Low-resolution Grid Research Articles

A method for preserving nominally-resolved flow patterns in low-resolution ocean simulations: Dynamical system reconstruction

Accurate representation of large-scale flow patterns in low-resolution ocean simulations is one of the most challenging problems in ocean modelling. The main difficulty is to correctly reproduce effects of unresolved small scales on the resolved large scales. For this purpose, most of current research is focused on development of parameterizations directly accounting for the small scales. In this work we propose an alternative to the mainstream ideas by showing how to reconstruct a dynamical system from the available reference solution data (our proxy for observations) and, then, how to use this system for modelling not only large-scale but also nominally-resolved flow patterns at low resolutions. This approach is advocated as a part of the novel framework for data-driven hyper-parameterization of mesoscale oceanic eddies in non-eddy-resolving models. The main characteristic of this framework is that it does not require to know the physics behind large–small scale interactions to reproduce both large and small scales in low-resolution ocean simulations. We tested it in the context of a three-layer, statistically equilibrated, steadily forced quasigeostrophic model for the beta-plane configuration and showed that non-eddy-resolving solution can be substantially improved towards the reference eddy-resolving benchmark. The proposed methodology robustly allows to retrieve a system of equations governing reduced dynamics of the observed data, while the additional adaptive nudging counteracts numerical instabilities by keeping solutions in the region of phase space occupied by the reference fields. Remarkably, its solutions simulate not only large-scale but also small-scale flow features, which can be nominally resolved by the low-resolution grid. In addition, the proposed method reproduces realistic vortex trajectories. One of the important and general conclusions that can be drawn from our results is that not only mesoscale eddy parameterization is possible in principle but also it can be highly accurate (up to reproducing individual vortices) for significantly reduced dynamics (down to 30 degrees of freedom). This conclusion provides great optimism for the ongoing parameterization studies, which are still far away from being completed.

Comparative evaluation of interpolation methods for the directivity of musical instruments

Measurements of the directivity of acoustic sound sources must be interpolated in almost all cases, either for spatial upsampling to higher resolution representations of the data, for spatial resampling to another sampling grid, or for use in simulations of sound propagation. The performance of different interpolation techniques applied to sparsely sampled directivity measurements depends on the sampling grid used but also on the radiation pattern of the sources themselves. Therefore, we evaluated three established approaches for interpolation from a low-resolution sampling grid using high-resolution measurements of a representative sample of musical instruments as a reference. The smallest global error on average occurs for thin plate pseudo-spline interpolation. For interpolation based on spherical harmonics (SH) decomposition, the SH order and the spatial sampling scheme applied have a strong and difficult to predict influence on the quality of the interpolation. The piece-wise linear, spherical triangular interpolation provides almost as good results as the first-order spline approach, albeit with on average 20 times higher computational effort. Therefore, for spatial interpolation of sparsely sampled directivity measurements of musical instruments, the thin plate pseudo-spline method applied to absolute-valued data is recommended and, if necessary, a subsequent modeling of the phase.

GBIF Data Processing and Validation

GBIF Data Processing and Validation

Application of Video-to-Video Translation Networks to Computational Fluid Dynamics

In recent years, the evolution of artificial intelligence, especially deep learning, has been remarkable, and its application to various fields has been growing rapidly. In this paper, I report the results of the application of generative adversarial networks (GANs), specifically video-to-video translation networks, to computational fluid dynamics (CFD) simulations. The purpose of this research is to reduce the computational cost of CFD simulations with GANs. The architecture of GANs in this research is a combination of the image-to-image translation networks (the so-called “pix2pix”) and Long Short-Term Memory (LSTM). It is shown that the results of high-cost and high-accuracy simulations (with high-resolution computational grids) can be estimated from those of low-cost and low-accuracy simulations (with low-resolution grids). In particular, the time evolution of density distributions in the cases of a high-resolution grid is reproduced from that in the cases of a low-resolution grid through GANs, and the density inhomogeneity estimated from the image generated by GANs recovers the ground truth with good accuracy. Qualitative and quantitative comparisons of the results of the proposed method with those of several super-resolution algorithms are also presented.

Ground Structures-Based Topology Optimization of a Morphing Wing Using a Metaheuristic Algorithm

This paper presents multi-objective topology and sizing optimization of a morphing wing structure. The purpose of this paper is to design a new aircraft wing structure with a tapered shape for ribs, spars, and skins including a torsion beam for external actuating torques, which is anticipated to modify the aeroelastic characteristic of the aircraft wing using multi-objective optimization. Two multi-objective topology optimization problems are proposed employing ground element structures with high- and low-grid resolutions. The design problem is to minimize mass, maximize difference of lift effectiveness, and maximize the buckling factor of an aircraft wing subject to aeroelastic and structural constraints including lift effectiveness, critical speed, and buckling factors. The design variables include aircraft wing structure dimensions and thickness distribution. The proposed optimization problems are solved by an efficient multi-objective metaheuristic algorithm while the results are compared and discussed. The Pareto optimal fronts obtained for all tests were compared based on a hypervolume metric. The objective function values for Case I and Case II at 10 selected optimal solutions exhibit a range of structural mass as 115.3216–411.6250 kg, 125.0137–440.5869 kg, lift effectiveness as 1.0514–1.1451, 1.0834–1.1639 and bucking factor as 38.895–1133.1864 Hz, 158.1264–1844.4355 Hz, respectively. The best results reveal unconventional aircraft wing structures that can be manufactured using additive manufacturing. This research is expected to serve as a foundation for future research into multi-objective topology optimization of morphing wing structures based on the ground element framework.

A robust solver for incompressible high-Reynolds-number two-fluid flows with high density contrast

A new numerical method is developed for the robust simulation of high-Reynolds number two-fluid flows with high density contrast. The proposed method is a combination of the consistent mass–momentum transport framework of Nangia et al. (2019) [5] and the coupled level-set and volume-of-fluid method of Sussman and Puckett (2000) [23]. The conservative form of the momentum equation is solved, and the convection equation of density is solved together with the momentum equation at all cell faces. Moreover, consistent spatial and temporal discretization schemes are used to advance the governing equations of density and momentum to ensure a stable simulation. In the proposed method, the diffusion of the density or viscosity around the interface is not needed. In the test of a canonical case, the convection of a high density droplet, the proposed method makes an accurate prediction of the interface dynamics with a relatively low grid resolution. This feature is useful for reducing the computational cost for two-fluid flows with complex interface geometries. Furthermore, the test results show that the simulation is also stable for high Reynolds number two-fluid flows. In the case of wave breaking, the proposed method is stable for a high Reynolds number of Re=108. In the test case of a collapsing and impinging water column, the present method makes good predictions on the water height and pressure that agree well with experimental results.

Particle-scale modelling of raceway dynamics in a blast furnace using a smoothing method

The lateral high-speed gas injection into a packed bed, forming a raceway cavity, has been commonly practised in chemical engineering applications such as ironmaking blast furnaces whereas the high Reynolds number gas flow and narrow orifice cannot be well resolved by the traditional unresolved CFD-DEM approach using low-resolution grids. In this work, a smoothing method is developed, in which the quantities are transferred between discrete particles and the continuum phase in a grid-independence fashion via solving an isotropic diffusion equation. The model is validated using two cases, i.e., sedimentation of one single particle in a rectangular box and gas-solid hydrodynamics in a spout fluidised bed. Then, the unresolved CFD-DEM approach with the smoothing method is applied to simulate raceway dynamics. The simulation results indicate that the smoothing method allowing high-resolution girds satisfactorily captures a plume-like raceway. The boundary and volume of the cavity are proposed as two criteria to determine the raceway profile quantitatively. The volume of the cavity is 3.03 × 10−3 m3, 3.91 × 10−3 m3, 4.49 × 10−3 m3 with three different inlet gas velocities of 210 m/s, 230 m/s, and 250 m/s, respectively. Higher inlet gas velocity needs a shorter time to establish an equilibrium state.

Efficient Point-in-Polygon Tests by Grids Without the Trouble of Tuning the Grid Resolutions.

The grid-based approach is popular for point-in-polygon tests. However, there is a trade-off between the preprocessing and the inclusion test, which always requires the grid resolutions to be tuned. In this article, we address this challenge by enhancing the grid structure using y-axis-aligned stripes, which are formed by the y-axis-aligned lines passing through the endpoints of the edge segments in the cell, thereby managing the edge segments in each grid cell. Moreover, we precompute the inclusion properties of the x-axis-aligned top borders of the stripes during preprocessing. Therefore, to answer a query point with the ray crossing method, we can emit a ray from the point to propagate upwards until the ray arrives at the top border of a stripe. We thoroughly consider singular cases to guarantee each query point can be answered in the stripe that contains the point. In our method, the computational load can be decreased, as one coordinate of the intersection point between the ray and an edge is known in advance, and parallel computing can be well exploited because the branching operations for determining whether an edge intersects with the ray are saved. Experimental results show that the efficiency of our method does not vary much with respect to the grid resolutions, so the trouble of tuning grid resolutions can be avoided. Ultimately, our method with a low grid resolution can reduce the preprocessing time and still achieve a higher inclusion test efficiency than the existing methods with a high grid resolution, especially on GPUs.

Comment on “Numerical approach to define a thermodynamically equivalent material for the conjugate heat transfer simulation of very thin coating layers” by P. Olmeda, X. Margot, P. Quintero, J. Escalona, International Journal of Heat and Mass Transfer, Vol. 162 (2020) 120377

In the recent paper “Numerical approach to define a thermodynamically equivalent material for the conjugate heat transfer simulation of very thin coating layers” by P. Olmeda, X. Margot, P. Quintero, J. Escalona, Int. J. Heat Mass Transfer 162 (2020) 120377 the authors develop a procedure to identify a thicker pseudo-material to mimic the dynamic response of a thin thermal barrier coating. A thicker layer is desired to allow efficient conjugate heat transfer analysis. They employ an ad hoc procedure for defining the thermal properties of the material to approximate dynamic similarity with low grid resolution. There exists a published analytical solution for this same problem that allows the pseudo-material’s thermal properties to be directly determined without a trial-and-error approach. The approach is elucidated and the effects of numerical resolution are explored.

The strong effect of network resolution on electricity system models with high shares of wind and solar

Energy system modellers typically choose a low spatial resolution for their models based on administrative boundaries such as countries, which eases data collection and reduces computation times. However, a low spatial resolution can lead to sub-optimal investment decisions for wind and solar generation. Ignoring power grid bottlenecks within regions tends to underestimate system costs, while combining locations with different wind and solar capacity factors in the same resource class tends to overestimate costs. We investigate these two competing effects in a capacity expansion model for Europe’s power system with a high share of renewables, taking advantage of newly-available high-resolution datasets as well as computational advances. We vary the number of nodes, interpolating between a 37-node model based on country and synchronous zone boundaries, and a 1024-node model based on the location of electricity substations. If we focus on the effect of renewable resource resolution and ignore network restrictions, we find that a higher resolution allows the optimal solution to concentrate wind and solar capacity at sites with better capacity factors and thus reduces system costs by up to 10% compared to a low resolution model. This results in a big swing from offshore to onshore wind investment. However, if we introduce grid bottlenecks by raising the network resolution, costs increase by up to 23% as generation has to be sourced more locally at sites with worse capacity factors. These effects are most pronounced in scenarios where grid expansion is limited, for example, by low local acceptance. We show that allowing grid expansion mitigates some of the effects of the low grid resolution, and lowers overall costs by around 16%.

Simple extended lattice Boltzmann methods for incompressible viscous single-phase and two-phase fluid flows

The lattice Boltzmann method (LBM) is a numerical method with second-order spatial accuracy for incompressible viscous fluid flows based on an analogy with the kinetic theory of gases. Recently, the collision model of the LBM has become more and more complicated as its numerical stability has been enhanced. In this paper, conversely, we propose simple extended LBMs having good numerical stability with simple collision models by using the lattice kinetic scheme (LKS), which is an extended LBM. First, several schemes for single-phase flows based on the LKS are presented. The LKS is a simple stable scheme but has higher-order dissipation errors in the calculation of high-Reynolds-number flows. To solve this problem, the LKS is improved by using the linkwise artificial compressibility method (LWACM). Then, the numerical stability and accuracy of the LBM, the LKS, the LWACM, and the improved LKS are compared in a simulation of a doubly periodic shear layer at high Reynolds number with low-resolution grids. Next, a simple scheme for two-phase flows with large density ratio is constructed on the basis of the LKS and the improved LKS. The scheme is stable even for two-phase flows with large density ratio. The validation of the scheme is studied in a simulation of a binary droplet collision.

A dynamic coarsening approach to immiscible multiphase flows in heterogeneous porous media

We have developed a sequential approach to accelerate immiscible multiphase flow modelling in heterogeneous porous media using discontinuous Galerkin methods and dynamic mesh coarsening. This approach involves dynamic domain decomposition and different solution strategies in the different flow regions, using a criterion that can be fastly evaluated. We use high-resolution grids and low order methods in the multiphase flow regions near the saturation discontinuity and a discontinuous Galerkin method along with low-resolution grids in single-phase flow regions of the domain. We present a fast technique to estimate the position of the saturation front and identify the flow zones that need high-resolution gridding. We demonstrate the accuracy of our approach through test cases from the second SPE10 model by comparing our results with fine-scale simulations.

Numerical Investigation of Tip Vortex Cavitation Inception and Noise of Underwater Propellers of Submarine Using Sequential Eulerian–Lagrangian Approaches

In this study, the high-fidelity numerical methods are developed to investigate the tip vortex cavitation (TVC) inception and noise of underwater propellers, namely, Model-A and Model-B, which are designed to investigate the effects of sweep angle on cavitation inception and noise. In addition, the entire body of the DARPA Suboff submarine is included to consider the effects of the inflow distortion originating from the boundary layer flow of the submarine body on the cavitating flow of the propellers. The Eulerian approach consisting of Reynolds-averaged Navier–Stokes (RANS) solver and the vortex model is coupled with the Lagrangian approach using the bubble dynamics equations and the acoustic analogy for nuclei initially distributed in inlet flow. First, three-dimensional incompressible unsteady RANS simulations are performed to predict the hydrodynamic flow field driven by underwater propellers installed on a DARPA Suboff submarine body. The Scully vortex model and dissipation vortex model (DVM) are used to regenerate the tip vortex dissipated by artificial numerical damping and low grid resolution around the vortex core center, which is identified by using minimum λ2-criterion in the swirling flow field originating from the propeller blade tip. Then, tip vortex cavitation inception is simulated by applying the bubble dynamics equations to nuclei initially distributed in the inflow region. The volume and location of each nucleus are obtained by solving the bubble dynamics equations on the flow field obtained using the Eulerian method. Finally, the cavitation noise is predicted by modeling each bubble with a point monopole source whose strength is proportional to its volume acceleration. The validity of the present numerical methods is confirmed by comparing the predicted acoustic pressure spectrum with the measured ones.

Application of a zonal hybrid URANS/LES turbulence model to high and low-resolution grids for engine simulation

A zonal hybrid unsteady Reynolds-averaged Navier–Stokes/large eddy simulation (URANS-LES) Zonal detached-eddy simulation (ZDES) model is applied to internal combustion engine (ICE) simulation and comparisons of predicted flow morphology and variability are carried out against on the transparent combustion chamber (TCC-III) particle image velocimetry (PIV) data set for motored conditions. To this aim, a previously developed model derived from a standard seamless-detached eddy simulation (DES) formulation is adopted for two different grid resolutions. In particular, two zonalization choices are evaluated based on previous single-grid results, in order to assess the model outcomes based on the joint turbulence treatment/grid density: the seamless-DES mode is applied (1) only to the cylinder (TCC-Z1) and (2) to the cylinder and intake port (TCC-Z2). Multi-cycle simulations (50 samples) are carried out and the results are compared to experimental data in terms of PIV images using multiple quality indices on multiple planes ( Y = 0 and X = 0). Finally, comparison of predicted mean flow fields is extended to standard URANS mode. Results show that the use of a cylinder-only seamless-DES treatment on a relatively coarse grid results in a quantitative agreement between simulated and measured (PIV) flow fields, both in terms of average morphology and flow variability, whereas the extension of the DES mode to the intake port does not introduce relevant variations. Quality indicators seem to be moderately sensitive to the grid resolution, thus confirming the adaptive potential of a ZDES–like model and promoting the use of DES–type turbulence modelling even on relatively low-resolution grids. The analysis of average fields compared to URANS simulations highlights the benefit for both grids of a scale-resolving ZDES modelling when the same underlying turbulence model ( k-ε RNG) is used. This study reinforces the recommendation in the use of hybrid URANS-LES models to simulate ICE flows. The adopted ZDES formulation based on the two-equation k-ε RNG model shows that high-quality results can be obtained even on engineering-grade grids, both in terms of average and cycle-to-cycle variation. The numerical results obtained using the two grids with variable resolution are consistent, and this further promotes a wider adoption of this class of models to simulate engine flows in industrial applications.

Modelling uncertainty using stochastic transport noise in a 2-layer quasi-geostrophic model

The stochastic variational approach for geophysical fluid dynamics was introduced by Holm (Proc Roy Soc A, 2015) as a framework for deriving stochastic parameterisations for unresolved scales. This paper applies the variational stochastic parameterisation in a two-layer quasi-geostrophic model for a $ \beta $-plane channel flow configuration. We present a new method for estimating the stochastic forcing (used in the parameterisation) to approximate unresolved components using data from the high resolution deterministic simulation, and describe a procedure for computing physically-consistent initial conditions for the stochastic model. We also quantify uncertainty of coarse grid simulations relative to the fine grid ones in homogeneous (teamed with small-scale vortices) and heterogeneous (featuring horizontally elongated large-scale jets) flows, and analyse how the spread of stochastic solutions depends on different parameters of the model. The parameterisation is tested by comparing it with the true eddy-resolving solution that has reached some statistical equilibrium and the deterministic solution modelled on a low-resolution grid. The results show that the proposed parameterisation significantly depends on the resolution of the stochastic model and gives good ensemble performance for both homogeneous and heterogeneous flows, and the parameterisation lays solid foundations for data assimilation.

A Multiscale Control Volume framework using the Multiscale Restriction Smooth Basis and a non-orthodox Multi-Point Flux Approximation for the simulation of two-phase flows on truly unstructured grids

In these days, the advances in the fields of geology have led to geocellular models containing up to hundreds millions cells. Meanwhile, the standard petroleum reservoir simulations are limited to models with only a fraction of this amount. Thus, the multiples simulation of multiphase flow in heterogeneous and anisotropic media on the geological scale are simply impractical. To overcome this problem Multiscale Finite Volume (MsFV) uses operators to project the fine-scale system of equations onto a coarse-scale space originated from a lower-resolution grid. The resulting coarse system is solved, and by using the multiscale operator projected back onto the higher-resolution grid. Notwithstanding, the MsFV is not capable of capturing geologic properties on unstructured grids, as in its classical form, it relies on a Two Point Flux Approximation (TPFA) for fluxes, which is only consistent for k-orthogonal grids. Furthermore, the algorithm used by the MsFV to generate the geometric entities, such as, coarse-scale and dual meshes and its centers are not valid for general unstructured grids. The Multiscale Restricted Smoothed Basis (MsRSB) method expands this framework by creating the algorithms capable of generating these structures and by proposing an iterative multiscale operator capable of handling simulation on unstructured coarse grids. However, it fails to produce consistent solutions on fine-scale unstructured grids and for arbitrary permeability tensors, as it uses the TPFA method. In this article, we couple a Multi-Point Flux Approximation with a Diamond stencil to the MsRSB, to extend its use to general unstructured grids. We call our framework the “Multiscale Control-Volume” (MsCV) method. Moreover, we bring the iterative Dirichlet pressure correction scheme and the upscaling flux correction to the unstructured multiscale context. On the first examples, we study the impact of these corrections on the simulation of one-phase flow using the SPE Model 2 benchmark. In addition, we show the behavior of the MsCV framework on the simulation of two-phase flows on general unstructured grids and highly heterogeneous and isotropic permeability fields.

An HLLC-type Riemann solver and high-resolution Godunov method for a two-phase model of reactive flow with general equations of state

A high-resolution Godunov method is developed for a two-phase model of reactive flow. The model considers general equations of state of Mie-Grüneisen form and different choices for the reaction rate, both relevant for simulations of the dynamical behavior of detonations in PBX-type granular explosives. The numerical approach employs a Riemann solver, and various options ranging from an exact solver to an approximate solver of HLLC type are described. A principal aim of the paper is an assessment of the approximate Riemann solvers in terms of the accuracy and efficiency of numerical solutions of the two-phase model. In particular, this study considers the state-sensitive behavior in different regimes of the solutions in a reverse-impact configuration, including compaction, run to detonation, and the evolution to compaction-led and reaction-led steady detonations. For these regimes, the convergence properties of the numerical approach are examined for the different choices of the Riemann solver, as is the error in the solutions at lower grid resolution. Finally, the computational performance of the time-stepping scheme is assessed for the different solvers.

Machine Learning Algorithms for Real-time Tsunami Inundation Forecasting: A Case Study in Nankai Region

The most acceptable method to estimate tsunami inundation caused by a submarine earthquake is by conducting a nonlinear tsunami simulation. However, this method has the disadvantages of a relatively high computational cost and the necessity for immediate warning announcements when a tsunami is imminent. In this study, to overcome this problem, we apply two machine learning models, a convolutional neural network and a multilayer perceptron, to estimate tsunami inundation in real time. We run multiple fault scenarios and store the result of the maximum tsunami amplitude in a low-resolution grid and the associated tsunami inundation in a high-resolution grid in the database. The convolutional neural network selects tsunami inundation in the high-resolution grid as the forecast based on pattern similarity between the input, which is the results of linear forward modeling in the low-resolution grid, and the precomputed patterns in the database. Slightly different from the convolutional neural network, instead of selecting the best-fit scenario in the database, the multilayer perceptron directly generates the inundation forecast based on knowledge acquired during the training process. We conduct an experiment using the hypothetical future Nankai megathrust earthquake with Atashika and Owase Bays in Japan as the study cases. The results show that our proposed methods are extremely fast (less than 1 s) and comparable with nonlinear forward modeling. Therefore, the proposed methods can be used as a deterministic model for real-time simulation.

Comparison of methodologies for generation of future weather data for building thermal energy simulation

In the last decade, building energy simulation (BES) became a central component in building energy systems’ design and optimization. For each building location, BES requires one year of hourly weather data. Most buildings are designed to last 50+ years, consequently, the building design phase should include BES with future weather files considering climate change. This paper presents a comparative study of two methods to produce future climate hourly data files for BES: Morphing and typical meteorological year of future climate (F-TMY). The study uses data from a high-resolution (9 km) regional climate atmospheric model simulation of Iberia, spanning 10 years of historical and future hourly data. This study compares both methods by analyzing anomalies in air temperature, and the impact in BES predictions of annual and peak energy consumption for space heating, cooling and ventilation in 4 buildings. Additionally, this study performs a sensitivity analysis of morphing method. The analysis shows that F-TMY is representative of the multi-year simulation for BES applications. A high-quality Morphed TMY weather file has a similar performance compared to F-TMY (average difference: 8% versus 7%). Morphing based on different baseline climates, low-grid resolution and/or outdated climate projections leads to BES average differences of 16%-20%.

Assessment and Validation of Very-Large-Eddy Simulation Turbulence Modeling for Strongly Swirling Turbulent Flow

Strongly swirling flow is widely encountered in engineering applications. However, accurate prediction of the flow is still challenging for turbulence modeling. The present study reports the assessment and validation of a newly developed self-adaptive turbulence modeling, denoted as very-large-eddy simulation (VLES), for the prediction of turbulent strongly swirling flow through a suddenly expanding circular pipe at Reynolds number of and , and the corresponding swirl numbers are 1.16 and 1.23, which are both very strongly swirling flow. The VLES method is a unified simulation approach enabling a seamless evolution from Reynolds-Averaged Navier–Stokes (RANS) to LES and finally approaching direct numerical simulation (DNS) depending on the numerical resolution. In the present work, a new proposed VLES turbulence closure model, namely, VLES BSL , and other two models, denoted as VLES and VLES , are applied for the strong swirling flow simulation. Two meshes containing about 0.9 million and 5.1 million cells are applied, with different mesh resolutions. The simulation results are compared with available experimental data and RANS results. It is observed that the present VLES models accurately predict the time-averaged and root-mean-square (rms) velocities compared with the measurements on both of the two meshes. The significant features of the present strongly swirling flow, including vortex breakdown and the vortex core precession, large recirculation region, and shear-layer instability, are well captured by the present VLES models. Furthermore, the anisotropy of the Reynolds stresses of the strongly swirling flow is also well predicted. Satisfactory predictions can be obtained using low grid resolution with the VLES models, which confirm the validity and accuracy of the VLES modeling for strongly swirling turbulent flow.