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All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Kelvin-wave-induced anomalous advection and the onset of surface warming in El Nino events

A simple advective model for tropical ocean surface warming can produce anomalous sea surface temperature (SST) fields similar to those of the first several months of the 1982 El Nino. The physics invoked assumes that the existing SST field is advected by anomalous currents to produce the anomalous warming, and that the anomalous currents are those induced subsequent to the passage of downwelling Kelvin wave fronts. Numerical experiments with a fully nonlinear and thermally active ocean model support the physical relevance of the more idealized study. The anomalous horizontal advection model also accounts for the initial SST evolution during the more common type of El Nino event.

Harrison, D. E.↗
NASA NTRS1986

Numerical advection by conservation of second-order moments

A new, accurate, and nondiffusive method for three-dimensional advection of trace species is presented. The method preserves tracer structures by conserving the second-order moments of the spatial distribution of tracer during advection. Upstream transport and second-order tracer distribution are described, and the moments of the tracer distribution about the center of a grid box are formally defined and related to the polynomial distribution. Formulas are presented which describe how the moments of a grid box are decomposed into a unique set of moments centered about each subbox and how they are reassembled into new grid boxes. A one-dimensional example if tracer transport is given, and limits necessary to maintain positive tracer concentrations are derived. The accuracy and stability of this method are analytically examined, and numerical experiments testing the effective resolution are presented. The method is compared with other methods for numerical advection of tracers.

Prather, M. J.↗
NASA NTRS1988

Universal limiter for transient interpolation modeling of the advective transport equations: The ULTIMATE conservative difference scheme

A fresh approach is taken to the embarrassingly difficult problem of adequately modeling simple pure advection. An explicit conservative control-volume formation makes use of a universal limiter for transient interpolation modeling of the advective transport equations. This ULTIMATE conservative difference scheme is applied to unsteady, one-dimensional scalar pure advection at constant velocity, using three critical test profiles: an isolated sine-squared wave, a discontinuous step, and a semi-ellipse. The goal, of course, is to devise a single robust scheme which achieves sharp monotonic resolution of the step without corrupting the other profiles. The semi-ellipse is particularly challenging because of its combination of sudden and gradual changes in gradient. The ULTIMATE strategy can be applied to explicit conservation schemes of any order of accuracy. Second-order schemes are unsatisfactory, showing steepening and clipping typical of currently popular so-called high resolution shock-capturing of TVD schemes. The ULTIMATE third-order upwind scheme is highly satisfactory for most flows of practical importance. Higher order methods give predictably better step resolution, although even-order schemes generate a (monotonic) waviness in the difficult semi-ellipse simulation. Little is to be gained above ULTIMATE fifth-order upwinding which gives results close to the ultimate for which one might hope.

Leonard, B. P.↗
NASA NTRS1990

Thermal advection and stratification effects on surface winds and the low level meridional mass transport

Statistical tests are performed on the Seasat scatterometer observations to examine if and to what degree thermal advection and stratification effects manifest themselves in these remotely sensed measurements of mean wind and wind stress over the ocean. On the basis of a two layer baroclinic boundary layer model which is presented, it is shown that the thermal advection and stratification of the entire boundary layer as well as the geostrophic forcing influence the modeled near surface wind and wind stress profiles. Evidence of diurnal variation in the stratification under barotropic conditions is found in the data, with the daytime marine boundary layer being more convective than its nighttime counterpart. The temporal and spacial sampling pattern of the satellite makes it impossible to recover the full diurnal cycle, however. The observed effects of the thermal advection are shown to be statistically significant during the day (and presumed more convective) hours, causing a systematic increase in the poleward transport of mass and heat. The statistical results are in a qualitative agreement with the model simulations and cannot be reproduced in randomized control tests.

Levy, Gad↗
NASA NTRS1993

A numerical treatment of geodynamic viscous flow problems involving the advection of material interfaces

Effective numerical treatment of multicomponent viscous flow problems involving the advection of sharp interfaces between materials of differing physical properties requires correction techniques to prevent spurious diffusion and dispersion. We develop a particular algorithm, based on modern shock-capture techniques, employing a two-step nonlinear method. The first step involves the global application of a high-order upwind scheme to a hyperbolic advection equation used to model the distribution of distinct material components in a flow field. The second step is corrective and involves the application of a global filter designed to remove dispersion errors that result from the advection of discontinuities (e.g., material interfaces) by high-order, minimally dissipative schemes. The filter introduces no additional diffusion error. Nonuniform viscosity across a material interface is allowed for by the implementation of a compositionally weighted-inverse interface viscosity scheme. The combined method approaches the optimal accuracy of modern shock-capture techniques with a minimal increase in computational time and memory. A key advantage of this method is its simplicity to incorporate into preexisting codes be they finite difference, element, or volume of two or three dimensions.

Lenardic, A.↗
NASA NTRS1999

Winter to Spring Transition in Europe 48-45 degrees N: From Temperature Control by Advection to Control by Insolation

As established in previous studies, and analyzed further herein for the years 1988-1998, warm advection from the North Atlantic is the predominant control of the surface-air temperature in northern-latitude Europe in late winter. This thesis is supported by the substantial correlation Cti between the speed of the southwesterly surface winds over the eastern North Atlantic, as quantified by a specific Index Ina, and the 2-meter level temperature Ts over central Europe (48-54 deg N; 5-25 deg E), for January, February and early March. In mid-March and subsequently, the correlation Cti drops drastically (quite often it is negative). The change in the relationship between Ts and Ina marks a transition in the control of the surface-air temperature. As (a) the sun rises higher in the sky, (b) the snows melt (the surface absorptivity can increase by a factor of 3.0), (c) the ocean-surface winds weaken, and (d) the temperature difference between land and ocean (which we analyze) becomes small, absorption of insolation replaces the warm advection as the dominant control of the continental temperature. We define the onset of spring by this transition, which evaluated for the period of our study occurs at pentad 16 (Julian Date 76, that is, March 16). The control by insolation means that the surface is cooler under cloudy conditions than under clear skies. This control produces a much smaller interannual variability of the surface temperature and of the lapse rate than prevailing in winter, when the control is by advection. Regional climatic data would be of greatest value for agriculture and forestry if compiled for well-defined seasons. For continental northern latitudes, analysis presented here of factors controlling the surface temperature appears an appropriate tool for this task.

Otterman, J.↗
NASA NTRS2002

Advection from the North Atlantic as the Forcing of Winter Greenhouse Effect Over Europe

In winter, large interannual fluctuations in the surface temperature are observed over central Europe. Comparing warm February 1990 with cold February 1996, a satellite-retrieved surface (skin) temperature difference of 9.8 K is observed for the region 50-60 degrees N; 5-35 degrees E. Previous studies show that advection from the North Atlantic constitutes the forcing to such fluctuations. The advection is quantified by Index I(sub na), the average of the ocean-surface wind speed over the eastern North Atlantic when the direction is from the southwest (when the wind is from another direction, it counts as a zero speed to the average). Average I(sub na) for February 1990 was 10.6 m/s, but for February 1996 I(sub na) was only 2.4 m/s. A large value of I(sub na) means a strong southwesterly flow which brings warm and moist air into central Europe at low level, producing a steeper tropospheric lapse rate. Strong ascending motions at 700 mb are observed in association with the occurrence of enhanced warm, moist advection from the ocean in February 1990 producing clouds and precipitation. Total precipitable water and cloud-cover fraction have larger values in February 1990 than in 1996. The difference in the greenhouse effect between these two scenarios, this reduction in heat loss to space, can be translated into a virtual radiative heating of 2.6 W/square m above the February 1990 surface/atmosphere system, which contributes to a warming of the surface on the order of 2.6 K. Accepting this estimate as quantitatively meaningful, we evaluate the direct effect, the rise in the surface temperature in Europe as a result of maritime-air inflow, as 7.2 K (9.8 K-2.6 K). Thus, fractional reinforcement by the greenhouse effect is 2.6/7.2, or 36%, a substantial positive feedback.

Otterman, J.↗
NASA NTRS2001

Advecting Procedural Textures for 2D Flow Animation

This paper proposes the use of specially generated 3D procedural textures for visualizing steady state 2D flow fields. We use the flow field to advect and animate the texture over time. However, using standard texture advection techniques and arbitrary textures will introduce some undesirable effects such as: (a) expanding texture from a critical source point, (b) streaking pattern from the boundary of the flowfield, (c) crowding of advected textures near an attracting spiral or sink, and (d) absent or lack of textures in some regions of the flow. This paper proposes a number of strategies to solve these problems. We demonstrate how the technique works using both synthetic data and computational fluid dynamics data.

Kao, David↗
NASA NTRS2002

North Atlantic Surface Winds Examined as the Source of Warm Advection into Europe in Winter

When from the southwest, North Atlantic ocean surface winds are known to bring warm and moist airmasses into central Europe in winter. By tracing backward trajectories from western Europe, we establish that these airmasses originate in the southwestern North Atlantic, in the very warm regions of the Gulf Stream. Over the eastern North Atlantic, Lt the gateway to Europe, the ocean-surface winds changed directions in the second half of the XXth century, those from the northwest and from the southeast becoming so infrequent, that the direction from the southwest became even more dominant. For the January-to-March period, the strength of south-westerlies in this region, as well as in the source region, shows in the years 1948-1995 a significant increase, above 0.2 m/sec/ decade. Based on the sensitivity of the surface temperature in Europe, slightly more than 1 C for a 1m/sec increase in the southwesterly wind, found in the previous studies, the trend in the warm advection accounts for a large part of the warming in Europe established for this period in several reports. However, for the most recent years, 1996-2001, the positive trend in the southwesterly advection appears to be is broken, which is consistent with unseasonally cold events reported in Europe in those winters. This study had, some bearing on evaluating the respective roles of the North Atlantic Oscillation and the Greenhouse Gas Global warming, GGG, in the strong winter warming observed for about half a century over the northern-latitude continents. Changes in the ocean-surface temperatures induced by GGG may have produced the dominant southwesterly direction of the North Atlantic winds. However, this implies a monotonically (apart from inherent interannual variability) increasing advection, and if the break in the trend which we observe after 1995 persists, this mechanism is counter-indicated. The 1948-1995 trend in the south-westerlies could then be considered to a large degree attributable to the North Atlantic Oscillation.

Otterman, J.↗
NASA NTRS2004

Rapid Measurements of Aerosol Ionic Composition and 3-10 nm Particle Size Distributions On The NASA P3 To Better Quantify Processes Affecting Aerosols Advected From East Asia

The Particle Into Liquid Sample (PILS) was deployed on the NASA P3 for airborne measurements of fine particle ionic chemical composition. The data have been quality assured and reside in the NASA data archive. We have analyzed our data to characterize the sources and atmospheric processing of fine aerosol particles advected from the region during the experiments. Fine particle water-soluble potassium was found to serve as a useful aerosol tracer for biomass smoke. Ratios of PILS potassium to sulfate are used as a means of estimating the percent contribution of biomass burning to fine particle mass in mixed plumes advecting from Asia. The high correlations between K+ and NO3(sup -) and NH4(sup +)' indicated that biomass burning was a significant source of these aerosol compounds in the region. It is noteworthy that the air mass containing the highest concentrations of fine particles recorded in all of ACE-Asia and TRACE-P appeared to be advecting from the Bejing/Tientsin urban region and also had the highest K(+), NO3(sup -) and NH4(sup +) concentrations of both studies. Based on K+/SO4(sup 2-) ratio's, we estimated that the plume was composed of approx. 60% biomass burning emissions, possibly from the use of bio-fuels in the urban regions.

Weber, Rodney J.↗
NASA NTRS2014

First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

A time-dependent extension of the first-order hyperbolic system method for advection-diffusion problems is introduced. Diffusive/viscous terms are written and discretized as a hyperbolic system, which recovers the original equation in the steady state. The resulting scheme offers advantages over traditional schemes: a dramatic simplification in the discretization, high-order accuracy in the solution gradients, and orders-of-magnitude convergence acceleration. The hyperbolic advection-diffusion system is discretized by the second-order upwind residual-distribution scheme in a unified manner, and the system of implicit-residual-equations is solved by Newton's method over every physical time step. The numerical results are presented for linear and nonlinear advection-diffusion problems, demonstrating solutions and gradients produced to the same order of accuracy, with rapid convergence over each physical time step, typically less than five Newton iterations.

Mazaheri, Alireza↗
DOE OSTI2023

Efficient Multigrid Reduction-in-Time for Method-of-Lines Discretizations of Linear Advection

Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems. It has been widely reported in the literature, however, that many of these methods perform quite poorly for advection-dominated problems. In this report we analyze the particular iterative parallel-in-time algorithm of multigrid reduction-in-time (MGRIT) for discretizations of constant-wave-speed linear advection problems. We focus on common method-of-lines discretizations that employ upwind finite differences in space and Runge-Kutta methods in time. Using a convergence framework we developed in previous work, we prove for a subclass of these discretizations that, if using the standard approach of rediscretizing the fine-grid problem on the coarse grid, robust MGRIT convergence with respect to CFL number and coarsening factor is not possible. This poor convergence and non-robustness is caused, at least in part, by an inadequate coarse-grid correction for smooth Fourier modes in space-time known as characteristic components. We propose an alternative coarse-grid operator that provides a better correction of these modes. This coarse-grid operator is related to previous work and uses a semi-Lagrangian discretization combined with an implicitly treated truncation error correction. Theory and numerical experiments show the proposed coarse-grid operator yields fast MGRIT convergence for many of the method-of-lines discretizations considered, including for both implicit and explicit discretizations of high order. Parallel results demonstrate speed-up over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Combining DPG in space with DPG time-marching scheme for the transient advection–reaction equation

In this article, we present a general methodology to combine the Discontinuous Petrov–Galerkin (DPG) method in space and time in the context of methods of lines for transient advection–reaction problems. We first introduce a semidiscretization in space with a DPG method redefining the ideas of optimal testing and practicality of the method in this context. Then, we apply the recently developed DPG-based time-marching scheme, which is of exponential-type, to the resulting system of Ordinary Differential Equations (ODEs). Further, we also discuss how to efficiently compute the action of the exponential of the matrix coming from the space semidiscretization without assembling the full matrix. Finally, we verify the proposed method for 1D+time advection–reaction problems showing optimal convergence rates for smooth solutions and more stable results for linear conservation laws comparing to the classical exponential integrators.

42 ENGINEERING↗
DOE OSTI2025

Understanding latent timescales in neural ordinary differential equation models of advection-dominated dynamical systems

The neural ordinary differential equation (ODE) framework has shown considerable promise in recent years in developing highly accelerated surrogate models for complex physical systems characterized by partial differential equations (PDEs). For PDE-based systems, state-of-the-art neural ODE strategies leverage a two-step procedure to achieve this acceleration: a nonlinear dimensionality reduction step provided by an autoencoder, and a time integration step provided by a neural-network based model for the resultant latent space dynamics (the neural ODE). This work explores the applicability of such autoencoder-based neural ODE strategies for PDEs in which advection terms play a critical role. More specifically, alongside predictive demonstrations, physical insight into the sources of model acceleration (i.e., how the neural ODE achieves its acceleration) is the scope of the current study. Such investigations are performed by quantifying the effects of both autoencoder and neural ODE components on latent system time-scales using eigenvalue analysis of dynamical system Jacobians. To this end, the sensitivity of various critical training parameters – de-coupled versus end-to-end training, latent space dimensionality, and the role of training trajectory length, for example – to both model accuracy and the discovered latent system timescales is quantified. Furthermore, this work specifically uncovers the key role played by the training trajectory length (the number of rollout steps in the loss function during training) on the latent system timescales: larger trajectory lengths correlate with an increase in limiting neural ODE time-scales, and optimal neural ODEs are found to recover the largest time-scales of the full-order (ground-truth) system. Demonstrations are performed across fundamentally different unsteady fluid dynamics configurations influenced by advection: (1) the Kuramoto–Sivashinsky equations (2) Hydrogen-Air channel detonations (the compressible reacting Navier–Stokes equations with detailed chemistry), and (3) 2D Atmospheric flow.

Advection-dominated dynamical systems↗
DOE OSTI2022

Combining DPG in space with DPG time-marching scheme for the transient advection-reaction equation

In this article, we present a general methodology to combine the Discontinuous PetrovGalerkin (DPG) method in space and time in the context of methods of lines for transient advection-reaction problems. We first introduce a semidiscretization in space with a DPG method redefining the ideas of optimal testing and practicality of the method in this context. Then, we apply the recently developed DPG-based time-marching scheme, which is of exponential-type, to the resulting system of Ordinary Differential Equations (ODEs). We also discuss how to efficiently compute the action of the exponential of the matrix coming from the space semidiscretization without assembling the full matrix. Finally, we verify the proposed method for 1D+time advection-reaction problems showing optimal convergence rates for smooth solutions and more stable results for linear conservation laws comparing to the classical exponential integrators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Optimizing multigrid reduction-in-time and Parareal coarse-grid operators for linear advection

Parallel-in-time methods, such as multigrid reduction-in-time (MGRIT) and Parareal, provide an attractive option for increasing concurrency when simulating time-dependent partial differential equations (PDEs) in modern high-performance computing environments. While these techniques have been very successful for parabolic equations, it has often been observed that their performance suffers dramatically when applied to advection-dominated problems or purely hyperbolic PDEs using standard rediscretization approaches on coarse grids. In this paper, we apply MGRIT or Parareal to the constant-coefficient linear advection equation, appealing to existing convergence theory to provide insight into the typically nonscalable or even divergent behavior of these solvers for this problem. To overcome these failings, we replace rediscretization on coarse grids with improved coarse-grid operators that are computed by applying optimization techniques to approximately minimize error estimates from the convergence theory. Therefore, one of our main findings is that, in order to obtain fast convergence as for parabolic problems, coarse-grid operators should take into account the behavior of the hyperbolic problem by tracking the characteristic curves. Our approach is tested for schemes of various orders using explicit or implicit Runge–Kutta methods combined with upwind-finite-difference spatial discretizations. In all cases, we obtain scalable convergence in just a handful of iterations, with parallel tests also showing significant speed-ups over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Moments-based interface reconstruction, remap and advection

Here, we present a new moment-of-fluid (MOF 2 ) interface reconstruction method. It uses the zeroth, first, and second moments of the fragment of material inside a cell of the mesh to reconstruct a convex material polygon or a union of convex polygons that approximate the respective material fragment. The new method requires information about the material moments only for the cell under consideration. The MOF 2 method allows to exactly reproduce several convex shapes: corners, filaments, and some concave shapes: cell-complements to corners and filaments. Interface reconstruction is formulated as a local (for each cell), non-linear, equality constrained optimization problem, which does not require additional communication and allows for an efficient parallel implementation. We present an extensive set of test problems, both for interface reconstruction on a single cell, and for reconstruction of a variety of shapes on a variety of meshes. We describe how to perform two-material advection using the MOF 2 method and present the results for the classical advection tests. We also show the examples of material interface remapping needed in the framework of multi-material arbitrary Lagrangian-Eulerian methods, and give a brief description of a procedure that can be used to update the material moments on the Lagrangian stage of those methods.

97 MATHEMATICS AND COMPUTING↗