Advection Scheme Research Articles

The High-resolution Intermediate Complexity Atmospheric Research (HICAR v1.1) model enables fast dynamic downscaling to the hectometer scale

Abstract. High-resolution (< 1 km) atmospheric modeling is increasingly used to study precipitation distributions in complex terrain and cryosphere–atmospheric processes. While this approach has yielded insightful results, studies over annual timescales or at the spatial extents of watersheds remain unrealistic due to the computational costs of running most atmospheric models. In this paper we introduce a high-resolution variant of the Intermediate Complexity Atmospheric Research (ICAR) model, HICAR. We detail the model development that enabled HICAR simulations at the hectometer scale, including changes to the advection scheme and the wind solver. The latter uses near-surface terrain parameters which allow HICAR to simulate complex topographic flow features. These model improvements clearly influence precipitation distributions at the ridge scale (50 m), suggesting that HICAR can approximate processes dependent on particle–flow interactions such as preferential deposition. A 250 m HICAR simulation over most of the Swiss Alps also shows monthly precipitation patterns similar to two different gridded precipitation products which assimilate available observations. Benchmarking runs show that HICAR uses 594 times fewer computational resources than the Weather Research and Forecasting (WRF) atmospheric model. This gain in efficiency makes dynamic downscaling accessible to ecohydrological research, where downscaled data are often required at hectometer resolution for whole basins at seasonal timescales. These results motivate further development of HICAR, including refinement of parameterizations used in the wind solver and coupling of the model with an intermediate-complexity snow model.

Development of Advective Dynamic Stabilization scheme for ISPH simulations of free-surface fluid flows

This study presents an enhanced version of a numerical stabilizing scheme, namely, the Dynamic Stabilization scheme (DS) by Tsuruta et al. (2013), referred to as the Advective DS scheme (ADS) for further enhancement of the numerical stability and accuracy in ISPH simulations of free-surface fluid flows. To ensure general stability of calculations, particle methods may benefit from particle regularization schemes including artificial repulsive force schemes to keep particles equally distanced. DS explicitly provides a stabilizing force based on the overlapped state of a target particle and its neighboring particle, resulting in a momentum-conservative repulsive force and stable simulations. However, DS may also result in numerical noises and numerical dissipation. Such numerical noises stem from the excess stabilizing forces because of consideration of the particle positions only. The approaching velocities of particles, corresponding to the divergence-free condition, are ignored. To precisely consider the dynamic states of particles in derivation of stabilizing forces, in ADS, the approaching velocities are additionally considered and the stabilizing forces are derived in a variationally consistent form based on time rate of particle overlapping state, to precisely recover the exact deteriorated particle regularity state. The enhanced performance of the proposed ADS scheme is shown through some benchmark tests including a Taylor-Green vortex, a dam break as a violent free-surface flow, an oscillating drop and a rotating square patch. The enhanced performance of ADS in terms of reproduced pressure and velocity fields, energy conservation and convergence are well demonstrated.

Forming Terrains by Glacial Erosion

We introduce the first solution for simulating the formation and evolution of glaciers, together with their attendant erosive effects, for periods covering the combination of glacial and inter-glacial cycles. Our efficient solution includes both a fast yet accurate deep learning-based estimation of highorder ice flows and a new, multi-scale advection scheme enabling us to account for the distinct time scales at which glaciers reach equilibrium compared to eroding the terrain. We combine the resulting glacial erosion model with finer-scale erosive phenomena to account for the transport of debris flowing from cliffs. This enables us to model the formation of terrain shapes not previously adequately modeled in Computer Graphics, ranging from U-shaped and hanging valleys to fjords and glacial lakes.

A study on the influence of the numerical scheme on the accuracy of blade-resolved simulations employed to evaluate the performance of the NREL 5 MW wind turbine rotor in full scale

We present a numerical investigation on the influence of the numerical arrangement in the accuracy of the NREL 5 MW wind turbine rotor performance evaluation in full scale, using a Computational Fluid Dynamics (CFD) methodology which employs the Finite Volume Method (FVM) implemented in the OpenFOAM software. The nonlinearity of the Navier–Stokes equation, which requires special treatment and still represents a subject under intense debate in the scientific community, is tackled by using two different discretization schemes for computing the convective term. In addition, since the advection scheme numerically interacts with the turbulence closure model employed in the numerical simulations, we considered the URANS k-ω SST and DES k-ω SST models to perform the blade-resolved simulations. A hybrid central/upwind scheme, namely the LUST scheme, was considered for discretizing the convective term for both URANS and DES simulations, while the second order accurate upwind given by the LUD scheme was considered only in the URANS simulation. Considering the LUST scheme, an investigation on the temporal and spatial discretization was performed for both turbulence closure models. The performance of the NREL 5 MW rotor for offshore application in full scale was assessed in terms of power production, generated thrust, and forces distribution along the blade span, for the operation condition of optimal wind-power conversion efficiency. We provide detailed information regarding the flow features and computational cost, and verified the results from each case by comparing the CFD results against values obtained using the blade element momentum theory implemented in OpenFAST. For the spatial discretization considered in one of the meshes, the LUD scheme showed low accuracy in the results, being more susceptible to the grid influence for the URANS simulations compared to LUST, while the URANS-LUST and DES-LUST approaches were both suitable options for all the meshes investigated. The DES-LUST approach was less affected by the variation in the size of the time step employed. Additionally, finer flow structures were captured with the DES-LUST simulations at an affordable computational cost.

Regulating Fine‐Scale Resolved Convection in High‐Resolution Models for Better Hurricane Track Prediction

AbstractHigh‐resolution atmospheric models are powerful tools for hurricane track and intensity predictions. Although using high resolution contributes to better representation of hurricane structure and intensity, its value in the prediction of steering flow and storm tracks is uncertain. Here we present experiments suggesting that biases in the predicted North Atlantic hurricane tracks in a high‐resolution (approximately 3 km grid‐spacing) model originates from the model's explicit simulation of deep convection. Differing behavior of explicit convection leads to changes in the synoptic‐scale pattern and thereby to the steering flow. Our results suggest that optimizing small‐scale convection activity, for example, through the model's horizontal advection scheme, can lead to significantly improved hurricane track prediction (∼10% reduction of mean track error) at lead times beyond 72 hr. This work calls attention to the behavior of explicit convection in high‐resolution models, and its often overlooked role in affecting larger‐scale circulations and hurricane track prediction.

A finite volume flux coordinate independent approach

We present a novel family of schemes as the merging between a one-dimensional advection scheme with the flux coordinate independent approach. The scheme can be used to discretize the field-aligned Navier-Stokes equations in three dimensions. Our approach consists of three major steps: (i) the formulation of the one-dimensional scheme in a locally field-aligned coordinate system, (ii) a numerical evaluation of the surface integrals over the field-aligned finite volumes and (iii) the introduction of smoothing into the numerical transformation operators to ensure stability of the resulting scheme.We study this approach at the example of a staggered finite volume scheme with a field-aligned cylinder as initial condition. We show superior stability and conservative properties over previous direct discretizations. In particular, the relative mass conservation is improved by several orders of magnitude. Without smoothing in the transformation operators the scheme is prone to oscillations in both parallel and perpendicular directions. In the presence of strong perpendicular gradients, additional parallel diffusion is needed to control spurious oscillations in the perpendicular planes.We provide parallel implementations for various platforms including GPUs freely in the C++ library Feltor

Error estimates for a finite volume scheme for advection–diffusion equations with rough coefficients

We study the implicit upwind finite volume scheme for numerically approximating the advection–diffusion equation with a vector field in the low regularity DiPerna–Lions setting. That is, we are concerned with advecting velocity fields that are spatially Sobolev regular and data that are merely integrable. We prove that on unstructured regular meshes the rate of convergence of approximate solutions generated by the upwind scheme towards the unique solution of the continuous model is at least one. The numerical error is estimated in terms of logarithmic Kantorovich–Rubinstein distances and provides a bound on the rate of weak convergence.

Hybrid numerical methods for modelling multi-physics mass transport in coal

It is a challenging task to predict and analyse the transient flow physics in unconventional complex geological formations such as coal seams. This is due to the multi-scale multi-physics nature of processes taking place in coal seam gas reservoirs. Therefore, numerical tools allowing the incorporation of various flow physics inherent to coal into the simulation routine are of particular importance. At the pore-scale, the rock images obtained by micro-computed tomography are frequently used for flow modelling in porous or fractured media by direct numerical simulations (Lattice Boltzman method or by solving Navier Stokes equations) or by utilising so-called pore-network modelling. Both methods have advantages and drawbacks, while their hybridisation may allow us avoid some of the major pitfalls. Due to a limited number of research dedicated to image-based pore-scale modelling in coal, we develop a hybrid numerical model that combines the Hagen-Poiseuille analytical solution and the volume of fluid advection scheme for fluid flow in fractures with the continuum Darcy flow in the coal matrix. The explicit coupling of fluid flow across the fracture-matrix domains is implemented via corresponding source terms in the governing equations. Besides, additional physics including sorption and matrix swelling-shrinkage phenomena are introduced into the numerical model. The hybrid solver is validated against analytical solutions and a previously developed Darcy-Brinkman-Stokes framework, which has similar functionality for modelling fluid flow in coal seams. To validate the developed model and show its capability to capture multi-scale multi-physics flow in coal, several illustrative simulations are conducted using synthetic and realistic digital images of coal. As a result, the accuracy of the hybrid solver was within 4% when compared to the Darcy-Brinkman-Stokes framework for flow simulation on realistic geometry. Besides, the non-parallelised hybrid model outperformed the parallelised direct numerical simulation, being more than 90 times faster in terms of computational time. The findings are beneficial for conducting larger core-scale simulations of multi-scale multi-physics flow in coal seams with potential applications to natural gas production, hydrogen storage, and carbon dioxide geosequestration.

A random choice scheme for scalar advection

SummaryThis paper is dedicated to a numerical method based on a random choice as proposed in Glimm's scheme. It is applied to the problem of advection of a scalar quantity. The numerical scheme proposed here relies on a fractional step approach for which: the first step is performed using any classical finite‐volume scheme, and the second step is a cell‐wise update. This second step is a projection based on a random choice. The resulting scheme possesses a very low level of numerical diffusion. In order to assess the capabilities of this approach, several test cases have been investigated including convergence studies with respect to the mesh‐size. The algorithm performs very well on one‐dimensional and multi‐dimensional problems. This algorithm is very easy to implement even for multi‐processor computations.

Cut-cell Eta Model: History and Challenges Overcome

Incentive for writing a limited area weather prediction model stemmed from the author’s several years stay at the University of California in Los Angeles, at the end of the sixties. Exposed to what he refers to as the Akio Arakawa approach, having had an idea for a scheme that was an improvement to what Arakawa was using, and being aware of the importance of topography for the weather of the country he was to continue his career in, led in 1973 to his first limited area 3D code, the forerunner of what was to become the Eta model. Refinements and enhancements introduced by the author in subsequent years and of the collaborator he acquired, Zaviša Janjić, resulted in the code that when installed at the then U.S. National Meteorological Center, attracted attention. Hallmarks of the model were Mesinger’s eta vertical coordinate, and Janjić’s transformation of the Arakawa horizontal advection scheme to the model’s semi-staggered B/E grid. In 1993 the Eta became the primary regional forecasting model of the U.S. Weather Bureau, and in 1998 its precipitation accuracy of 24-48 h forecasts became higher across all intensity thresholds than that of its predecessor, the Nested Grid Model (NGM) for its 00-24 h forecasts. Lately, the Eta is extensively used also as a regional climate model (RCM), mostly over the South American domain, and in near-real time as a tool for the North American Regional Reanalysis (NARR), run by the U.S. National Centers for Environmental Prediction/Climate Prediction Center. Several later unique numerical refinements of the Eta addressing problems noticed are summarized in a “before and after” fashion, and results are mentioned of its ensemble skill compared to that of its highly acclaimed driver European Centre for Medium-Range Weather Forecasts (ECMWF) model.

FEOTS v0.0.0: a new offline code for the fast equilibration of tracers in the ocean

Abstract. In this paper we introduce a new software framework for the offline calculation of tracer transport in the ocean. The Fast Equilibration of Ocean Tracers Software (FEOTS) is an end-to-end set of tools to efficiently calculate tracer distributions on a global or regional sub-domain using transport operators diagnosed from a comprehensive ocean model. To the best of our knowledge, this is the first application of a transport matrix model to an eddying ocean state. While a Newton–Krylov-based equilibration capability is still under development and not presented here, we demonstrate in this paper the transient modeling capabilities of FEOTS in an application focused on the Argentine Basin, where intense eddy activity and the Zapiola Anticyclone lead to strong mixing of water masses. The demonstration illustrates progress in developing offline passive tracer simulation capabilities, while highlighting the challenges of the impulse response functions approach in capturing tracer transports by a non-linear advection scheme. Our future work will focus on improving the computational efficiency of the code to reduce time-to-solution, using different basis functions to better represent non-linear advection operators, applying FEOTS to a parent model with unstructured grids (Ocean Model for Prediction Across Scales, MPAS-Ocean), and fully implementing a Newton–Krylov steady-state solver.

Sliding or Stumbling on the Staircase: Numerics of Ocean Circulation Along Piecewise‐Constant Coastlines

AbstractCoastlines in most ocean general circulation models are piecewise constant. Accurate representation of boundary currents along staircase‐like coastlines is a long‐standing issue in ocean modeling. Pioneering work by Adcroft and Marshall (1998, https://doi.org/10.3402/tellusa.v50i1.14514) revealed that artificial indentation of model coastlines, obtained by rotating the numerical mesh within an idealized square basin, generates a spurious form drag that slows down the circulation. Here, we revisit this problem and show how this spurious drag may be eliminated. First, we find that physical convergence to spatial resolution (i.e., the main characteristics of the flow are insensitive to the increase of the mesh resolution) allows simulations to become independent of the mesh orientation. An advection scheme with a wider stencil also reduces sensitivity to mesh orientation from coarser resolution. Second, we show that indented coastlines behave as straight and slippery shores when a true mirror boundary condition on the flow is imposed. This finding applies to both symmetric and rotational‐divergence formulations of the stress tensor, and to both flux and vector‐invariant forms of the equations. Finally, we demonstrate that the detachment of a vortex flowing past an outgoing corner of the coastline is missed with a free‐slip (zero vorticity) condition at the corner. These results provide guidance for a better numerical treatment of coastlines (and isobaths) in ocean general circulation models.

Improving trajectory calculations by FLEXPART 10.4+ using single-image super-resolution

Abstract. Lagrangian trajectory or particle dispersion models as well as semi-Lagrangian advection schemes require meteorological data such as wind, temperature and geopotential at the exact spatiotemporal locations of the particles that move independently from a regular grid. Traditionally, these high-resolution data have been obtained by interpolating the meteorological parameters from the gridded data of a meteorological model or reanalysis, e.g., using linear interpolation in space and time. However, interpolation is a large source of error for these models. Reducing them requires meteorological input fields with high space and time resolution, which may not always be available and can cause severe data storage and transfer problems. Here, we interpret this problem as a single-image super-resolution task. That is, we interpret meteorological fields available at their native resolution as low-resolution images and train deep neural networks to upscale them to a higher resolution, thereby providing more accurate data for Lagrangian models. We train various versions of the state-of-the-art enhanced deep residual networks for super-resolution (EDSR) on low-resolution ERA5 reanalysis data with the goal to upscale these data to an arbitrary spatial resolution. We show that the resulting upscaled wind fields have root-mean-squared errors half the size of the winds obtained with linear spatial interpolation at acceptable computational inference costs. In a test setup using the Lagrangian particle dispersion model FLEXPART and reduced-resolution wind fields, we find that absolute horizontal transport deviations of calculated trajectories from “true” trajectories calculated with un-degraded 0.5∘ × 0.5∘ winds are reduced by at least 49.5 % (21.8 %) after 48 h relative to trajectories using linear interpolation of the wind data when training on 2∘ × 2∘ to 1∘ × 1∘ (4∘ × 4∘ to 2∘ × 2∘) resolution data.

A scheme using finite‐volume method for local horizontal derivatives in spectral model: Hydrostatic case

AbstractThe Yin‐He Global Spectral Model (YHGSM) is a dry‐mass conserving hydrostatic global spectral model, relying on spectral transforms to compute horizontal derivatives. We present an extension of YHGSM core named YHGSM‐FVM which uses a second‐order finite‐volume method (FVM) to compute the horizontal derivatives in grid‐point space instead of the spectral approach. With this approach, the computational efficiency of the spectral model is improved since part of the spectral transforms is superseded by FVM which only needs local data and the computational demand is lower. More importantly, YHGSM‐FVM is still a spectral model solving the Helmholtz equation directly in spectral space with a highly efficient semi‐implicit semi‐Lagrangian advection scheme. The comparisons between YHGSM‐FVM and YHGSM are conducted, and the results show that both models have comparable prediction skill, but YHGSM‐FVM outperforms YHGSM in computational efficiency.

Impact of wettability on interface deformation and droplet breakup in microcapillaries

The objective of this research paper is to relate the influence of dynamic wetting in a liquid/liquid/solid system to the breakup of emulsion droplets in capillaries. Therefore, modeling and simulation of liquid/liquid flow through a capillary constriction have been performed with varying dynamic contact angles from highly hydrophilic to highly hydrophobic. Advanced advection schemes with geometric interface reconstruction (isoAdvector) are incorporated for high interface advection accuracy. A sharp surface tension force model is used to reduce spurious currents originating from the numerical treatment and geometric reconstruction of the surface curvature at the interface. Stress singularities from the boundary condition at the three-phase contact line are removed by applying a Navier-slip boundary condition. The simulation results illustrate the strong dependency of the wettability and the contact line and interface deformation.

Large-eddy simulation of separated turbulent flows over a three-dimensional hill using WRF and OpenFOAM

It is not clearly known about the limitations of the large-eddy simulation (LES) mode of an atmospheric model (WRF) in predicting the microscale flows for engineering purpose. This study chooses a typical separated turbulent flow past a three-dimensional axisymmetric hill and investigates the performance of WRF-LES in comparison with the popular CFD solver (OpenFOAM). The numerical models and conditions are set similarly between the two codes. The instantaneous visualization shows that both WRF-LES and OpenFOAM-LES can produce the primary flow features, including hairpin vortices, horseshoes, and surface-shear-induced vortices at different scales, with high similarity. Nevertheless, the turbulent kinetic energy in the near wake produced by WRF-LES is underestimated, in comparison with WRF-LES. The energy spectra suggest that WRF-LES using the high-order advection schemes has a stronger capacity of generating and maintaining small-scale turbulent motions than OpenFOAM-LES. Furthermore, the deviation of numerical dissipation behavior is examined between the two solvers.

Cooperative Filtering and Parameter Identification for Advection–Diffusion Processes Using a Mobile Sensor Network

This article presents an online parameter identification scheme for advection–diffusion processes using data collected by a mobile sensor network. The advection–diffusion equation is incorporated into the information dynamics associated with the trajectories of the mobile sensors. A constrained cooperative Kalman filter is developed to provide estimates of the field values and gradients along the trajectories of the mobile sensors so that the temporal variations in the field values can be estimated. This leads to a co-design scheme for state estimation and parameter identification for advection–diffusion processes that is different from comparable schemes using sensors installed at fixed spatial locations. Using state estimates from the constrained cooperative Kalman filter, a recursive least-square (RLS) algorithm is designed to estimate unknown model parameters of the advection–diffusion processes. Theoretical justifications are provided for the convergence of the proposed cooperative Kalman filter by deriving a set of sufficient conditions regarding the formation shape and the motion of the mobile sensor network. Simulation and experimental results show satisfactory performance and demonstrate the robustness of the algorithm under realistic uncertainties and disturbances.

Understanding Energy Pathways in the Gulf Stream

Abstract The Gulf Stream (GS) is one of the strongest ocean currents on the planet. Eddy-rich resolution models are needed to properly represent the dynamics of the GS; however, kinetic energy (KE) can be in excess in these models if not dissipated efficiently. The question of how and how much energy is dissipated and in particular how it flows through ocean scales thus remains an important and largely unanswered question. Using a high-resolution (∼2 km) ocean model [Coastal and Regional Ocean Community (CROCO)], we characterize the spatial and temporal distribution of turbulent cascades in the GS based on a coarse-grained method. We show that the balanced flow is associated with an inverse cascade while the forward cascade is explained by ageostrophic advection associated with frontogenesis. Downscale fluxes are dominant at scales smaller than about 20 km near the surface and most intense at the GS North Wall. There is also strong seasonal variability in KE flux, with the forward cascade intensifying in winter and the inverse cascade later in spring. The forward cascade, which represents an interior route to dissipation, is compared with both numerical and boundary dissipation processes. The contribution of interior dissipation is an order of magnitude smaller than that of the other energy sinks. We thus evaluate the sensitivity of horizontal momentum advection schemes on energy dissipation and show that the decrease in numerical dissipation in a high-order scheme leads to an increase in dissipation at the boundaries, not in the downscale flux.

Three‐Dimensional Simulation of Equatorial Spread F: Effects of Field‐Aligned Plasma Flow and Ionospheric Conductivity

AbstractRecently a Three‐dimensional EquatoriaL spread F (TELF) model using high‐resolving power advection schemes have been developed at the University of Science and Technology of China. With the inclusion of the field‐aligned plasma flow and realistic ionospheric conductivity configuration, the TELF model reproduced typical features of the observed equatorial spread F (ESF) phenomena, including plasma depletions along flux tubes, geomagnetic conjugate irregularities, and ESF morphology as seen in ground optical and satellite observations. Through control simulations, the effects of field‐aligned plasma flow and ionospheric conductivity on ESF are investigated. It is found that field‐aligned plasma flow could inhibit the growth of bubbles by modulating the ionospheric conductivity distribution along field lines, and the plasma bubbles from the TELF model behave more physically in the topside F‐region than those from the 2D model due to the realistic ionospheric conductivity specification. Additionally, the simulations demonstrate that the amplitude and altitude of the initial perturbations can also affect the growth rate of ESF by modulating the polarization electric fields.

Validation and verification of RANS solvers for TUDa-GLR-OpenStage transonic axial compressor

This paper presents a comprehensive validation and verification study of turbomachinery Reynolds-averaged Navier-Stokes flow solvers on the transonic axial compressor TUDa-GLR-OpenStage. Two commercial solvers namely Ansys CFX and Numeca FineTurbo are adopted to provide the benchmark solutions, which can be used for verification of other RANS solvers in the future. Based on these solvers, five sets of grids, two advection schemes (i.e., central difference and second-order upwind), four turbulence models (i.e., SA, SA-RC, SST and EARSM) and two rotor-stator interface models (i.e., mixing plane and sliding plane) are investigated to quantify their effects on predicting the performance and the flow field of the compressor stage. Results show that the choices of grid density and turbulence model are most sensitive to the prediction, leading to 5% and 7% variation in compressor performance characteristics, respectively. Regarding the choice of grid density, a method to estimate the grid discretization error is demonstrated, which is transferrable to other cases. Regarding the choice of turbulence model, the EARSM model is found overall most accurate among the investigated models, and the limitations and deficiencies of the rest models are discussed in detail based on the analysis of the mean flow fields and the eddy viscosity fields. The grids and the major CFD results presented in this work are open-accessed to the community for further research. The results and discussions presented in this paper provide a useful reference for future practices of RANS simulations for compressors.