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All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

COSMIC REIONIZATION ON COMPUTERS: NUMERICAL AND PHYSICAL CONVERGENCE

In this paper I show that simulations of reionization performed under the Cosmic Reionization On Computers project do converge in space and mass, albeit rather slowly. A fully converged solution (for a given star formation and feedback model) can be determined at a level of precision of about 20%, but such a solution is useless in practice, since achieving it in production-grade simulations would require a large set of runs at various mass and spatial resolutions, and computational resources for such an undertaking are not yet readily available. In order to make progress in the interim, I introduce a weak convergence correction factor in the star formation recipe, which allows one to approximate the fully converged solution with finite-resolution simulations. The accuracy of weakly converged simulations approaches a comparable, ∼20% level of precision for star formation histories of individual galactic halos and other galactic properties that are directly related to star formation rates, such as stellar masses and metallicities. Yet other properties of model galaxies, for example, their H i masses, are recovered in the weakly converged runs only within a factor of 2.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Experimental and Numerical Study on the Effect of Nitric Oxide on Autoignition and Knock in a Direct-Injection Spark-Ignition Engine

We report Nitric Oxide (NO) can significantly influence the autoignition reactivity and this can affect knock limits in conventional stoichiometric SI engines. Previous studies also revealed that the role of NO changes with fuel type. Fuels with high RON (Research Octane Number) and high Octane Sensitivity (S = RON – MON (Motor Octane Number)) exhibited monotonically retarding knocklimited combustion phasing (KL-CA50) with increasing NO. In contrast, for a high-RON, low-S fuel, the addition of NO initially resulted in a strongly retarded KL-CA50 but beyond the certain amount of NO, KL-CA50 advanced again. The current study focuses on same high-RON, low-S Alkylate fuel to better understand the mechanisms responsible for the reversal in the effect of NO on KLCA50 beyond a certain amount of NO. Experiments were conducted to measure the responses of KL-CA50 and trace-autoignition CA50, the latter being indicative of CA50 at which end-gas autoignition starts to become measurable from the apparent heat-release rate. Chemical-kinetics simulations were conducted to reveal the role of NO for end-gas autoignition, with a specific focus on sequential autoignition in a thermally stratified end-gas. The simulation results reveal that the magnitude of low-temperature heat release (LTHR) generally increases with NO. However, the relative importance of NO for enhancing LTHR diminishes when the LTHR inherent to a fuel’s chemistry is strong, such as at lower temperatures in a thermal boundary layer. This rendered more uniform LTHR within a hypothetical thermal boundary and led to a more sequential (i.e. slower) autoignition event. It was also revealed that a change in compression ratio influences the importance of intermediate-temperature heat release (ITHR) due to changes of the temperature-pressure history of the end-gas. Together with the condition where end-gas autoignition occurs more sequentially, the shorter time spent in LTHR and ITHR regime can counter the increase in autoignition reactivity at high NO levels and allow KLCA50 to advance

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS1999

The Analysis and Design of Low Boom Configurations Using CFD and Numerical Optimization Techniques

The use of computational fluid dynamics (CFD) for the analysis of sonic booms generated by aircraft has been shown to increase the accuracy and reliability of predictions. CFD takes into account important three-dimensional and nonlinear effects that are generally neglected by modified linear theory (MLT) methods. Up to the present time, CFD methods have been primarily used for analysis or prediction. Some investigators have used CFD to impact the design of low boom configurations using trial and error methods. One investigator developed a hybrid design method using a combination of Modified Linear Theory (e.g. F-functions) and CFD to provide equivalent area due to lift driven by a numerical optimizer to redesign or modify an existing configuration to achieve a shaped sonic boom signature. A three-dimensional design methodology has not yet been developed that completely uses nonlinear methods or CFD. Constrained numerical optimization techniques have existed for some time. Many of these methods use gradients to search for the minimum of a specified objective function subject to a variety of design variable bounds, linear and nonlinear constraints. Gradient based design optimization methods require the determination of the objective function gradients with respect to each of the design variables. These optimization methods are efficient and work well if the gradients can be obtained analytically. If analytical gradients are not available, the objective gradients or derivatives with respect to the design variables must be obtained numerically. To obtain numerical gradients, say, for 10 design variables, might require anywhere from 10 to 20 objective function evaluations. Typically, 5-10 global iterations of the optimizer are required to minimize the objective function. In terms of using CFD as a design optimization tool, the numerical evaluation of gradients can require anywhere from 100 to 200 CFD computations per design for only 10 design variables. If one CFD computation requires an hour of computational time on a Cray computer, one can see that the use of constrained numerical optimization quickly becomes impractical.Hence, in order to practically couple a numerical design optimization technique with a CFD method, the CFD method must be extremely efficient with running times on the order of only minutes. The CFD Euler code developed under NASA sponsorship and referred to as MIM3D-SB for the most part fulfills these efficiency requirements. Analysis of wing- body configurations can be computed in a matter of a few minutes. The present study will concentrate on the feasibility of the use of this CFD code in conjunction with a numerical design optimization technique for the sonic boom reduction of candidate HSCT configurations. A preliminary supersonic aircraft design system has been established that utilizes the numerical design optimization code NPSOL developed at Stanford University coupled with the supersonic NUM3D-SB CFD code. Many questions still need to be answered in regard to using CFD and numerical optimizers as design tools. There are difficulties related to both the CFD codes and the numerical optimizers. Numerical optimizers can converge to a local minima rather than a global minima. This behavior is largely a function of the initial guess in the design space. The optimizer also is searching for a minimum of the function in terms of its derivative without any regard to the actual function value. Numerically (i.e. CFD) determined gradients can also generate spurious numerical local minima. In addition, for the sonic boom problem, grid fineness will also determine the accuracy of the final design solution. Design optimization methods work well on problems defined by continuous objective functions. The sonic boom signature design problem is not necessarily defined by a continuous objective function. The signature can have a variety of shapes; i.e. from N-wave to multiple shocks. The far-field or ground signature may not transition continuously from one shape to another and hence, may exhibit discontinuous behavior. This is also a source of difficulty in using design optimization methods.In the following sections, several low boom and one reference aircraft configuration will be analyzed to predict their sonic boom signature characteristics. Modifications to some of these designs will also be presented to demonstrate the feasibility of using CFD as a design tool and to demonstrate the feasibility of designing shaped sonic boom signatures. Design modifications to some configurations will be presented to demonstrate the feasibility of achieving shaped signatures with reduced levels and not necessarily to represent realistic or aerodynamically efficient design modifications. Fuselage volume or camber are used as design variables in order to have a minimal effect on the primary wing aerodynamics. The paper will also seek to demonstrate whether a hybrid or ramped signature is feasible to achieve. For the low-boom configurations, the CFD predicted signatures will be compared qualitatively to their MLT design signatures.

Siclari, Michael J.↗
DOE OSTI2017

Numerical Uncertainties vs. Model Uncertainties in Two-phase Flow Simulations

In recent years, verification, validation and uncertainty quantification (VVUQ) have become a common practice in thermal-hydraulics analysis. In general, these activities deal with propagations of uncertainties in computer code simulations, e.g., through system analysis codes. However, most existing such activities in thermal-hydraulics analysis have been primarily focused on model uncertainties, while numerical uncertainties were largely overlooked. Numerical uncertainties (or numerical errors) can appear in many different forms, e.g., round-off error, statistical sampling error, and discretization error. As pointed out by Oberkampf and Roy, discretization error is usually the largest however the most difficult type of error to estimate reliably. In thermal-hydraulics analysis, especially two-phase flow simulations commonly encountered in reactor safety analysis, the lack of consideration on discretization error is mainly due to the difficulty in estimating them. Accurate estimations on discretization error require continuous mesh refinement and/or implementation of high-order numerical schemes in system analysis code, both of which are unfortunately difficult to achieve for existing codes. At first, it should be emphasized that mesh refinement (or mesh sensitivity study) is a well-understood concept in the thermal-hydraulics field. However, it is not commonly practiced for many reasons, e.g., lack of understanding on numerical errors by code users, consideration on computational cost, deteriorated numerical stability performance with refined meshes, and etc. Secondly, high-order (e.g., second-order) numerical schemes are simply unavailable in almost any existing system analysis code. Implementation of high-order numerical schemes in these codes is difficult, if not impossible, given the complexity of these codes. On the other hand, people tend to argue that numerical uncertainties (or discretization error as we have emphasized) are not as important as the commonly large uncertainties in two-phase flow models, e.g., closure correlations. As a result, nodalization is sometimes played unintentionally, or maybe intentionally, to match experimental data, which is referred as 'user effects' or 'compensating errors' in thermal-hydraulics community. Such a practice is highly criticized by Levy. In this work, we will at first build a computer code that incorporates both first-order and second-order numerical methods to solve the two-phase flow problems. The first-order method resembles the one used in many existing system analysis codes; and the second-order method works as the reference to estimate numerical errors. Numerical verifications on spatial discretization schemes will be presented in the form of mesh convergence study. It will also be demonstrated that, in practical scenarios, discretization errors can be as large as, or even larger than, model uncertainties via case studies.

42 ENGINEERING↗
DOE OSTI2014

Numerical Simulation of Carbon Dioxide Injection in the Western Section of the Farnsworth Unit

Numerical simulation is an invaluable analytical tool for scientists and engineers in making predictions about of the fate of carbon dioxide injected into deep geologic formations for long-term storage. Current numerical simulators for assessing storage in deep saline formations have capabilities for modeling strongly coupled processes involving multifluid flow, heat transfer, chemistry, and rock mechanics in geologic media. Except for moderate pressure conditions, numerical simulators for deep saline formations only require the tracking of two immiscible phases and a limited number of phase components, beyond those comprising the geochemical reactive system. The requirements for numerically simulating the utilization and storage of carbon dioxide in partially depleted petroleum reservoirs are more numerous than those for deep saline formations. The minimum number of immiscible phases increases to three, the number of phase components may easily increase fourfold, and the coupled processes of heat transfer, geochemistry, and geomechanics remain. Public and scientific confidence in the ability of numerical simulators used for carbon dioxide sequestration in deep saline formations has advanced via a natural progression of the simulators being proven against benchmark problems, code comparisons, laboratory-scale experiments, pilot-scale injections, and commercial-scale injections. This paper describes a new numerical simulator for the scientific investigation of carbon dioxide utilization and storage in partially depleted petroleum reservoirs, with an emphasis on its unique features for scientific investigations; and documents the numerical simulation of the utilization of carbon dioxide for enhanced oil recovery in the western section of the Farnsworth Unit and represents an early stage in the progression of numerical simulators for carbon utilization and storage in depleted oil reservoirs.

carbon sequestration↗
DOE OSTI2021

Computational general relativistic force-free electrodynamics: II. Characterization of numerical diffusivity

Scientific codes are an indispensable link between theory and experiment; in (astro-)plasma physics, such numerical tools are one window into the universe’s most extreme flows of energy. The discretization of Maxwell’s equations – needed to make highly magnetized (astro)physical plasma amenable to its numerical modeling – introduces numerical diffusion. It acts as a source of dissipation independent of the system’s physical constituents. Understanding the numerical diffusion of scientific codes is the key to classifying their reliability. It gives specific limits in which the results of numerical experiments are physical. We aim at quantifying and characterizing the numerical diffusion properties of our recently developed numerical tool for the simulation of general relativistic force-free electrodynamics by calibrating and comparing it with other strategies found in the literature. Our code correctly models smooth waves of highly magnetized plasma. We evaluate the limits of general relativistic force-free electrodynamics in the context of current sheets and tearing mode instabilities. We identify that the current parallel to the magnetic field (j ∥ ), in combination with the breakdown of general relativistic force-free electrodynamics across current sheets, impairs the physical modeling of resistive instabilities. We find that at least eight numerical cells per characteristic size of interest (e.g., the wavelength in plasma waves or the transverse width of a current sheet) are needed to find consistency between resistivity of numerical and of physical origins. High-order discretization of the force-free current allows us to provide almost ideal orders of convergence for (smooth) plasma wave dynamics. The physical modeling of resistive layers requires suitable current prescriptions or a sub-grid modeling for the evolution of j ∥ .

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

A simple and effective five-equation two-phase numerical model for liquid-vapor phase transition in cavitating flows

Numerical difficulties, notably the non-monotonic behavior of the Wood speed of sound and the volume fraction positivity, associated with the reduced five-equation two-phase flow model of Kapila et al. (2001) [A.K. Kapila, R. Menikoff, J.B. Bdzil, S.F. Son, D.S. Stewart, 2001. Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Physics of Fluids 13(10), 3002–3024] have been resolved in the past through the introduction of a frozen speed of sound and an algebraic approach for mechanical relaxation afforded by a pressure non-equilibrium six-equation model proposed by [R. Saurel, F. Petitpas, R.A. Berry, 2009. Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixture, J. Comput. Phys. 228, 1678–1712]. By contrast, it is explored and demonstrated in this work that these difficulties can in fact still be resolved within the numerical scheme for solving the reduced five-equation model by numerically replacing the Wood speed of sound for the estimates of wave speeds in the approximate Riemann solver HLLC with the monotonic mixture speed of sound for a transport five-equation model. For shock interface (artificial mixture separating pure or nearly pure fluids) interaction problems, with the apparent advantage of monotonic behavior of the speed of sound in the interface, the effect of the numerical replacement is also confined to the interface. Differences other than the behavior of the speed of sound within the interface in the solutions due to the replacement diminish with increasing resolution when reasonable solution can be obtained with Wood speed of sound. For cavitating/expansion problems in physical fluid mixture, it is pointed out and explained why acoustics in the numerical solutions still propagate at the Wood speed of sound (therefore consistent with the reduced five-equation model) even though in some cases a much higher speed of sound like the numerical replacement above for solving the reduced five-equation model or the frozen speed of sound for solving a six-equation model is used for the estimates of wave speeds in the HLLC scheme. A variant of the five-equation two-phase flow model by Saurel et al. (2008) [R. Saurel, F. Petitpas, R. Abgrall, 2008. Modelling phase transition in metastable liquids: application to cavitating and flashing flows, J. Fluid Mech. 607, 313–350] is then constructed for liquid-vapor phase transition in cavitating flows. The relaxation toward thermo-chemical equilibrium during phase transition is achieved by solving a simple system of algebraic equations for the equilibrium state variables for better efficiency, following Pelanti and Shyue (2014) [M. Pelanti, K.-M. Shyue, 2014. A mixture-energy-consistent six-equation two-phase numerical model for fluid with interfaces, cavitation and evaporation waves. J. Comput. Phys. 259, 331–357]. Therefore, the current model retains both the simplicity afforded by the five-equation model and the efficiency of the algebraic relaxation solver. An alternative algebraic approach for handling the non-conservative term (the so-called K∇ · u term) in the reduced five-equation model for mechanical equilibrium of a liquid-vapor mixture is also explored by enforcing the thermal equilibrium at the same time. Finally, numerical results of sample tests in both one and two dimensions in the literature as well as that in three dimensions demonstrate the effectiveness and ability of the proposed model to simulate cavitating flows. An interesting mechanism of shock generation by acoustics in water due to phase transition is then found by the numerical simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Quantification of Physical and Numerical Mixing in a Coastal Ocean Model Using Salinity Variance Budgets

Numerical mixing, the spurious mixing primarily generated by the discretization of advection, is often significant in estuarine and coastal models due to sharp, energetic fronts. In this study, we compare on- and offline estimates of numerical mixing in a submesoscale-resolving realistic simulation of the ocean state over the Texas-Louisiana continental shelf. While offline estimates of numerical mixing differ from online estimates, offline methods may be the only analysis available. This study offers insight into the differences between the on- and offline methods. We use two methods to estimate numerical mixing offline, based on salinity squared $s^2$ and volume-mean salinity variance $s^{\prime^2}$. Numerical mixing estimated from the $s^{\prime^2}$ budget is generally within 60\% of the magnitude for the online method but captures the temporal variability well. However, the $s^2$ budget compares poorly due to larger truncation errors associated with the tendency and advection terms, which can be reduced by increasing the model output frequency. We also investigate the effects of horizontal resolution on numerical mixing using a two-way nested grid. The volume-integrated numerical mixing constitutes 57\% of the bulk physical mixing -- the mixing prescribed by the turbulence closure scheme -- in the coarse model and may exceed the physical mixing by half an order of magnitude. We find that numerical mixing is reduced by 35\% on average in the nested model, less than expected based on scaling of the numerical mixing for an upwind advection scheme, likely due to new dynamical processes that emerge in the nested simulation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

Force-controlled absorption in a fully-nonlinear numerical wave tank

An active control methodology for the absorption of water waves in a numerical wave tank is introduced. This methodology is based upon a force-feedback technique which has previously been shown to be very effective in physical wave tanks. Unlike other methods, an a-priori knowledge of the wave conditions in the tank is not required; the absorption controller being designed to automatically respond to a wide range of wave conditions. In comparison to numerical sponge layers, effective wave absorption is achieved on the boundary, thereby minimising the spatial extent of the numerical wave tank. In contrast to the imposition of radiation conditions, the scheme is inherently capable of absorbing irregular waves. Most importantly, simultaneous generation and absorption can be achieved. This is an important advance when considering inclusion of reflective bodies within the numerical wave tank. In designing the absorption controller, an infinite impulse response filter is adopted, thereby eliminating the problem of non-causality in the controller optimisation. Two alternative controllers are considered, both implemented in a fully-nonlinear wave tank based on a multiple-flux boundary element scheme. To simplify the problem under consideration, the present analysis is limited to water waves propagating in a two-dimensional domain. The paper presents an extensive numerical validation which demonstrates the success of the method for a wide range of wave conditions including regular, focused and random waves. The numerical investigation also highlights some of the limitations of the method, particularly in simultaneously generating and absorbing large amplitude or highly-nonlinear waves. The findings of the present numerical study are directly applicable to related fields where optimum absorption is sought; these include physical wavemaking, wave power absorption and a wide range of numerical wave tank schemes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2021

An Evaluation of Size-Resolved Cloud Microphysics Scheme Numerics for use with Radar Observations Part II: Condensation and Evaporation

Accurate numerical modeling of clouds and precipitation is essential for weather forecasting and climate change research. While size-resolved (bin) cloud microphysics models predict particle size distributions without imposing shapes, results are subject to artificial size distribution broadening owing to numerical diffusion associated with various processes. Whereas Part 1 addressed collision-coalescence, here we investigate numerical diffusion that occurs in solving condensation and evaporation. In a parcel model framework, all of the numerical schemes examined converge to one solution of condensation and evaporation as the mass grid is refined, and the advection-based schemes are recommended over the reassigning schemes. Including Eulerian vertical advection in a column limits the convergence to some extent, but that limitation occurs at a sufficiently fine mass grid, and the number of iterations in solving vertical advection should be minimized to reduce numerical diffusion. Insubstantial numerical diffusion in solving condensation can be amplified if collision-coalescence is also active, which in turn can be substantially diminished if turbulence effects on collision are incorporated. Large-eddy simulations of a drizzling stratocumulus field reveal that changes in moments of Doppler spectra obtained using different mass grids are consistent with those obtained from the simplified framework, and that spectral moments obtained using a mass grid designed to effectively reduce numerical diffusion are generally closer to observations. Notable differences between the simulations and observations still exist, and our results suggest a need to consider whether factors other than numerical diffusion in the fundamental process schemes employed can cause such differences.

Cloud microphysics↗
DOE OSTI2025

Machine Learned Empirical Numerical Integrator from Simulated Data

Recently, a number of state-of-the-art surrogate machine learning (ML) models have been designed for global weather and climate prediction, which have been trained using reanalysis data products. Reanalysis data products are constructed using numerical model simulations that combine numerical integration of partial differential equations and parameterization schemes. These products are typically only archived and made available using coarsened spatial and temporal resolutions. This study explores the impact of the numerical generation methods used to produce the training datasets and the temporal resolution of those datasets on machine learning surrogate models. Using the nonlinear vector autoregression (NVAR) machine as an explainable ML technique, simple dynamical systems are emulated with ML models trained on data produced by three classical numerical integration schemes. NVAR is validated as a skillful ML method, capable of producing accurate predictions and, more importantly, reconstructing both the underlying dynamics and the numerical integration scheme used to generate the training data. However, the machine fails to generalize predictions on unseen test data generated by different numerical integration schemes, despite the underlying dynamical system being the same. This result provides a word of caution for the growing field of machine learning emulation of weather and climate dynamics. Furthermore, we illustrate using NVAR that training on temporally coarsened data may increase the required complexity of ML models and potentially introduce new numerical challenges. Finally, we discover that empirical integration schemes with arbitrary time-stepping sizes can be constructed directly from the data, which implies a potential for the development of empirical numerical integration schemes.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2020

An Overview of the Null-Field Method. II: Convergence and Numerical Stability

In this paper we provide an analysis of the convergence and numerical stability of the null-field method with discrete sources. We show that (i) if the null-field scheme is numerically stable then we can decide whether or not convergence can be achieved; (ii) if the null-field scheme is numerically unstable then we cannot draw any conclusion about the convergence issue; and (iii) the numerical stability is closely related to the property of a tangential system of radiating discrete sources to form a Riesz basis. Our numerical analysis indicates that for prolate spheroids and localized vector spherical wave functions, the null-field scheme is numerically unstable (this system of vector functions does not form a Riesz basis), while for distributed vector spherical wave functions, the numerical instability is not so pronounced (this system of discrete sources almost possesses the property of being a Riesz basis). We also describe an analytical method for computing the surface integrals in the framework of the conventional null-field method with localized vector spherical wave functions which increases the stability of the numerical scheme.

Null-field method↗
DOE OSTI2026

Numerical-heating effects in atmospheric pressure streamer discharges simulated with a PIC code

Artificial heating in plasma simulations is a well-known phenomenon which occurs when, among other things, the Debye length is poorly resolved by the simulation mesh. Here, in this work, the degree to which numerical-heating occurs during a simulation of a nanosecond atmospheric pressure streamer discharge is examined. The streamer is simulated using a two-dimensional finite-element, particle-in-cell code Empire, which uses direct simulation Monte Carlo for binary particle interactions. Initially, an estimate of the numerical-heating rate applied to Empire is performed using a simple plasma model. Second, a positive atmospheric pressure streamer discharge simulation is performed to study the effects of numerical heating on plasma density, electron temperature, and streamer velocity. The nominal Debye length is approximately 1 μm and the amount of numerical heating introduced in the simulation is varied by using mesh sizes ranging from 2 μm to 20 μm. A measurable numerical heating quantity is proposed that can be used to estimate the appropriate element size and quantify the numerical-heating that can be expected over the simulation time for an atmospheric pressure streamer. In conclusion while Δx/λ D violations can be an issue it is not likely to be an issue with streamer discharges that are temporally short and occur in environments where collision frequencies are high. This result validates the rationale of grid size choices for a large amount of previously published works where Δx/λ D violation was not clearly addressed. Primary finding of this work is that numerical heating is of minor concern for plasma simulations where electron–neutral collisions are numerous such that multiple collisions can occur within a single plasma period.

Nikic, Dejan [University of New Mexico, Albuquerqu↗
DOE OSTI2021

An evaluation of size-resolved cloud microphysics scheme numerics for use with radar observations Part II: Condensation and evaporation

Accurate numerical modeling of clouds and precipitation is essential for weather forecasting and climate change research. While size-resolved (bin) cloud microphysics models predict particle size distributions without imposing shapes, results are subject to artificial size distribution broadening owing to numerical diffusion associated with various processes. Whereas Part I of this study addressed collision–coalescence, here we investigate numerical diffusion that occurs in solving condensation and evaporation. In a parcel model framework, all of the numerical schemes examined converge to one solution of condensation and evaporation as the mass grid is refined, and the advection-based schemes are recommended over the reassigning schemes. Including Eulerian vertical advection in a column limits the convergence to some extent, but that limitation occurs at a sufficiently fine mass grid, and the number of iterations in solving vertical advection should be minimized to reduce numerical diffusion. Insubstantial numerical diffusion in solving condensation can be amplified if collision–coalescence is also active, which in turn can be substantially diminished if turbulence effects on collision are incorporated. Here, large-eddy simulations of a drizzling stratocumulus field reveal that changes in moments of Doppler spectra obtained using different mass grids are consistent with those obtained from the simplified framework, and that spectral moments obtained using a mass grid designed to effectively reduce numerical diffusion are generally closer to observations. Notable differences between the simulations and observations still exist, and our results suggest a need to consider whether factors other than numerical diffusion in the fundamental process schemes employed can cause such differences.

54 ENVIRONMENTAL SCIENCES↗