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Results for “conditional probability”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Investigation of Surface Skidding Response of PBX 9501 and PBX 9502

Introduction: Assess the hazards of handling polymer bonder explosives(PBX) for the case of skidding with grit particles in the frictional interface. High explosive (HE) materials tested: PBX 9501 and 9502. High melting point materials at the skidding interface between HE and a substrate is known to increase the probability of ignition by creating hot spots not subject to reduced heating from the melting of HE material. Skidding occurred at peak forces of 6-26 kN normal force, and 0.6-3.4 kN of frictional force. Velocities for skidding range from 5-30 m/s, see figure 7. Sparse amounts of 300 μm silica grit is applied loosely to the HE surface before testing. Previous works have tested ignition by grit. Testing parameters include angle of impact, drop height, grit size, grit density, substrate material. This study focuses on pre ignition conditions and detailed thermal imaging of the frictional interface. Conclusions: Temperature hot spots were observed at high points in HE surface topology. These high points may be created by grit particles. Since these points impact first high frictional work is concentrated and quickly increases temperature. Small amounts of grit do not affect the overall frictional force but do concentrate the frictional work to create hot spots.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Assessing climate-change-induced flood risk in the Conasauga River watershed: an application of ensemble hydrodynamic inundation modeling

Abstract. This study evaluates the impact of potential future climate change on flood regimes, floodplain protection, and electricity infrastructures across the Conasauga River watershed in the southeastern United States through ensemble hydrodynamic inundation modeling. The ensemble streamflow scenarios were simulated by the Distributed Hydrology Soil Vegetation Model (DHSVM) driven by (1) 1981–2012 Daymet meteorological observations and (2) 11 sets of downscaled global climate models (GCMs) during the 1966–2005 historical and 2011–2050 future periods. Surface inundation was simulated using a GPU-accelerated Two-dimensional Runoff Inundation Toolkit for Operational Needs (TRITON) hydrodynamic model. A total of 9 out of the 11 GCMs exhibit an increase in the mean ensemble flood inundation areas. Moreover, at the 1 % annual exceedance probability level, the flood inundation frequency curves indicate a ∼ 16 km2 increase in floodplain area. The assessment also shows that even after flood-proofing, four of the substations could still be affected in the projected future period. The increase in floodplain area and substation vulnerability highlights the need to account for climate change in floodplain management. Overall, this study provides a proof-of-concept demonstration of how the computationally intensive hydrodynamic inundation modeling can be used to enhance flood frequency maps and vulnerability assessment under the changing climatic conditions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Pore-resolved investigation of turbulent open channel flow over a randomly packed permeable sediment bed

Pore-resolved direct numerical simulations are performed to investigate the interactions between streamflow turbulence and groundwater flow through a randomly packed porous sediment bed for three permeability Reynolds numbers, Re K = 2.56 , 5.17 and 8.94, representative of natural stream or river systems. Time–space averaging is used to quantify the Reynolds stress, form-induced stress, mean flow and shear penetration depths, and mixing length at the sediment–water interface (SWI). Here, the mean flow and shear penetration depths increase with Re K and are found to be nonlinear functions of non-dimensional permeability. The peaks and significant values of the Reynolds stresses, form-induced stresses, and pressure variations are shown to occur in the top layer of the bed, which is also confirmed by conducting simulations of just the top layer as roughness elements over an impermeable wall. The probability distribution functions (p.d.f.s) of normalized local bed stress are found to collapse for all Reynolds numbers, and their root-mean-square fluctuations are assumed to follow logarithmic correlations. The fluctuations in local bed stress and resultant drag and lift forces on sediment grains are mainly a result of the top layer; their p.d.f.s are symmetric with heavy tails, and can be well represented by a non-Gaussian model fit. The bed stress statistics and the pressure data at the SWI potentially can be used in providing better boundary conditions in modelling of incipient motion and reach-scale transport in the hyporheic zone.

turbulence simulation↗
DOE OSTI2020

Flash droughts present a new challenge for subseasonal-to-seasonal prediction

Flash droughts are a recently recognized type of extreme event distinguished by sudden onset and rapid intensification of drought conditions with severe impacts. They unfold on subseasonal-to-seasonal timescales (weeks to months), presenting a new challenge for the surge of interest in improving subseasonal-to-seasonal prediction. In this perspective we discuss existing prediction capability for flash droughts and what is needed to establish their predictability. We place them in the context of synoptic to centennial phenomena, consider how they could be incorporated into early warning systems and risk management, and propose two definitions. The growing awareness that flash droughts involve particular processes and severe impacts, and probably a climate change dimension, makes them a compelling frontier for research, monitoring and prediction.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Pre-equilibrium evolution of conserved charges with initial conditions in the ICCING Monte Carlo event generator

Heavy-ion collisions can be well described through relativistic viscous hydrodynamics, but questions still remain when hydrodynamics is applicable because the initial state may begin very far from equilibrium. Thus, a pre-equilibrium evolution phase is used to bridge the gap between the initial state and hydrodynamics. KøMPøST is one such pre-equilibrium model that propagates the energy-momentum tensor by decomposing it into the background and fluctuations around that background, whose evolution is captured by Green's functions. We extend this formalism to include conserved charges and calculate the corresponding nonequilibrium Green's functions in the relaxation-time approximation. The ICCING algorithm initializes conserved charges in the initial state by sampling $g$ → $q$$\overline{q}$ splitting probabilities and is, thus, perfectly positioned to implement Green's functions for charge propagation. As a result, we show that this method alters the initial-state charge geometries and is applicable in central to mid-central collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Spectroscopic evidence for the Fe3+ spin transition in iron-bearing δ-AlOOH at high pressure

δ-AlOOH has emerged as a promising candidate for water storage in the lower mantle and could have delivered water into the bottom of the mantle. To date, it still remains unclear how the presence of iron affects its elastic, rheological, vibrational, and transport properties, especially across the spin crossover. In this study, we conducted high-pressure X-ray emission spectroscopy experiments on a δ-(Al 0.85 Fe 0.15 ) OOH sample up to 53 GPa using silicone oil as the pressure transmitting medium in a diamond-anvil cell. We also carried out laser Raman measurements on δ-(Al 0.85 Fe 0.15 )OOH and δ-(Al 0.52 Fe 0.48 )OOH up to 57 and 62 GPa, respectively, using neon as the pressure-transmitting medium. Evolution of Raman spectra of δ-(Al 0.85 Fe 0.15 )OOH with pressure shows two new bands at 226 and 632 cm –1 at 6.0 GPa, in agreement with the transition from an ordered ( P 2 1 nm ) to a disordered hydrogen bonding structure ( Pnnm ) for δ-AlOOH. Similarly, the two new Raman bands at 155 and 539 cm –1 appear in δ-(Al 0.52 Fe 0.48 )OOH between 8.5 and 15.8 GPa, indicating that the incorporation of 48 mol% FeOOH could postpone the order-disorder transition upon compression. On the other hand, the satellite peak ( K β') intensity of δ-(Al 0.85 Fe 0.15 )OOH starts to decrease at ~30 GPa and it disappears completely at 42 GPa. That is, δ-(Al 0.85 Fe 0.15 )OOH undergoes a gradual electronic spin-pairing transition at 30–42 GPa. Furthermore, the pressure dependence of Raman shifts of δ-(Al 0.85 Fe 0.15 )OOH discontinuously decreases at 32–37 GPa, suggesting that the improved hydrostaticity by the use of neon pressure medium could lead to a relatively narrow spin crossover. Notably, the pressure dependence of Raman shifts and optical color of δ-(Al 0.52 Fe 0.48 )OOH dramatically change at 41–45 GPa, suggesting that it probably undergoes a relatively sharp spin transition in the neon pressure medium. Together with literature data on the solid solutions between δ-AlOOH and ε-FeOOH, we found that the onset pressure of the spin transition in δ-(Al,Fe)OOH increases with increasing FeOOH content. These results shed new insights into the effects of iron on the structural evolution and vibrational properties of δ-AlOOH. The presence of FeOOH in δ-AlOOH can substantially influence its high-pressure behavior and stability at the deep mantle conditions and play an important role in the deep-water cycle

58 GEOSCIENCES↗
DOE OSTI2024

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Scrambling Dynamics with Imperfections in a Solvable Model

We study how probes of quantum scrambling dynamics respond to two kinds of imperfections -- unequal forward and backward evolutions and decoherence -- in a solvable Brownian circuit model. We calculate a ``renormalized'' out-of-time-order correlator (ROTOC) in the model with $N$ qubits, and we show that the circuit-averaged ROTOC is controlled by an effective probability distribution in operator weight space which obeys a system of $N$ non-linear equations of motion. These equations can be easily solved numerically for large system sizes which are beyond the reach of exact methods. Moreover, for an operator initially concentrated on weight one $w_0=1$, we provide an exact solution to the equations in the thermodynamic limit of many qubits that is valid for all times, all non-vanishing perturbation strengths $p\gtrsim 1/\sqrt{N}$, and all decoherence strengths. We also show that a generic initial condition $w_0 >1$ leads to a metastable state that eventually collapses to the $w_0=1$ case after a lifetime $\sim \log(N/w_0)$. Our results highlight situations where it is still possible to extract the unperturbed chaos exponent even in the presence of imperfections, and we comment on the applications of our results to existing experiments with nuclear spins and to future scrambling experiments.

FOS: Physical sciences↗
DOE OSTI2023

Flammability and dispersion of tritium in confined release scenarios

Ignition of a flammable tritium-air mixture is the most probable means to produce the water form (T 2 O or HTO), which is more easily absorbed by living tissue and is hence ~10,000 times more hazardous to human health when uptake occurs compared to the gaseous form (T 2 or HT; per Mishima and Steele, 2002). Tritium-air mixtures with T 2 concentrations below 4 mol% are considered sub-flammable and will not readily convert to the more hazardous water form. It is therefore desirable from a safety perspective to understand the dispersion behavior of tritium under different release conditions, especially since tritium is often stored in quantities and pressures much lower than is typical for normal hydrogen. The formation of a flammable layer at the ceiling is a scenario of particular concern because the rate of dispersion to nonflammable conditions is slowest in this configuration, which maximizes the time window over which the flammable tritium may encounter an ignition source. This report describes the processes of buoyant rise and dispersion of tritium. Accumulation of flammable concentrations of tritium next to the ceiling is a common safety concern for hydrogen, but this situation can only occur if dispersion rates are slow with respect to rates of release and rise. Theory and simulations demonstrate that buoyancy does not cause regions with flammable concentrations to form within buildings from sources that have previously been mixed to sub-flammable concentrations. A simulated series of tritium release events with their associated dispersion behavior are reported herein; these simulations apply computational fluid dynamics to rooms with three different ceiling heights and a variety of tritium release rates. Safety related quantities from these simulations are reported, including the mass and volume of tritium occurring in a flammable mixture, the presence or absence of a flammable layer at the ceiling, and the time required for dispersion to nonflammable conditions after the end of the tritium release event. These safety metrics are influenced by the magnitude and rate of the tritium release with respect to the air volume in the room and also the momentum of the plume or jet with respect to the ceiling height. Several screening criteria are recommended to assess whether a specific tritium release scenario is likely to form a flammable layer at the ceiling. The methods and results in this modeling study have applicability to explosion safety analysis for other buoyant flammable gases, including the lighter isotopes of hydrogen.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2024

Parametric description of intermittent probability distribution functions in solar wind and magnetohydrodynamic turbulence

ABSTRACT In this work, we find empirical evidence that the scale-dependent statistical properties of solar wind and magnetohydrodynamic (MHD) turbulence can be described in terms of a family of parametric probability distribution functions (PDFs) known as Normal Inverse Gaussian (NIG). Understanding these PDFs is one of the most important goals in turbulence theory, as they are inherently connected to the intermittent properties of solar wind turbulence. We investigate the properties of PDFs of Elsasser increments based on a large statistical sample from solar wind observations and high-resolution numerical simulations of MHD turbulence. In order to measure the PDFs and their corresponding properties, three experiments are presented: fast and slow solar wind for experimental data and a simulation of reduced MHD (RMHD) turbulence. Conditional statistics on a 23-yr-long sample of WIND data near 1 au and high-resolution pseudo-spectral simulation of steadily driven RMHD turbulence on a $2048^3$ mesh are used to construct scale-dependent PDFs. The empirical PDFs are fitted to NIG distributions, which depend on four free parameters. Our analysis shows that NIG distributions accurately capture the evolution of the PDFs, with scale-dependent parameters, from large scales characterized by a Gaussian distribution, turning to exponential tails within the inertial range and stretched exponentials at dissipative scales. We also show that empirically-measured NIG parameters exhibit well-defined scaling properties that are similar across the three empirical data sets, which may be indicative of universal behaviour.

Astronomy & Astrophysics↗
DOE OSTI2020

Improving air leakage prediction of buildings using the fan pressurization method with the Weighted Line of Organic Correlation

In many countries, the fan pressurization method is the most frequently chosen approach for measuring the air leakage of houses. The measurements are usually performed at pressures that far exceed pressures to which buildings are exposed to under normal conditions. A fit of these tests to the power-law formulation allows an extrapolation to data points outside the measured pressure range. With the Ordinary Least Square (OLS) fitting method, the pressure exponent and flow coefficient can be determined. However, the measurement results are highly sensitive to uncertainties induced by external factors like changing wind conditions during the tests, which is neglected by OLS. This may lead to errors in the prediction of flows at lower pressures. The Weighted Line of Organic Correlation (WLOC) is an alternative approach and takes measurement uncertainty into account. In this paper, a statistical analysis of an extensive data set of pressurization measurements has been performed. Both regression techniques have been compared for almost 7500 fan pressurization measurements of six houses in 109 different house leak configurations. The variability in predicting pressure exponent and flow coefficient for both WLOC and OLS regression was analyzed using probability density functions. It was found that the Weighted Line of Organic Correlation significantly decreases the uncertainty in predicting pressure exponent, flow coefficient, and other low-pressure air leakage metrics compared to the Ordinary Least Square fitting. Here, the authors highly recommend the implementation of WLOC in current measurement standards and test equipment.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Minimum Detectable Quantity Calculation for Radiation Portal Monitors

The minimum detectable quantity of a radiation portal monitor is the smallest amount of radioactive material that can be detected passing through the monitor (with a specified detection probability). The minimum detectable quantity is a function of many factors, including isotope, velocity, distance between pillars, height of portal and vehicle, source distribution and position, background radiation, background suppression, detector volume and positions, detector efficiency, decision metrics and algorithms, the presence of NORM (naturally occurring radioactive material), and alarm thresholds. Experimentally testing a radiation portal monitor to failure for all combinations of these factors is extremely time-consuming and often cost prohibitive. This document outlines a straightforward method for quickly estimating the minimum detectable quantity for moving sources over a large variety of conditions with a minimal number of static measurements. The document also describes a proof of concept software application that the International Atomic Energy Agency has designed based on the described method that can be used by Member States to estimate a monitor’s minimum detectable quantity.

Blessinger, Christopher S.↗
DOE OSTI2020

Toward lower-diameter large-scale HPC and data center networks with co-packaged optics

We investigate the advantages of using co-packaged optics for building low-diameter, large-scale high-performance computing (HPC) and data center networks. The increased escape bandwidth offered by co-packaged optics can enable high-radix switch implementations of more than 150 switch ports, which can be combined with data rates of up to 400 Gb/s per port. From the network architecture perspective, the key benefits of using co-packaged optics in future fat-tree networks include (a) the ability to implement large-scale topologies of > <#comment/> 11 , 000 end points by eliminating the need for a third switching layer and (b) the ability to provide up to 4 × <#comment/> higher bisection bandwidth compared to existing solutions, reducing at the same time the number of required switch application-specific integrated circuits by > <#comment/> 80 % <#comment/> . From the network operation perspective, both reduced energy consumption and lower packet delays can be achieved since fewer hops are required; i.e., packets need to traverse fewer serializer/deserializer lanes and fewer switch buffers, which reduces the probability of contending with other packets and improves the tolerance of network congestion. The performance of the proposed architecture is evaluated via discrete-event simulations for a wide range of representative HPC synthetic-traffic cases that include both hotspot and non-hotspot scenarios. The simulation results suggest that co-packaged optics form a promising solution to keep up with bandwidth scaling in future networks, while the reduced number of switching layers can lead to significant mean packet delay improvements that start from 30% and reach up to 74% for high-load conditions.

Maniotis, Pavlos (ORCID:0000000244905253)↗
DOE OSTI2023

Galaxy Spin Classification. I. Z-wise versus S-wise Spirals with the Chirality Equivariant Residual Network

The angular momentum of galaxies (galaxy spin) contains rich information about the initial condition of the universe, yet it is challenging to efficiently measure the spin direction for the tremendous amount of galaxies that are being mapped by ongoing and forthcoming cosmological surveys. We present a machine-learning-based classifier for the Z-wise versus S-wise spirals, which can help to break the degeneracy in the galaxy spin direction measurement. The proposed chirality equivariant residual network (CE-ResNet) is manifestly equivariant under a reflection of the input image, which guarantees that there is no inherent asymmetry between the Z-wise and S-wise probability estimators. We train the model with Sloan Digital Sky Survey images, with the training labels given by the Galaxy Zoo 1 project. A combination of data augmentation techniques is used during the training, making the model more robust to be applied to other surveys. We find an ~30% increase in both types of spirals when Dark Energy Spectroscopic Instrument (DESI) images are used for classification, due to the better imaging quality of DESI. We verify that the ~7σ difference between the numbers of Z-wise and S-wise spirals is due to human bias, since the discrepancy drops to <1.8σ with our CE-ResNet classification results. We discuss the potential systematics relevant to future cosmological applications.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

A Pseudoreversible Normalizing Flow for Stochastic Dynamical Systems with Various Initial Distributions

Here, we present a pseudoreversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with various initial distributions. The primary objective is to construct an accurate and efficient sampler that can be used as a surrogate model for computationally expensive numerical integration of SDEs, such as those employed in particle simulation. After training, the normalizing flow model can directly generate samples of the SDE’s final state without simulating trajectories. The existing normalizing flow model for SDEs depends on the initial distribution, meaning the model needs to be retrained when the initial distribution changes. The main novelty of our normalizing flow model is that it can learn the conditional distribution of the state, i.e., the distribution of the final state conditional on any initial state, such that the model only needs to be trained once and the trained model can be used to handle various initial distributions. This feature can provide a significant computational saving in studies of how the final state varies with the initial distribution. Additionally, we propose to use a pseudoreversible network architecture to define the normalizing flow model, which has sufficient expressive power and training efficiency for a variety of SDEs in science and engineering, e.g., in particle physics. We provide a rigorous convergence analysis of the pseudoreversible normalizing flow model to the target probability density function in the Kullback–Leibler divergence metric. Numerical experiments are provided to demonstrate the effectiveness of the proposed normalizing flow model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Extinction Dynamics of the Foot-and-Mouth Disease Virus Carrier State Under Natural Conditions

Foot-and-mouth disease (FMD) is one of the most economically important livestock diseases worldwide. Following the clinical phase of FMD, a large proportion of ruminants remain persistently infected for extended periods. Although extinction of this carrier state occurs continuously at the animal and population levels, studies vary widely in their estimates of the duration of persistent infection. There is a need for robust statistical models to capture the dynamics of persistent infection for the sake of guiding FMD control and trade policies. The goal of the current study was to develop and assess statistical models to describe the extinction of FMD virus (FMDV) persistent infection using data from primary longitudinal studies of naturally infected cattle and Asian buffalo in Vietnam and India. Specifically, accelerated failure time (AFT) models and generalized linear mixed models (GLMM) were developed to predict the probability of persistent infection in seropositive animals and identified carriers at the individual animal level at sequential time points after outbreaks. The primary studies were analyzed by country and combined using an individual-participant data meta-analysis approach. The models estimated similar trends in the duration of persistent infection for the study/species groups included in the analyses, however the significance of the trends differed between the models. The overall probabilities of persistent infection were similar as predicted by the AFT and GLMM models: 6 months: 99% (AFT) /80% (GLMM), 12 months: 51% (AFT) /32% (GLMM), 18 months: 6% (AFT) /5% (GLMM), 24 months: 0.8% (AFT) /0.6% (GLMM). These models utilizing diverse and robust data sets predict higher probabilities of persistence than previously published, suggesting greater endurance of carriers subsequent to an outbreak. This study demonstrates the utility of statistical models to investigate the dynamics of persistent infection and the importance of large datasets, which can be achieved by combining data from several smaller studies in meta-analyses. Results of this study enhance current knowledge of the FMDV carrier state and may inform policy decisions regarding FMDV persistent infection.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

An ensemble data assimilation modeling system for operational outdoor microalgae growth forecasting

Microalgae have received increasing attention as a potential feedstock for biofuel or biobased products. Forecasting the microalgae growth is beneficial for managers in planning pond operations and harvesting decisions. This study proposed a biomass forecasting system comprised of the Huesemann Algae Biomass Growth Model (BGM), the Modular Aquatic Simulation System in Two Dimensions (MASS2), ensemble data assimilation (DA), and numerical weather prediction Global Ensemble Forecast System (GEFS) ensemble meteorological forecasts. The novelty of this study is to seek the use of ensemble DA to improve both BGM and MASS2 model initial conditions with the assimilation of biomass and water temperature measurements and consequently improve short-term biomass forecasting skills. This study introduces the theory behind the proposed integrated biomass forecasting system, with an application undertaken in pseudo-real-time in three outdoor ponds cultured with Chlorella sorokiniana in Delhi, California, United States. Results from all three case studies demonstrate that the biomass forecasting system improved the short-term (i.e., 7-day) biomass forecasting skills by about 60% on average, comparing to forecasts without using the ensemble DA method. Given the satisfactory performances achieved in this study, it is probable that the integrated BGM-MASS2-DA forecasting system can be used operationally to inform managers in making pond operation and harvesting planning decisions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Comparison of exponential integrators and traditional time integration schemes for the shallow water equations

We report the time integration scheme is probably one of the most fundamental choices in the development of an ocean model. In this paper, we investigate several time integration schemes when applied to the shallow water equations. This set of equations is accurate enough for the modeling of a shallow ocean and is also relevant to study as it is the one solved for the barotropic (i.e. vertically averaged) component of a three dimensional ocean model. We analyze different time stepping algorithms for the linearized shallow water equations. High order explicit schemes are accurate but the time step is constrained by the Courant-Friedrichs-Lewy stability condition. Implicit schemes can be unconditionally stable but, in practice lack accuracy when used with large time steps. In this paper we propose a detailed comparison of such classical schemes with exponential integrators. The accuracy and the computational costs are analyzed in different configurations.

97 MATHEMATICS AND COMPUTING↗