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At least 55 records · Page 3

Development of a Filtered CFD-DEM Drag Model with Multiscale Markers Using an Artificial Neural Network and Nonlinear Regression

Here, the accuracy of coarse-grained Euler-Lagrangian simulations of fluidized beds heavily depends on the mesoscale drag models to account for the influences of the unresolved sub-grid structures. Traditional filtered drag models are regressed with mesoscale markers such as voidage and slip velocities. In this research, a filtered drag was regressed with both mesoscale and macro-scale markers using fine grid Computational Fluid Dynamics - Discrete Element Method (CFD-DEM) simulations. The traditional non-linear regression method was compared with machine learning regression using an Artificial Neural Network (ANN) implemented in PyTorch and coupled with MFiX. The new drag showed higher accuracy than the Wen-Yu drag and another filtered drag derived from the two-fluid model. The nonlinear regression shows slightly better results than ANN regression in cases with similar R 2 values. The utilization of the gas inlet velocity as an additional macro-scale marker reduced the errors by up to 55.3% in the tested cases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

ZND Verification Tests for Reactive Burn Models in FLAG

The ZND theory, named after Zeldovich, von Neumann, and Doering, provides a simple model for one-dimensional ideal steady-state detonation. It assumes that the detonation wave front starts with a shock that is a discontinuous jump and is followed by a finite-length reaction zone. Reactive burn (also called reactive flow) models are based on ZND theory, as they model the shock initiation and detonation process with a finite reaction rate. The ZND wave propagation test is essentially the only available test case where an analytic solution exists for verification of reactive burn models in numerical codes. However, there are extensions and variants of the ZND test that have been devised for verification of multidimensional flows. The objective of this work is to provide verification of the reactive burn models currently implemented in the Lagrangian hydrocode FLAG and investigate the influence of mesh resolution, artificial viscosity models, and the Arbitrary Lagrangian-Eulerian (ALE) Euler relaxer on the simulation results. The burn models of interest are the Wescott-Stewart-Davis (WSD) model, the Scaled Uniform Reactive Flow (SURF) model (specifically with the SURFplus model extension), and the Arrhenius shock temperature state dependent WSD (AWSD) model. Previously, Ralph Menikoff has used ZND tests for verification of the SURF and SURFplus models in the Eulerian hydrocode xRAGE. The ZND tests here are somewhat different than the approach by Menikoff. In particular, we use a piston-driven ZND detonation wave (via a prescribed constant velocity boundary condition) in a Lagrangian framework whereas Menikoff had a ZND wave followed by a invariant rarefaction wave. The xRAGE simulations were carried out on uniform grids and adaptive mesh refinement (AMR) grids. Although AMR was recently implemented in FLAG and now fully functional for 2D simulations, it will not be evaluated with ZND tests at this time. Some work has been done previously for validating the reactive burn models in FLAG. For example, the validation studies of SURF with shock-to-detonation (SDT) tests, cylinder tests, and gap-stick tests. Further validation of the AWSD, WSD, and SURF models is described in for SDT, multi-shock, cylinder, and corner-turning tests. Recently, a large parameter study with approximately twenty SDT tests was performed to validate the AWSD, WSD, SURF, and SURFplus models while also investigating mesh resolution and artificial viscosity settings. To the best of our knowledge, the current work represents the first documented verification of these burn models in FLAG. The reader should note that many of the tables and figures in this report use units of cm/g/µs, which are the default units for FLAG. However, some lengths and velocities are expressed in µm and mm/µs, respectively, which are typical units for detonation analyses.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Large-eddy simulation of non-vaporizing sprays using the spectral-element method

Predictive simulations of high-pressure sprays require accurate representation of the turbulent gaseous flow field generated by liquid jet. Typically, the accuracy that can be obtained with low-order numerical methods (e.g. finite volume, finite element) is limited by stability issues in fine grids and the order of convergence of the method. In this work, we resolve the turbulent flow field in an Eulerian manner using the high-order spectral element method, coupled with a Lagrangian parcels approach to model the atomizing liquid jet. Large eddy simulations of single-hole sprays under non-evaporative conditions were conducted and compared against experimental data from Margot et al. (2008) and Spray A data from the Engine Combustion Network. The sensitivity of liquid penetration and droplet sizes to different breakup model parameters was studied. The effect of different numerical parameters, such as polynomial order of the solution (grid resolution), on liquid penetration was also analyzed. The method achieved grid-independent results using p-refinement, achieving finer resolution (by a factor of x 1.7 - x 3.5) in the gas-phase solution than in state-of-the-art simulations using the finite-volume method. Here the results showed good agreement with experimental data, demonstrating the ability of the current method to accurately capture liquid penetration and the shape of the spray.

97 MATHEMATICS AND COMPUTING↗

Lagrangian large eddy simulations via physics-informed machine learning

High-Reynolds number homogeneous isotropic turbulence (HIT) is fully described within the Navier–Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as large eddy simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about effects of subgrid scales on the resolved scales. Here, we take an alternative approach and design LES heuristics stated in terms of Lagrangian particles moving with the flow. Our Lagrangian LES, thus L-LES, is described by equations generalizing the weakly compressible smoothed particle hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from direct numerical simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The subgrid-scale contributions are modeled separately with physical constraints to account for the effects from unresolved scales. We build the resulting model under the differentiable programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our L-LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Development of an Encoding Method on an Co-simulation Platform for Mitigating the Impact of Unreliable Communication

This report presents a hardware-in-the-loop (HIL) based modeling approach for simulating impacts of unreliable communication on the performance of centralized volt-var control and for developing an encoding method to mitigate the impacts. First, an asynchronous real-time HIL simulation platform is introduced to enable multi-rate co-simulation of a distribution system with many inverter-based distributed energy resources (DERs). The distribution system is modeled by milliseconds phasor-based models and the DERs are modeled by micro-seconds power electronic models. Communication connections between a centralized volt-var controller (modeled externally to the HIL testbed) and smart inverters are built by implementing Modbus links and the Long Term Evolution network. On this co-simulation platform, an enhanced, augmented Lagrangian multiplier based encoded data recovery (EALM-EDR) algorithm for mitigating the impact of unreliable communication is developed and validated. Simulation results demonstrate the efficacy of using the HIL-based co-simulation platform as a power grid digital twin for developing algorithms that coordinate a large number of heterogeneous control systems through wired and wireless communication links.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Reynolds number dependence of Lagrangian dispersion in direct numerical simulations of anisotropic magnetohydrodynamic turbulence

Large-scale magnetic fields thread through the electrically conducting matter of the interplanetary and interstellar medium, stellar interiors and other astrophysical plasmas, producing anisotropic flows with regions of high-Reynolds-number turbulence. It is common to encounter turbulent flows structured by a magnetic field with a strength approximately equal to the root-mean-square magnetic fluctuations. In this work, direct numerical simulations of anisotropic magnetohydrodynamic (MHD) turbulence influenced by such a magnetic field are conducted for a series of cases that have identical resolution, and increasing grid sizes up to $2048^3$ . The result is a series of closely comparable simulations at Reynolds numbers ranging from 1400 up to 21 000. We investigate the influence of the Reynolds number from the Lagrangian viewpoint by tracking fluid particles and calculating single-particle and two-particle statistics. The influence of Alfvénic fluctuations and the fundamental anisotropy on the MHD turbulence in these statistics is discussed. Single-particle diffusion curves exhibit mildly superdiffusive behaviours that differ in the direction aligned with the magnetic field and the direction perpendicular to it. Competing alignment processes affect the dispersion of particle pairs, in particular at the beginning of the inertial subrange of time scales. Scalings for relative dispersion, which become clearer in the inertial subrange for a larger Reynolds number, can be observed that are steeper than indicated by the Richardson prediction.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Conservative High-Order Time Integration for Lagrangian Hydrodynamics

In tis study, we develop novel time integration methods for the compressible Euler equations in the Lagrangian frame that are of arbitrary high order and exactly preserve the mass, momentum, and total energy of the system. The equations are considered in nonconservative form, that is, common for staggered grid hydrodynamics (SGH) methods; namely, the evolved quantities are mass, momentum, and internal energy. A general family of time integration schemes is formulated, and practical pairs for orders three and four are derived. Numerical results on standard hydrodynamics benchmarks confirm the high-order convergence on smooth problems and the exact numerical preservation of all physically conserved quantities.

97 MATHEMATICS AND COMPUTING↗

Islet: interpolation semi-Lagrangian element-based transport

Abstract. Advection of trace species, or tracers, also called tracer transport, in models of the atmosphere and other physical domains is an important and potentially computationally expensive part of a model's dynamical core. Semi-Lagrangian (SL) advection methods are efficient because they permit a time step much larger than the advective stability limit for explicit Eulerian methods without requiring the solution of a globally coupled system of equations as implicit Eulerian methods do. Thus, to reduce the computational expense of tracer transport, dynamical cores often use SL methods to advect tracers. The class of interpolation semi-Lagrangian (ISL) methods contains potentially extremely efficient SL methods. We describe a finite-element ISL transport method that we call the interpolation semi-Lagrangian element-based transport (Islet) method, such as for use with atmosphere models discretized using the spectral element method. The Islet method uses three grids that share an element grid: a dynamics grid supporting, for example, the Gauss–Legendre–Lobatto basis of degree three; a physics parameterizations grid with a configurable number of finite-volume subcells per element; and a tracer grid supporting use of Islet bases with particular basis again configurable. This method provides extremely accurate tracer transport and excellent diagnostic values in a number of verification problems.

58 GEOSCIENCES↗

Parallel-in-Time Integration for Nonlinear Hyperbolic Problems (Final Report)

The work for the subcontract was situated in the area of parallel-in-time integration for hyperbolic partial differential equations (PDEs). Parallel-in-time integration is an active area of research due to its ability to enable faster numerical simulations for applications throughout many areas of science. Over the past two decades, much progress has been made in this area; however, this progress has largely been limited to diffusion-dominated PDEs, with some recent success in scalar linear hyperbolic PDEs. Given the ubiquity of numerical simulations of hyperbolic PDEs throughout the sciences, in particular, nonlinear hyperbolic systems, there is a strong need to develop efficient parallel-in-time techniques for hyperbolic problems beyond simple scalar and linear cases, which is the main topic of this subcontract. The main focus of the work was to further develop and perfect coarse-grid operators for the Multigrid Reduction-inTime (MGRIT) method applied to hyperbolic PDEs that were recently proposed in PhD thesis, based on a modified semi-Lagrangian approach.

97 MATHEMATICS AND COMPUTING↗

Evaluating Sea Breezes and Associated Convective Cloud Evolution in the Model Gray Zone

We characterize convective clouds associated with sea‐breeze circulations (SBC) using multi‐agency observations and multi‐case ensemble model simulations. The focus is on assessing convective cloud lifecycle properties and their merging behavior, as well as the environmental conditions they are embedded in, particularly SBC features. In total, 46 SBC days over the Houston‐Galveston region are selected and simulated using the Weather Research and Forecasting (WRF) model at a gray zone scale with a forecast‐like parameterization setup. Advanced techniques, including change‐point detection, a Lagrangian cloud tracking method, and a newly developed cell merging and splitting detection algorithm, are applied and/or developed for this study. Our findings indicate that the WRF model at 1 km grid spacing well represents the thermodynamic conditions over the region, as well as SBC timing and intensity. However, for the associated convective cells, WRF overestimates the 30‐dBZ echo top height, cell area, and maximum radar reflectivity compared to radar observations. This overestimation is potentially due to under‐resolved entrainment processes, an overestimated merging frequency, and the overestimation of updraft intensity. Furthermore, the model exhibits a deficiency in simulating congestus clouds, showing a more rapid transition from shallow to deep convection compared to observed behavior. Moreover, observations indicate stronger, deeper, and wider clouds when merging happens. Conversely, in simulations, the merging process does not necessarily lead to higher or longer‐lived cells, as many cases experience rapid and frequent merging and splitting which may result in more variance in convective updraft velocity during the convection lifetime.

54 ENVIRONMENTAL SCIENCES↗

Geometric remapping of particle distributions in the Discrete Element Model for Sea Ice (DEMSI v0.0)

Abstract. A new sea ice dynamical core, the Discrete Element Model for Sea Ice (DEMSI), is under development for use in coupled Earth system models. DEMSI is based on the discrete element method, which models collections of ice floes as interacting Lagrangian particles. In basin-scale sea ice simulations the Lagrangian motion results in significant convergence and ridging, which requires periodic remapping of sea ice variables from a deformed particle configuration back to an undeformed initial distribution. At the resolution required for Earth system models we cannot resolve individual sea ice floes, so we adopt the sub-grid-scale thickness distribution used in continuum sea ice models. This choice leads to a series of hierarchical tracers depending on ice fractional area or concentration that must be remapped consistently. The circular discrete elements employed in DEMSI help improve the computational efficiency at the cost of increased complexity in the effective element area definitions for sea ice cover that are required for the accurate enforcement of conservation. An additional challenge is the accurate remapping of element values along the ice edge, the location of which varies due to the Lagrangian motion of the particles. In this paper we describe a particle-to-particle remapping approach based on well-established geometric remapping ideas that enforces conservation, bounds preservation, and compatibility between associated tracer quantities, while also robustly managing remapping at the ice edge. One element of the remapping algorithm is a novel optimization-based flux correction that enforces concentration bounds in the case of nonuniform motion. We demonstrate the accuracy and utility of the algorithm in a series of numerical test cases.

58 GEOSCIENCES↗

Models and Strategies for Optimal Demand Side Management in the Chemical Industries

Deregulation and the increase of renewable electricity generation from wind and solar photovoltaics have transformed the U.S. electricity market. Economic and environmental benefits notwithstanding, the presence of renewables has increased variability and uncertainty on the supply side of the grid. Managing demand, rather than generation – a strategy referred to as “demand response (DR)” – is an attractive approach for mitigating this imbalance. DR efforts aim to reduce electricity usage during peak demand times, lessening stress on the grid. Industrial users are particularly attractive entities for DR participation since they present large, localized loads that can provide significant relief on grid demand and –unlike other large loads, such as buildings – are minimally dependent on human needs and preferences. In this project, we accomplished three main objectives. (1) We developed data-driven low-order DR scheduling-relevant dynamic models of chemical processes. Concurrently, we studied the formulation and solution of the associated optimal DR production scheduling problems. (a) A prototype air separation unit (ASU) model was used to generate simulated operating data for initial modeling efforts, which enabled the later use of industrial data for data-driven modeling. (b) We utilized Hammerstein-Wiener (HW) and Finite Step Response (FSR) models to represent nonlinear plant dynamics. (c) The HW models were linearized using exact linearization so they could potentially be embedded in power system models, which are formulated as mixed integer linear programs (MILPs). (d) We solved DR optimization problems under uncertainty and found that even naïve predictions of electricity price and product demand led to significant cost savings benefits. (2) Our DR scheduling optimization problem formulations are amenable to real-time solution. (a) We utilized Lagrangian Relaxation (LR) to efficiently solve the optimization problem by decoupling subproblems linked by complicating constraints. (b) We have achieved computation times for the 3-day DR scheduling problem of an ASU as low as 1.88 minutes. (3) Our representations of the DR behavior of chemical process as grid-level batteries were embedded in power system models. (a) For a small-scale grid, we found that incorporating the dynamics of the chemical plant in the optimal power flow calculations resulted in better resource management leading to up to 15% and 46% cost reduction for the grid and chemical plant operations, respectively, during periods of power line congestion. We have published several works dedicated to modeling and solving DR optimization problems from the user side. These were published in top peer-reviewed journals and are summarized in this report. The most recent work (and papers in preparation) considers DR scheduling from the grid side. Future efforts will consider networked plants (e.g., air separation units operating on a common pipeline) for DR participation, which is expected to amplify the capabilities of industrial DR participants to perform load-shifting. Our consideration of uncertainty in DR has inspired future directions in this area as well: we plan to develop multistage methods to fully account for the effects of uncertainty in DR scheduling.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Lagrangian–Eulerian multidensity topology optimization with the material point method

Abstract In this paper, a hybrid Lagrangian–Eulerian topology optimization (LETO) method is proposed to solve the elastic force equilibrium with the Material Point Method (MPM). LETO transfers density information from freely movable Lagrangian carrier particles to a fixed set of Eulerian quadrature points. This transfer is based on a smooth radial kernel involved in the compliance objective to avoid the artificial checkerboard pattern. The quadrature points act as MPM particles embedded in a lower‐resolution grid and enable a subcell multidensity resolution of intricate structures with a reduced computational cost. A quadrature‐level connectivity graph‐based method is adopted to avoid the artificial checkerboard issues commonly existing in multiresolution topology optimization methods. Numerical experiments are provided to demonstrate the efficacy of the proposed approach.

Li, Yue↗

Comparison of Eulerian Bin and Lagrangian Particle-Based Microphysics in Simulations of Nonprecipitating Cumulus

A single nonprecipitating cumulus congestus setup is applied to compare droplet spectra grown by the diffusion of water vapor in Eulerian bin and particle-based Lagrangian microphysics schemes. Bin microphysics represent droplet spectral evolution applying the spectral density function. In the Lagrangian microphysics, computational particles referred to as superdroplets are followed in time and space with each superdroplet representing a multiplicity of natural cloud droplets. The same cloud condensation nuclei (CCN) activation and identical representation of the droplet diffusional growth allow the comparison. The piggybacking method is used with the two schemes operating in a single simulation, one scheme driving the dynamics and the other one piggybacking the simulated flow. Piggybacking allows point-by-point comparison of droplet spectra predicted by the two schemes. Overall, the results show the impact of inherent limitations of the two microphysics simulation methods, numerical diffusion in the Eulerian scheme and a limited number of superdroplets in the Lagrangian scheme. Numerical diffusion in the Eulerian scheme results in a more dilution of the cloud upper half and thus smaller cloud droplet mean radius. The Lagrangian scheme typically has larger spatial fluctuations of droplet spectral properties. A significantly larger mean spectral width in the bin microphysics across the entire cloud depth is the largest difference between the two schemes. A fourfold increase of the number of superdroplets per grid volume and a twofold increase of the spectral resolution and thus the number of bins have small impact on the results and provide only minor changes to the comparison between simulated cloud properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Cloud droplet diffusional growth in homogeneous isotropic turbulence: bin microphysics versus Lagrangian super-droplet simulations

The increase in the spectral width of an initially monodisperse population of cloud droplets in homogeneous isotropic turbulence is investigated by applying a finite-difference fluid flow model combined with either Eulerian bin microphysics or a Lagrangian particle-based scheme. The turbulence is forced applying a variant of the so-called linear forcing method that maintains the mean turbulent kinetic energy (TKE) and the TKE partitioning between velocity components. The latter is important for maintaining the quasi-steady forcing of the supersaturation fluctuations that drive the increase in the spectral width. We apply a large computational domain (64 3 m 3 ), one of the domains considered in Thomas et al. (2020). The simulations apply 1 m grid length and are in the spirit of the implicit large eddy simulation (ILES), that is, with small-scale dissipation provided by the model numerics. This is in contrast to the scaled-up direct numerical simulation (DNS) applied in Thomas et al. (2020). Two TKE intensities and three different droplet concentrations are considered. Analytic solutions derived in Sardina et al. (2015), valid for the case when the turbulence integral timescale is much larger than the droplet phase relaxation timescale, are used to guide the comparison between the two microphysics simulation techniques. The Lagrangian approach reproduces the scalings relatively well. Representing the spectral width increase in time is more challenging for the bin microphysics because appropriately high resolution in the bin space is needed. The bin width of 0.5 µm is only sufficient for the lowest droplet concentration (26 cm -3 ). For the highest droplet concentration (650 cm -3 ), an order of magnitude smaller bin size is barely sufficient. The scalings are not expected to be valid for the lowest droplet concentration and the high-TKE case, and the two microphysics schemes represent similar departures. Finally, because the fluid flow is the same for all simulations featuring either low or high TKE, one can compare point-by-point simulation results. Such a comparison shows very close temperature and water vapor point-by-point values across the computational domain and larger differences between simulated mean droplet radii and spectral width. The latter are explained by fundamental differences in the two simulation methodologies, numerical diffusion in the Eulerian bin approach and a relatively small number of Lagrangian particles that are used in the particle-based microphysics.

54 ENVIRONMENTAL SCIENCES↗

Observations of supermicron-sized aerosols originating from biomass burning in southern Central Africa

During the 3 years of the ObseRvations of Aerosols above CLouds and their intEractionS (ORACLES) campaign, the NASA Orion P-3 was equipped with a 2D stereo (2D-S) probe that imaged particles with maximum dimension (D) ranging from 10 < D < 1280 µm. The 2D-S recorded supermicron-sized aerosol particles (SAPs) outside of clouds within biomass burning plumes during flights over the southeastern Atlantic off Africa's coast. Numerous SAPs with 10 < D < 1520 µm were observed in 2017 and 2018 at altitudes between 1230 and 4000 m, 1000 km from the coastline, mostly between 7–11° S. No SAPs were observed in 2016 as flights were conducted further south and further from the coastline. Number concentrations of refractory black carbon (rBC) measured by a single particle soot photometer ranged from 200 to 1200 cm –3 when SAPs were observed. Transmission electron microscopy images of submicron particulates, collected on Holey carbon grid filters, revealed particles with potassium salts, black carbon (BC), and organics. Energy-dispersive X-ray spectroscopy spectra also detected potassium, a tracer for biomass burning. These measurements provided evidence that the submicron particles originated from biomass burning. NOAA Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) 3 d back trajectories show a source in northern Angola for times when large SAPs were observed. Fire Information for Resource Management System (FIRMS) Moderate Resolution Imaging Spectroradiometer (MODIS) 6 active fire maps showed extensive biomass burning at these locations. Given the back trajectories, the high number concentrations of rBC, and the presence of elemental tracers indicative of biomass burning, it is hypothesized that the SAPs imaged by the 2D-S are examples of BC aerosol, ash, or unburned plant material.

54 ENVIRONMENTAL SCIENCES↗

Statistical properties of homogeneous and isotropic turbulence in He II measured via particle tracking velocimetry

Despite being a quantum two-fluid system, superfluid helium-4 (He II) is observed to behave similarly to classical fluids when a flow is generated by mechanical forcing. This similarity has brought up the feasibility of utilizing He II for high Reynolds number classical turbulence research, considering the small kinematic viscosity of He II. However, it has been suggested that the nonclassical dissipation mechanism in He II at small scales may alter its turbulent statistics and intermittency. In this work, we report our study of a nearly homogeneous and isotropic turbulence (HIT) generated by a towed grid in He II. We measure the velocity field using particle tracking velocimetry with solidified deuterium particles as the tracers. By correlating the velocities measured simultaneously on different particle trajectories or at different times along the same particle trajectory, we are able to conduct both Eulerian and Lagrangian flow analyses. Spatial velocity structure functions obtained through the Eulerian analysis show scaling behaviors in the inertial subrange similar to that for classical HIT but with enhanced intermittency. The Lagrangian analysis allows us to examine the flow statistics down to below the dissipation length scale. Interestingly, abnormal deviations from the classical scaling behaviors are observed in this regime. Lastly, we discuss how these deviations may relate to the motion of quantized vortices in the superfluid component in He II.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Comparison of Lagrangian Superdroplet and Eulerian Double-Moment Spectral Microphysics Schemes in Large-Eddy Simulations of an Isolated Cumulus Congestus Cloud

Abstract Advanced microphysics schemes (such as Eulerian bin and Lagrangian superdroplet) are becoming standard tools for cloud physics research and parameterization development. This study compares a double-moment bin scheme and a Lagrangian superdroplet scheme via large-eddy simulations of nonprecipitating and precipitating cumulus congestus clouds. Cloud water mixing ratio in the bin simulations is reduced compared to the Lagrangian simulations in the upper part of the cloud, likely from numerical diffusion, which is absent in the Lagrangian approach. Greater diffusion in the bin simulations is compensated by more secondary droplet activation (activation above cloud base), leading to similar or somewhat higher droplet number concentrations and smaller mean droplet radius than the Lagrangian simulations for the nonprecipitating case. The bin scheme also produces a significantly larger standard deviation of droplet radius than the superdroplet method, likely due to diffusion associated with the vertical advection of bin variables. However, the spectral width in the bin simulations is insensitive to the grid spacing between 50 and 100 m, suggesting other mechanisms may be compensating for diffusion as the grid spacing is modified. For the precipitating case, larger spectral width in the bin simulations initiates rain earlier and enhances rain development in a positive feedback loop. However, with time, rain formation in the superdroplet simulations catches up to the bin simulations. Offline calculations using the same drop size distributions in both schemes show that the different numerical methods for treating collision–coalescence also contribute to differences in rain formation. The stochastic collision–coalescence in the superdroplet method introduces more variability in drop growth for a given rain mixing ratio.

54 ENVIRONMENTAL SCIENCES↗