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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Stability Analysis of Coupled Advection-Diffusion Models with Bulk Interface Condition

Numerical stability is of critical importance in general circulation models because it affects the design of algorithms, time to solution, and computational costs associated with the simulations, which are very expensive in practice. In this paper we extend the stability analysis for ocean-atmosphere coupling proposed in [Zhang et al., J. Sci. Comput. 84, 44(2020)] to a more realistic model that includes horizontal advection. We analyze various time-stepping strategies. We find that advection has a stabilizing effect in scenarios common to climate models when bulk interface condition and explicit flux coupling are used. We also show that our method can be used to study the stability impact of advection for other interface conditions such as Dirichlet-Neumann conditions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Fast Advective Water Flow through Nanochannels in Clay Interlayers: Implications for Moisture Transport in Soils and Unconventional Oil/Gas Production

Water flow in nanometer or sub-nanometer hydrophilic channels bears special importance in diverse fields of science and engineering. However, the nature of such water flow remains elusive. In this work, we report our molecular-modeling results on water flow in a sub-nanometer clay interlayer between two montmorillonite layers. We show that a fast advective flow can be induced by evaporation at one end of the interlayer channel, that is, a large suction pressure created by evaporation (~818 MPa) is able to drive the fast water flow through the channel (~0.88 m/s for a 46 Å-long channel). Scaled up for the pressure gradient to a 2 μm particle, the velocity of water is estimated to be about 95 μm/s, indicating that water can quickly flow through a μm-sized clay particle within seconds. The prediction seems to be confirmed by our thermogravimetric analysis of bentonite hydration and dehydration processes, which indicates that water transport at the early stage of the dehydration is a fast advective process, followed by a slow diffusion process. The possible occurrence of a fast advective water flow in clay interlayers prompts us to reassess water transport in a broad set of natural and engineered systems such as clay swelling/shrinking, moisture transport in soils, water uptake by plants, water imbibition/release in unconventional hydrocarbon reservoirs, and cap rock integrity of supercritical CO 2 storage.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Evaluation of Atmospheric Boundary Layer Height From Wind Profiling Radar and Slab Models and Its Responses to Seasonality of Land Cover, Subsidence, and Advection

In this study, we evaluated the effect of land cover, atmospheric subsidence, and advection on the annual dynamics of atmospheric boundary layer (ABL) height from two contrasting sites. The first site is the Walker Branch forest, a deciduous forest of temperate climate, complex topography, and cloudy summers. The second site is the Sacramento-San Joaquin River Delta, a site of Mediterranean climate, flat terrain on a local scale, and clear summers. After testing a new algorithm to calculate ABL heights from 915 MHz radar wind profilers, we evaluated a hierarchy of three slab models to recreate the diurnal and annual patterns of ABL growth. We found that the lower ABL heights in the Delta, particularly during late summer, are driven by the combined effects of increased atmospheric subsidence and marine air advection. In both sites, the annual pattern of ABL height was strongly correlated to total daily incoming radiation, and in the Delta, the annual pattern of ABL height closely followed the seasonal patterns of sensible heat flux from a mosaic of different land covers. A land composite of latent and sensible heat fluxes obtained through a meso-network of eddy covariance measurements and the ECOsystem Spaceborne Thermal Radiometer Experiment on Space Station (ECOSTRESS) mission resulted in higher model skill, thus showing that land cover heterogeneity is an important driver of ABL growth. To conclude, model simulations show that in the Delta, restoring agricultural land to wetlands with large open water areas could result in a reduction of ABL height during those months with low subsidence and advection.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders

A common strategy for the dimensionality reduction of nonlinear partial differential equations (PDEs) relies on the use of the proper orthogonal decomposition (POD) to identify a reduced subspace and the Galerkin projection for evolving dynamics in this reduced space. However, advection-dominated PDEs are represented poorly by this methodology since the process of truncation discards important interactions between higher-order modes during time evolution. In this study, we demonstrate that encoding using convolutional autoencoders (CAEs) followed by a reduced-space time evolution by recurrent neural networks overcomes this limitation effectively. We demonstrate that a truncated system of only two latent space dimensions can reproduce a sharp advecting shock profile for the viscous Burgers equation with very low viscosities, and a six-dimensional latent space can recreate the evolution of the inviscid shallow water equations. Additionally, the proposed framework is extended to a parametric reduced-order model by directly embedding parametric information into the latent space to detect trends in system evolution. Furthermore, our results show that these advection-dominated systems are more amenable to low-dimensional encoding and time evolution by a CAE and recurrent neural network combination than the POD-Galerkin technique.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A Hybrid Lagrangian/Eulerian Collocated Velocity Advection and Projection Method for Fluid Simulation

Abstract We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. Our approach supports both particle‐based Lagrangian advection in very detailed regions of the flow and efficient Eulerian grid‐based advection in other regions of the flow. A novel Backward Semi‐Lagrangian method is derived to improve accuracy of grid based advection. Our approach utilizes the implicit formula associated with solutions of the inviscid Burgers’ equation. We solve this equation using Newton's method enabled by C 1 continuous grid interpolation. We enforce incompressibility over collocated, rather than staggered grids. Our projection technique is variational and designed for B‐spline interpolation over regular grids where multiquadratic interpolation is used for velocity and multilinear interpolation for pressure. Despite our use of regular grids, we extend the variational technique to allow for cut‐cell definition of irregular flow domains for both Dirichlet and free surface boundary conditions.

Gagniere, S.↗
DOE OSTI2023

Analysis of an Arctic cold air outbreak during autumn and related air mass transformations forced by surface changes and advection in higher altitudes

During marine cold air outbreaks (MCAOs), cold and dry Arctic air masses are transported from the central Arctic southward across the closed sea ice and much warmer open oceans. They experience significant transformations including a rapid heating and moistening, often leading to cloud formation. While intense wintertime MCAOs have been analyzed widely, the air mass transformations during other seasons have been studied sparsely. We address this gap by investigating an MCAO case observed in September 2020. To study the transformation processes, we combine the fifth generation of atmospheric reanalyses of the global climate (ERA5), trajectory calculations, as well as shipborne and airborne measurements. In the central Arctic, observations acquired from aboard the research vessel (RV) Polarstern during the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition characterized the initial state of the air mass over closed sea ice. Trajectories indicated the pathway the air mass took from RV Polarstern southward to the Fram Strait. For the first 24 h of the southbound drift, the air masses remained quasi-stationary. Then, still 15 h ahead of the marginal sea ice zone, differential advection across the boundary layer flow introduced humidity and clouds at higher altitudes between 1.5 and 2.5 km. ERA5-derived temperature and humidity tendencies indicated complex vertical interactions. Radiative cloud-top cooling, entrainment, and turbulence were significantly reduced in the lower and enhanced in the upper advected cloud layer. Eventually, the lower cloud deck dissipated. After this confluence of 2 different air masses, observations gathered by Polar 5 in Fram Strait as part of the MOSAiC Airborne observations in the Central Arctic campaign revealed cloudy, moist layers throughout the lowest 3.5 km and an increasing boundary layer height. Comparing the initial with the final state 48 h later, the largest net heating of +8 K was found close to the surface, yet the largest net moistening of +2.5 g kg -1 at an altitude of 1 km, as the initial profile was exceptionally dry here. We conclude that the observed air mass transformations were driven by the surface changes from sea ice to open ocean but additionally strongly impacted by the differential advection of clouds and moisture across the near-surface MCAO flow.

54 ENVIRONMENTAL SCIENCES↗
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↗
DOE OSTI2021

Physics-Informed Neural Network Method for Forward and Backward Advection-Dispersion Equations

Advection-dispersion equations (ADEs) are commonly used to describe transport phenomena in porous media. Even though mature discretization-based numerical methods for ADEs exist, some challenges still remain, especially when it comes to solving advection-dominated forward ADEs and diffusion-dominated backward ADEs. The latter problem usually arises in the source identification context and leads to numerically unstable grid-based solutions that require a form of regularization or should be treated as an inverse problem that is computationally more expensive because it requires solving the forward problem multiple times. In this study, we propose a discretization-free approach based on the physics-informed neural network (PINN) method for solving coupled ADE and Darcy flow equations with space-dependent hydraulic conductivity. In this approach, the hydraulic conductivity, hydraulic head, and concentration fields are approximated with deep neural networks (DNNs). We assume that the conductivity field is given by its values on a grid, and we use these values to train the conductivity DNN. The head and concentration DNNs are trained by minimizing the residuals of the flow equation and ADE and using the initial and boundary conditions as additional constraints. The PINN method is applied to one- and two-dimensional forward ADE problems, where its performance for various P\'{e}clet numbers ($Pe$) is compared with the analytical and numerical solutions. We find that the PINN method is accurate with errors of less than 1\% and outperforms some conventional discretization-based methods for $Pe$ larger that 100. Next, we demonstrate that the PINN method remains accurate for the backward ADEs, with the relative errors in most cases staying under 5\% compared to the reference concentration field. Finally, we show that when available, the concentration measurements can be easily incorporated in the PINN method and significantly improve (by more than 50\% in the considered cases) the accuracy of the PINN solution of the backward ADE.

He, Qizhi↗
DOE OSTI2026

Advected carbon younger than the sediment fuels microbial metabolism in a pumped deep aquifer

Ever deeper wells are drilled worldwide to pump potable groundwater. Recent studies argue that overpumping compresses clays and releases reactive dissolved organic carbon (DOC), which in turn drives a series of microbial reactions that affect groundwater potability including arsenic concentrations. Here, we use a novel method to measure the radiocarbon ages of microbial RNA to determine the source of reactive or metabolizable DOC and argue against the compression of clays as the sole source of carbon. We show that microbial RNA (5,230; 5,550; 6,250 yr; n = 3 wells), DOC (280-10,800 yr; n = 13), and methane (modern to 6,240 yr; n = 3), from an overpumped deep aquifer in Bangladesh are much younger than the overlying clay layers deposited during the Pleistocene over 12,000 years ago. Mass-balance indicates that at least half of the carbon incorporated into RNA has to come from reactive DOC or methane that is advected downward via vertical recharge. This metabolism of advected organic carbon could have implications for the quality of water pumped from deep aquifers.

Biological and medical sciences↗
DOE OSTI2022

Geological activity shapes the microbiome in deep-subsurface aquifers by advection

Subsurface environments host diverse microorganisms in fluid-filled fractures; however, little is known about how geological and hydrological processes shape the subterranean biosphere. Here, we sampled three flowing boreholes weekly for 10 mo in a 1478-m-deep fractured rock aquifer to study the role of fracture activity (defined as seismically or aseismically induced fracture aperture change) and advection on fluid-associated microbial community composition. We found that despite a largely stable deep-subsurface fluid microbiome, drastic community-level shifts occurred after events signifying physical changes in the permeable fracture network. The community-level shifts include the emergence of microbial families from undetected to over 50% relative abundance, as well as the replacement of the community in one borehole by the earlier community from a different borehole. Null-model analysis indicates that the observed spatial and temporal community turnover was primarily driven by stochastic processes (as opposed to deterministic processes). We, therefore, conclude that the observed community-level shifts resulted from the physical transport of distinct microbial communities from other fracture(s) that outpaced environmental selection. Given that geological activity is a major cause of fracture activity and that geological activity is ubiquitous across space and time on Earth, our findings suggest that advection induced by geological activity is a general mechanism shaping the microbial biogeography and diversity in deep-subsurface habitats across the globe.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Idealized Large-Eddy Simulations of Stratocumulus Advecting over Cold Water. Part I: Boundary Layer Decoupling

Abstract We explore the decoupling physics of a stratocumulus-topped boundary layer (STBL) moving over cooler water, a situation mimicking warm-air advection (WADV). We simulate an initially well-mixed STBL over a doubly periodic domain with the sea surface temperature decreasing linearly over time using the System for Atmospheric Modeling large-eddy model. Due to the surface cooling, the STBL becomes increasingly stably stratified, manifested as a near-surface temperature inversion topped by a well-mixed cloud-containing layer. Unlike the stably stratified STBL in cold-air advection (CADV) that is characterized by cumulus coupling, the stratocumulus deck in the WADV is unambiguously decoupled from the sea surface, manifested as weakly negative buoyancy flux throughout the subcloud layer. Without the influxes of buoyancy from the surface, the convective circulation in the well-mixed cloud-containing layer is driven by cloud-top radiative cooling. In such a regime, the downdrafts propel the circulation, in contrast to that in CADV regime for which the cumulus updrafts play a more determinant role. Such a contrast in convection regime explains the difference in many aspects of the STBLs including the entrainment rate, cloud homogeneity, vertical exchanges of heat and moisture, and lifetime of the stratocumulus deck, with the last being subject to a more thorough investigation in Part II. Finally, we investigate under what conditions a secondary stratus near the surface (or fog) can form in the WADV. We found that weaker subsidence favors the formation of fog whereas a more rapid surface cooling rate does not. Significant Statement The low-lying blanketlike clouds, called stratocumulus (Sc), reflect much incoming sunlight, substantially modulating Earth’s temperature. While much is known about how the Sc evolves when it moves over warmer water, few studies examine the opposite situation of Sc moving over colder water. We used a high-resolution numerical model to simulate such a case. When moving over cold water, the Sc becomes unambiguously decoupled from the water surface, distinctive from its warm counterpart in which the Sc interacts with the water surface via intermittent cauliflower-like clouds called cumulus clouds. Such decoupling influences many aspects of the Sc–sea surface system, which combine to alter the ability of the Sc to reflect sunlight, thereby influencing the climate. This work laid the foundation for future work that quantifies the contribution of such a decoupled Sc regime to Earth’s radiative budget and climate change.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Development of a forced advection sampling technique (FAST) for quantification of methane emissions from orphaned wells

Abstract. Orphaned wells, meaning unplugged and non-producing wells lacking responsible owners, pose a significant and undersampled environmental challenge due to their vast number and unknown associated emissions. We propose, develop and test an alternative method for estimating emissions from orphaned wells using a forced advection sampling technique (FAST) that can overcome many of the limitations in current methods (cost, accuracy, safety). In contrast to existing ambient Gaussian plume methods, our approach uses a fan-generated flow to force advection between the emission source and a point methane (CH4) sensor. The fan flow field is characterized using a colocated sonic anemometer to measure the 3D wind profile generated by the fan. Using time-series measurements of CH4 concentration and wind, a simple estimate of the CH4 emission rate of the source can be inferred. The method was calibrated using outdoor controlled-release experiments and then tested on four orphaned wells in Lufkin, TX, and Osage County, OK. Our results suggest that the FAST method can provide a low-cost, portable, fast and safe alternative to existing methods with reasonable estimates of orphaned well emissions over a range of leak rates below 40 g h−1 and within certain geometric and atmospheric constraints.

Dubey, Mohit L↗
DOE OSTI2020

Parallel Particle Advection Bake-Off for Scientific Visualization Workloads

There are multiple algorithms for parallelizing particle advection for scientific visualization workloads. While many previous studies have contributed to the understanding of individual algorithms, our study aims to provide a holistic understanding of how algorithms perform relative to each other on various workloads. To accomplish this, we consider four popular parallelization algorithms and run a “bake-off” study (i.e., an empirical study) to identify the best matches for each. The study includes 216 tests, going to a concurrency of up to 8192 cores and considering data sets as large as 34 billion cells with 300 million particles. Overall, our study informs three important research questions: (1) which parallelization algorithms perform best for a given workload?, (2) why?, and (3) what are the unsolved problems in parallel particle advection? In terms of findings, we find that the seeding box is the most important factor in choosing the best algorithm, and also that there is a significant opportunity for improvement in execution time, scalability, and efficiency.

Pugmire, Dave↗