibit strong scale dependency in temporal evolution and vertical structure. The prevalent understandings of CMT characteristics in terms of upgradient/downgradient transport are applicable to updrafts but not downdrafts across a wide range of grid spacings (4-512 km). For the small-to-median grid spacings (4~64 km), GKI97 reproduces some aspects of CIPG scale dependency except for underestimating the variations of CIPG as grid spacing decreases. However, for large grid spacings (128~512 km), GKI97 might even less adequately parameterize CIPG because it omits the contribution from either the nonlinear shear or buoyancy forcings. Further diagnosis of CRM results suggests that inclusion of nonlinear shear forcing in GKI97 is needed for the large grid spacings, and use of the three-updraft and one downdraft approach proposed in an earlier study may help a modified GKI97 capture more variations of CIPG as grid spacing decreases for the small-to-median grid spacings. Further, the optimal coefficients used in GKI97 seems insensitive to grid spacings, but they might be different for updrafts and downdrafts, for different MCS types, and for zonal and meridional components.

Performance assessment of an underground gas storage cavern using water-shed scale groundwater flow modeling with large grid spacing

In this study, we simulated the water-shed scale groundwater flow near an underground LPG storage cavern system to assess its performance. To consider the effects of the storage cavern system on groundwater flow with large grid spacing, we proposed a mathematical model of a head-dependent flux boundary condition for a storage cavern system. Then, we examined its applicability by comparing the simulation results from assigning head-dependent flux boundary conditions, to those from assigning constant head boundary conditions for a hypothetical storage cavern system. Then, we applied this new simulation to the performance assessment of a real underground LPG storage cavern system. The results show that the influence of a storage cavern system on groundwater flow can be modeled in a 3-D water-shed scale with large cells by applying the proposed head-dependent flux boundary condition. The proposed model for a head-dependent flux boundary condition was used for performance assessment of the storage cavern systems and discussion of future works for their performance.

Defining the Influence of Horizontal Grid Spacing on Ensemble Uncertainty within a Regional Modeling Framework

Abstract Numerical weather prediction (NWP) models are limited with respect to initial and boundary condition data and possess an incomplete description of underlying physical processes. To account for this, modelers have adopted the method of ensemble prediction to quantify the uncertainty within a model framework; however, the generation of ensemble members requires considerably more computational time and/or resources than a single deterministic simulation, especially at convection-allowing horizontal grid spacings. One approach to solving this issue is the development of both a large and small horizontal grid spacing model framework over the same domain for ensemble and deterministic simulations, respectively. This approach assumes that model grid spacing has no influence on model uncertainty; therefore, the objective of this paper is to quantify the influence of horizontal grid spacing on the statistical spread of NWP model ensembles over a regional domain. A series of 24-h simulations using the Weather Research and Forecast (WRF) Model are generated over a static domain with horizontal grid spacings of 35, 25, 15, and 9 km, using both a stochastic kinetic energy backscatter scheme and a multiphysics ensemble approach. Results indicate that horizontal grid spacing does influence the magnitude of uncertainty within an ensemble, although the exact magnitude and type of statistical relationship (direct versus inverse) varies by case. As such, at shorter lead times (<12 h) the dominant atmospheric process associated with each event and the type of ensemble being used outweigh the individual impacts of horizontal grid spacing on ensemble spread.

An efficient 3D traveltime calculation using coarse-grid mesh for shallow-depth source

3D Kirchhoff pre-stack depth migration requires an efficient algorithm to compute first-arrival traveltimes. In this paper, we exploited a wave-equation-based traveltime calculation algorithm, which is called the suppressed wave equation estimation of traveltime (SWEET), and the equivalent source distribution (ESD) algorithm. The motivation of using the SWEET algorithm is to solve the Laplace-domain wave equation using coarse grid spacing to calculate first-arrival traveltimes. However, if a real source is located at shallow-depth close to free surface, we cannot accurately calculate the wavefield using coarse grid spacing. So, we need an additional algorithm to correctly simulate the shallow source even for the coarse grid mesh. The ESD algorithm is a method to define a set of distributed nodal sources that approximate a point source at the inter-nodal location in a velocity model with large grid spacing. Thanks to the ESD algorithm, we can efficiently calculate the first-arrival traveltimes of waves emitted from shallow source point even when we solve the Laplace-domain wave equation using a coarse-grid mesh. The proposed algorithm is applied to the SEG/EAGE 3D salt model. From the result, we note that the combination of SWEET and ESD algorithms can be successfully used for the traveltime calculation under the condition of a shallow-depth source. We also confirmed that our algorithm using coarse-grid mesh requires less computational time than the conventional SWEET algorithm using relatively fine-grid mesh.

Update to ACE‐molecule: Projector augmented wave method on lagrange‐sinc basis set

The projector augmented wave (PAW) method was implemented in a quantum chemistry package that uses Lagrange‐sinc basis set, namely ACE‐Molecule. Its numerical accuracy has been assessed for the AE6 test set and compared with that of Hartwigsen‐Goedecker‐Hutter type pseudopotentials with nonlinear core correction. The PAW method shows a rapid convergence toward complete basis set limits of all electron calculations, whereas the pseudopotential method has a significant deviation even at small grid spacing. To alleviate spurious egg‐box effects, the so‐called supersampling method is adopted to the operation of projector functions. It improved accuracy of total energy calculations at substantially large grid spacing but did not show significant difference in atomization energies from the results without supersampling, which is due to error cancellation. © 2016 Wiley Periodicals, Inc.

Supersampling method for efficient grid-based electronic structure calculations.

The egg-box effect, the spurious variation of energy and force due to the discretization of continuous space, is an inherent vexing problem in grid-based electronic structure calculations. Its effective suppression allowing for large grid spacing is thus crucial for accurate and efficient computations. We here report that the supersampling method drastically alleviates it by eliminating the rapidly varying part of a target function along both radial and angular directions. In particular, the use of the sinc filtering function performs best because as an ideal low pass filter it clearly cuts out the high frequency region beyond allowed by a given grid spacing.

Coupled numerical–analytical approach to landscape evolution modeling

ABSTRACTThe Earth's topography is shaped by surface processes that operate on various scales. In particular, river processes control landscape dynamics over large length scales, whereas hillslope processes control the dynamics over smaller length scales. This scale separation challenges numerical treatments of landscape evolution that use space discretization. Large grid spacing cannot account for the dynamics of water divides that control drainage area competition, and erosion rate and slope distribution. Small grid spacing that properly accounts for divide dynamics is computationally inefficient when studying large domains. Here we propose a new approach for landscape evolution modeling that couples irregular grid‐based numerical solutions for the large‐scale fluvial dynamics and continuum‐based analytical solutions for the small‐scale fluvial and hillslope dynamics. The new approach is implemented in the landscape evolution model DAC (divide and capture). The geometrical and topological characteristics of DAC's landscapes show compatibility with those of natural landscapes. A comparative study shows that, even with large grid spacing, DAC predictions fit well an analytical solution for divide migration in the presence of horizontal advection of topography. In addition, DAC is used to study some outstanding problems in landscape evolution. (i) The time to steady‐state is investigated and simulations show that steady‐state requires much more time to achieve than predicted by fixed area calculations, due to divides migration and persistent reorganization of low‐order streams. (ii) Large‐scale stream captures in a strike‐slip environment are studied and show a distinct pattern of erosion rates that can be used to identify recent capture events. (iii) Three tectono‐climatic mechanisms that can lead to asymmetric mountains are studied. Each of the mechanisms produces a distinct morphology and erosion rate distribution. Application to the Southern Alps of New Zealand suggests that tectonic advection, precipitation gradients and non‐uniform tectonic uplift act together to shape the first‐order topography of this mountain range. Copyright © 2014 John Wiley & Sons, Ltd.

Force estimation from incompressible flow field data using a momentum balance approach

This study investigates how aerodynamic forces on a body can be evaluated using only instantaneous or averaged velocity field data through a control volume approach in an incompressible flow. The method allows for velocity field data to be missing inside the control volume, but requires that the product of the acceleration, the volume of the solid body, and the fluid density are negligible compared to the forces of interest. Validation of the method for accuracy has been conducted using three-dimensional data from a numerical simulation of unsteady flow around a static airfoil and has shown good agreement between actual and estimated force. Additionally, the method is tested using phase-averaged PIV data from flexible flapping membrane wings to calculate flapping cycle averaged forces that are compared with directly measured time-averaged forces. The numerical validation suggests that the method is accurate, while it is only able to give a rough estimate for the noisier experimental data. The lower accuracy of the forces estimated from the PIV data can be explained through experimental constraints, such as too large grid spacing in one of the three dimensions (in one of the cases), having to interpolate data on the control volume surface especially where the PIV laser light is shaded by the wing, and not covering the entire span of the wing.

Experimental assessment of Textile Reinforced Sprayed Mortar strengthening system for brickwork wallettes

This work explores the feasibility of strengthening masonry with Textile Reinforced Mortar (TRM) by projecting it to save application time. Nineteen tests on masonry samples strengthened with TRM have been carried out to assess this new application method. Different mortars and fibre grids were considered for studying their influence and applicability with this new technique. Three points bending tests have been performed on the specimens to compare the flexural strength between cases with manually applied mortar (TRM) and sprayed application (TRSM) of the mortar layer. It was noticed that the strengthening mortar has a significant influence on the failure mode. Results show a remarkable (between 2 and 6 times more) productivity increase when using TRSM and a load-bearing capacity rise for the cases with larger grid spacing and projectable mortar when using TRSM instead of TRM. Greater ductility values were also observed for the TRSM cases in comparison with the analogue TRM cases (same grid and mortar).

Evaluation of topographic index in relation to terrain roughness and DEM grid spacing

Topographic index is an important attribute of digital elevation model (DEM) which indicates soil saturation. It is used for estimation of run-off, soil moisture, depth of ground water and hydrological simulation. Topographic index is derived from DEMs; hence the accuracy of DEM influences its computation. Commonly the raster based grid DEM is widely used to simulate hydrological model parameter, and accuracy varies with respect to DEM grid size and morphological characteristics of terrain. In this study topographic index is evaluated in terms of DEM grid size and terrain roughness. The study was carried out on four small watersheds, having different roughness characteristics, located over the Himalayan terrain. Topographic index surface is derived for each watershed from different grid spacing DEM (10–150 m), analysed and validated. It is found that DEM grid spacing affects the topographic index. The surface representation is smooth in the coarse grid spacing and the pattern of topographic index changes with grid spacing. The spatial autocorrelation of topographic index surface reduces when calculated from larger spacing DEM. The mean of the topographic index surface increases and standard deviation decreases with the increase of grid spacing and the effect is more pronounced in the rough terrain. Accuracy of the topographic index is also evaluated with respect to grid spacing and terrain roughness by comparing the topographic index surface with respect to reference data (10 m grid spacing topographic index surface). The RMSE and mean error of topographic index surface increases in larger grid spacing and the effect is more in rugged terrain.

Wide-area assessment of topographical and meteorological effects on sound propagation by time-domain modeling

Noise mapping with a three-dimensional finite-difference time-domain (FDTD) model over larger areas suffers from its high computational demand. This study shows that an FDTD model in combination with a meteorological model can be used for at least qualitative assessments of topographical and meteorological effects on sound propagation in domains of even some kilometers extension. This is achieved by restricting the acoustical simulations to low frequencies which allow the use of a rather large numerical grid spacing.

Discretizing the Fracture‐Matrix Interface to Simulate Solute Transport

This article examines the required spatial discretization perpendicular to the fracture-matrix interface (FMI) for numerical simulation of solute transport in discretely fractured porous media. The discrete-fracture, finite-element model HydroGeoSphere (Therrien et al. 2005) and a discrete-fracture implementation of MT3DMS (Zheng 1990) were used to model solute transport in a single fracture, and the results were compared to the analytical solution of Tang et al. (1981). To match analytical results on the relatively short timescales simulated in this study, very fine grid spacing perpendicular to the FMI of the scale of the fracture aperture is necessary if advection and/or dispersion in the fracture is high compared to diffusion in the matrix. The requirement of such extremely fine spatial discretization has not been previously reported in the literature. In cases of high matrix diffusion, matching the analytical results is achieved with larger grid spacing at the FMI. Cases where matrix diffusion is lower can employ a larger grid multiplier moving away from the FMI. The very fine spatial discretization identified in this study for cases of low matrix diffusion may limit the applicability of numerical discrete-fracture models in such cases.

Optimization of compact finite difference method for wave acoustic simulation

Recently, the finite difference method, a tool for wave acoustic simulations, can be applied to practical analysis. However, the numerical dispersion which makes propagation speed in simulations change according to the wave length, is a severe problem to maintain high accuracy in the analysis. The numerical error accompanied by the time integration hinders to carry out an accurate simulation. An examination of a compact finite difference scheme which can approximate differentiation precisely on a comparatively large grid spacing was made. It was shown that the adjusting the coefficients in the compact finite difference scheme can simulate a wave propagation accurately with a small amount of computation. The improvement method of the time integration was also discussed. The possibility of improvement of accuracy through a multi‐step integration is shown.