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NASA NTRS1992

Reanalysis of x ray emission from M87 II: Multiphase models

In a previous paper by the authors (hereafter TB), it was shown that the hot intracluster gas around M87 could not be adequately explained in terms of a spherically symmetric, single phase model. It was found that although data from the Einstein satellite High Resolution Imager (HRI), Imaging Proportional Counter (IPC), and Focal Point Crystal Spectrometer (FPCS) could indeed be simultaneously explained by a single phase model, data from the Solid State Spectrometer (SSS) and optically determined mass estimates could not be similarly explained. A qualitative discussion was then given to indicate how the adoption of a specific multiphase model could plausibly improve upon the single phase model, but a detailed discussion was delayed until now. The x ray data is reanalyzed for the gas around M87 in the same spirit as the work in TB. That is, by assuming several cooling flow models, the shortcomings are improved upon. The procedure of TB was adopted and the data reanalyzed in the following manner: a multiphase model is assumed which can compute the surface brightness as seen by HRI and IPC. Also, the line fluxes can be computed of the lines seen by the FPCS and the mass profile after assuming hydrostatic equilibrium. The parameters of the model are then adjusted to fit the data. A check is then made to see whether the resulting model is consistent with the SSS spectrum and the equivalent width of the 7 keV complex of Fe lines as seen by large field of view instruments.

Tsai, John C.↗

DOE OSTI2015

Fault-Related CO 2 Degassing, Geothermics, and Fluid Flow in Southern California Basins--Physiochemical Evidence and Modeling

Our studies have had an important impact on societal issues. Experimental and field observations show that CO 2 degassing, such as might occur from stored CO 2 reservoir gas, can result in significant stable isotopic disequilibrium. In the offshore South Ellwood field of the Santa Barbara channel, we show how oil production has reduced natural seep rates in the area, thereby reducing greenhouse gases. Permeability is calculated to be ~20-30 millidarcys for km-scale fault-focused fluid flow, using changes in natural gas seepage rates from well production, and poroelastic changes in formation pore-water pressure. In the Los Angeles (LA) basin, our characterization of formation water chemistry, including stable isotopic studies, allows the distinction between deep and shallow formations waters. Our multiphase computational-based modeling of petroleum migration demonstrates the important role of major faults on geological-scale fluid migration in the LA basin, and show how petroleum was dammed up against the Newport-Inglewood fault zone in a “geologically fast” interval of time (less than 0.5 million years). Furthermore, these fluid studies also will allow evaluation of potential cross-formational mixing of formation fluids. Lastly, our new study of helium isotopes in the LA basin shows a significant leakage of mantle helium along the Newport Inglewood fault zone (NIFZ), at flow rates up to 2 cm/yr. Crustal-scale fault permeability (~60 microdarcys) and advective versus conductive heat transport rates have been estimated using the observed helium isotopic data. The NIFZ is an important deep-seated fault that may crosscut a proposed basin decollement fault in this heavily populated area, and appears to allow seepage of helium from the mantle sources about 30 km beneath Los Angeles. The helium study has been widely cited in recent weeks by the news media, both in radio and on numerous web sites.

58 GEOSCIENCES↗

DOE OSTI2025

Development of a conduction-based model for analyzing frozen startup of alkali-metal heat pipes

One key area of interest in heat pipe modeling/simulation is to analyze the startup behavior of the liquid-metal heat pipes (LMHPs) from a frozen state. This so-called ‘frozen startup’ process involves a complex set of nonlinear mass and heat transport phenomena, including phase transitions from solid to liquid and vapor, multiphase interactions, microporous wick flow, and compressible vapor dynamics. The complexity of these processes makes it challenging to simulate LMHP’s frozen startup using conventional numerical methods or commercial computational fluid dynamics (CFD) software. This paper presents a simplified conduction-based modeling approach that can provide practical insights into the entire LMHP frozen startup process, while alleviating the challenges of modeling its complex physics. The theoretical foundation and physical assumptions of the proposed model are based solely on heat-conduction equation, allowing for a more tractable simulation without sacrificing essential physical accuracy. The proposed model was implemented in a commercial CFD software, and its prediction was compared with the experimental data obtained from sodium heat-pipe startup experiments. The comparison highlights the proposed model's ability to capture the transient thermal behavior of LMHP during frozen startup. This study not only validates the conduction-based frozen startup modeling method but also shows its potential as a practical and efficient tool for understanding the startup performance of the LMHP systems.

Microreactor↗

DOE OSTI2021

Full-Loop Simulation of the Combustion of Biomass in a Circulating Fluidized Bed Combustor

Interest in circulating fluidized bed (CFB) boilers as a power generation technology has skyrocketed in recent years because of several advantages this technology offers over conventional boilers, such as increased gas-solid mixing, which results in higher combustion efficiency, and the ability to use lower rank fuels. CFB combustors are operated at lower temperatures than conventional thermal power generation combustors, thus reducing NO x emissions, while SO 2 emissions can be conveniently controlled through the addition of Ca-based sulfur sorbents within the combustor. This report summarizes the development of a comprehensive computational fluid dynamics (CFD) model for biomass combustion in a 50 kW th CFB combustor employing the multiphase particle-in-cell (PIC) approach in the open-source Multiphase Flow with Interphase eXchanges (MFiX) Software Suite at the U.S. Department of Energy (DOE) National Energy Technology Laboratory (NETL). The experimental combustor was designed, built, and operated at CanmetENERGY, Natural Resources Canada in Ottawa, Canada. This work is the culmination of a multi-year collaboration between NETL and CanmetENERGY. The hydrodynamics in the full loop are validated against cold-flow experiments conducted at CanmetENERGY. To mimic the dense packing in the standpipe in the absence of a collisional model in the MFiX-PIC approach, the ram valve in the return leg is partially closed to obstruct the flow. A combustion reaction scheme was developed that considers the volatiles released by the fuel as a lumped species that fully converts to CO 2 and H 2 O. The so-called enhanced simplified combustion scheme produces an excellent match with experimental data in terms of the species concentrations of CO 2 and O 2 at the outlet and the freeboard, demonstrating the utility of the comprehensive model for a range of flow conditions and operating temperatures. Furthermore, the model can be readily adapted to simulate combustion of a variety of biomass fuels as well as co-fired systems under air and oxy-fuel conditions.

09 BIOMASS FUELS↗

DOE OSTI2017

Evaluating the Practicability of Multiphase CFD for BWR Fuel Assembly Analysis

Multiphase computational fluid dynamics (M-CFD) models of a boiling water reactor (BWR) fuel assembly have been generated in the commercial CFD code, STAR-CCM+ Ver.11.04.010-R8. The Eulerian multiphase approach was employed, in combination with a baseline ‘Zero Closure model’ for two-phase flow boiling, applicable to high void fraction regimes. The capability and practicability of MCFD for BWR fuel assembly were evaluated against the international OECD/NRC BWR Full-size Finemesh Bundle Test (BFBT) benchmark data. The benchmark selected, BFBT-4101-61, is a steady-state full power case, with high void fraction conditions. Geometrical modeling and mesh construction of BWR assemblies introduce challenges in generating high quality computational meshes, while retaining a low cell count to allow acceptable runtimes. In order to evaluate the scalability of the CFD code, parallel CFD simulations were carried out with the High Performance Computing (HPC) system of the Idaho National Laboratory. M-CFD results display good agreement with the experimental data for both local void fraction distribution and exit quality. The parallel speedup factor is linearly proportional to the number of processors up to 500 cores, and retains over 92% efficiency with 1000 cores. The execution time of the simulation decreased exponentially with increasing number of processors while the cost of the simulation increased linearly. The proposed baseline closure, in combination with the parallel performance of the STAR-CCM+ code demonstrated promising capabilities for analyzing BWR fuel assemblies.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Small-scale flow topologies in decaying isotropic turbulence laden with finite-size droplets

The topology of the fine-scale motions in decaying isotropic turbulence laden with droplets of super-Kolmogorov size is investigated using results from direct numerical simulations. The invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors are computed in the carrier phase. The joint probability density functions of the invariants are calculated and conditioned on different distances from the droplet surface. The results show that outside the viscous region near the interface, the flow topologies favor stable focus/stretching and unstable node/saddle/saddle structures, which is in agreement with those found in canonical homogeneous isotropic turbulence. Inside the viscous layer at the droplet surface, the flow topologies shift from a preference for high-enstrophy/low-dissipation motions to favoring low-enstrophy/high-dissipation. At the droplet surface, there is a strong tendency for boundary-layer-like and vortex-sheet flow topologies in which the strain and rotation rates are positively correlated. Furthermore, an interesting observation is that the shapes of the invariant distributions at the droplet surface are remarkably similar to those reported in the viscous sublayer of turbulent wall-bounded flows. Also, the results show that the smallest hydrodynamic length scale of the carrier fluid turbulence is located at the droplet interface and that this length scale is two to three times smaller than that of the surrounding bulk flow. From a computational viewpoint, this suggests a more stringent spatial resolution requirement for the direct numerical simulation of finite-size droplets in isotropic turbulence than its single-phase counterpart.

42 ENGINEERING↗

DOE OSTI2022

The influence of random packed column parameters on the liquid holdup and interfacial area

Abstract Carbon dioxide capture via solvent absorption in packed columns has emerged as a potential technology to mitigate coal‐fired power plant CO 2 emissions. Parameters, including packing types, solvent properties, and operating conditions, could potentially affect the packed column CO 2 capture efficiency. To understand the importance of those parameters and help packed column optimization, a design of experiments (DoEs) method was proposed to generate input parameter matrix. Combined with multiphase computational fluid dynamics (CFD), the random packed column parameter influence on the liquid holdup and interfacial area can be efficiently investigated. Surrogate‐based sensitivity analysis shows that the solvent flow rate and contact angle are key factors dictating liquid holdup and interfacial area. On the other hand, solvent viscosity has a marginal impact on the interfacial area. The sensitivity scores were calculated for each input parameter to guide the selection of dimensionless numbers for the liquid holdup and interfacial area correlation development.

42 ENGINEERING↗

DOE OSTI2019

Device-scale computational fluid dynamics modeling of carbon dioxide absorption using encapsulated sorbents

Micro-encapsulated carbon dioxide sorbent (MECS) is considered to be a promising material for carbon capture system because of high capture rate, low fabrication cost, and efficient energy consumption. To accelerate the development of MECS technology for industrial deployment, device-scale computational fluid dynamics (CFD) simulations are performed to study hydrodynamics and CO2 absorption behavior in a conceptual fluidized bed reactor. The two-fluid model solver, built in the Multiphase Flow with Interphase eXchanges (MFIX), is adopted to solve the multiphase flow hydrodynamics by representing both fluid and solids as continuous phases. Filtered models are implemented to capture the sub-grid effects that normally cannot be directly considered because MECS particles are too small to be explicitly resolved at such a large scale. Using established CFD tools, this study aims to characterize MECS behavior and predict its carbon capture performance in a conceptual device-scale absorber. The MECS particle size and gas flow rate have significant impact on CO2 capture efficiency. The CO2 capture efficiency decreases with increasing gas flow rate. Smaller particle size lead to better gas-solid homogeneity, as a results CO2 absorption efficiency increases.

Wang, Chao (ORCID:0000000279406614)↗

DOE OSTI2018

Performance Assessment of a Generic Nuclear Waste Repository in Shale - 18392

A performance assessment (PA) is an important component of a comprehensive safety analysis for a nuclear waste repository. In a PA, probabilistic simulations of the total repository system are performed, and results are evaluated against performance metrics. Uncertainty and sensitivity analyses help prioritize additional research and model development. The United States Department of Energy (DOE) has been developing a state of the art PA simulation software tool-kit, Geologic Disposal Safety Assessment (GDSA) Framework, that couples increasingly higher fidelity models of subsystem processes into total system PA simulations. Over the past several years, PAs of generic repositories in three geologic media (salt, shale, and crystalline rock) have demonstrated ongoing developments in capability. The current PA of a nuclear waste repository in a generic shale formation showcases GDSA Framework, including capabilities in domain discretization (Cubit), multi-physics simulations (PFLOTRAN), uncertainty and sensitivity analysis (Dakota), and visualization (Paraview). The generic shale reference case considers the disposal of 22,000 metric tons heavy metal of commercial spent nuclear fuel (SNF) in a generic shale formation. PA simulations account for the thermal load and radionuclide inventory of the waste form, components of the engineered barrier system including waste package and buffer, and components of the natural barrier system including the host rock shale and underlying and overlying stratigraphic units. Two repository layouts are considered, one for emplacement of waste packages containing 12 pressurized water reactor (PWR) assemblies, and one for 4-PWR waste package emplacement. Model domains are half-symmetry and contain between 7 and 22 million grid cells. Grid refinement captures the detail of individual waste packages, emplacement drifts, access drifts, and shafts. Simulations are run in a high-performance computing (HPC) environment on 512 or 2048 processes. The governing equations describing coupled heat and fluid flow and reactive transport are solved with PFLOTRAN, an open-source, massively parallel multiphase flow and reactive transport code. Additional simulated processes include waste package degradation; waste form dissolution; radioactive decay and ingrowth in aqueous, solid, and adsorbed phases; and a simple biosphere based on a pumping well. Simulations are run to 106 y; dose and radionuclide concentrations are observed within aquifers at a point approximately 5 km downgradient of the repository. Dakota is used to sample likely ranges of input parameters including waste form and waste package degradation rates and properties of engineered and natural materials to quantify uncertainty in predicted concentrations and sensitivity to input parameters. Given the assumptions of the reference case, results of 12-PWR and 4-PWR simulations are very similar. Dose at the pumping well 5-km downgradient of the repository does not exceed 10-9 Sv/y. I-129 is the largest contributor to dose. The dose due to Cl-36, the next largest contributor, is orders of magnitude smaller. At the pumping well, the concentration of I-129 5-km downgradient does not exceed 10-14 mol/L. Rank correlation coefficients indicate that the maximum concentration of I-129 within the aquifer is sensitive to shale (repository host rock) porosity and aquifer permeability. These results affirm that HPC-capable codes can be used to simulate important multi-physics couplings directly in a total system performance assessment of a geologic repository, and can be used in prioritization of future research and model development. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

MPLBM-UT: Multiphase LBM library for permeable media analysis

MPLBM-UT is a specialized lattice-Boltzmann library that makes running single- and two-phase flow simulations in porous media accessible to everyone. We provide a suite of tools to pre-process computational domains for simulation, to set up custom boundary conditions, to run simulations, to post-process simulation outputs, and to visualize simulation results and data. All of these tools are easily accessible to users through the mplbm_utils Python package included in and automatically installed with MPLBM-UT. The high-performance, highly parallel library Palabos is used as the solver backend. MPLBM-UT is easily deployed in a variety of systems, from laptops to supercomputer clusters. MPLBM-UT also features multiple examples and benchmark templates that allow for fast prototyping of different porous media problems. We also provide an interface for reading in different file types and downloading domains from the Digital Rocks Portal to perform simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

The Onset of Nucleate Boiling Prediction in a Mini Channel with the Eulerian Multiphase Flow

The prediction of boiling incipience is a critical issue for a reactor. Vapor lock causes operating instability and undesirable temperature rise, especially for small channels. This study uses the Eulerian multiphase flow boiling model to predict the onset of nucleate boiling in a millimeter scale rectangular channel. Two wall boiling models, namely the RPI (Rensselaer Polytechnic Institute) and the non-equilibrium sub cooled model are applied. Computational fluid dynamics is employed for this study to investigate the impact of operating conditions like liquid flow rate, operating pressure, heat flux, velocity profile, turbulence model, and inlet liquid temperature. Here, the effect of fundamental boiling parameters on the surface wall temperature and vapor volume fraction is also studied. The parameters under consideration are the bubble departure diameter, bubble departure frequency, nucleate site density, quenching time period, and interface heat transfer coefficients. A series of CFD calculations is conducted by varying the considered variables systematically in a wide range of flow conditions covering laminar, transition, and turbulent flows. The sub-component heat fluxes like the liquid convective, the vapor convective, the evaporative, and the quenching terms are monitored to infer the boiling dynamics in the transition region from the single-phase flow to the nucleate boiling zone. It is found that the CFD approach to detecting the boiling incipience point agrees reasonably with available experimental data. However, its limitations, like inaccuracy for lower flow rates and early transition to boiling flow, are also noticed due to the nature of the considered RPI model.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

An Open-Source Framework for the Computational Analysis and Design of Autothermal Chemical Processes

The main project object was to develop software tools for simulating non-equilibrium autothermal processes, improving the prospects for identifying and designing such systems. The project demonstrates the use of these tools to simulate autothermal pyrolysis, a process recently developed at the pilot-plant scale at Iowa State University. In such process, instead of externally heating a reactor to pro-vide the enthalpy of pyrolysis, sufficient oxygen in the form of air is introduced into the reactor to support partial oxidation of reactants and products with the exothermic energy released supporting endothermic pyrolysis reactions. A fluidized bed is used to assure good mixing of biomass and oxidant and provide an isothermal reaction environment. The amount of oxygen required depends upon the kind of biomass being pyrolyzed and parasitic heat losses from the reactor. For example, for woody biomass pyrolyzed under conditions that simulate adiabatic operation, equivalence ratios can be as low as 0.06, compared to 0.20 or higher for autothermal gasifiers. By removing the heat transfer bottleneck of conventional pyrolysis, operation in autothermal mode allowed a significant increase in reactor throughput process, approaching five times the throughput of the conventionally operated pyrolyzer. Different simulation strategies were considered and developed: a zero-dimensional chemistry model was used to verify the applicability of kinetic schemes to predict biomass fast pyrolysis in autothermal conditions. Conventional chemical reactor models such as the plug flow reactor and the partially stirred reactor were used to investigate the role of mixing in the fluidized bed pyrolyzer and to establish the impact of mixing time on the gas-phase reactions. A comprehensive multiphase computational fluid dynamics (mCFD) framework, including polydisperse granular phase modeling and detailed chemical kinetics was formulated and used to model the experimental setup for autothermal biomass fast pyrolysis at ISU. Multiphase CFD was also used to investigate the role of biomass feed positioning on the mixing of biomass in the pyrolizer. Finally, a reduced order model (ROM), suitable to be implemented in process simulators was obtained. Both the mCFD and the ROM were validated against experiments.

09 BIOMASS FUELS↗

DOE OSTI2020

Scaling of two-phase water-steam relative permeability and thermal fluxes in porous media

Two-phase water-steam flow conditions are frequently encountered in many engineering applications, including geothermal reservoirs. Although routine calculations are based on the multiphase Darcy’s law, the role of the topology of the flowing phases at the pore-scale is usually neglected in the estimation of relative permeabilities. Instead, the latter are frequently computed using empirical models like the Corey correlation. In this work, we first apply the model for relative permeabilities based on pore-scale flow regimes developed by Picchi and Battiato (2019), Relative permeability scaling from pore-scale flow regimes, Water Resour. Res. 55, 3215–3233, to scenarios typical of geothermal reservoirs and then extend it by deriving the scaling laws for the transmissibilities and the thermal properties as a function of temperature. First, we discuss the scaling behavior of normalized relative permeabilities in terms of viscosity ratio and capillary number of water-steam systems and, then, we provide a validation of the model against experimental data available in the literature. The model captures well the data trends collected in real 3D porous media. These results suggest that water-steam relative permeabilities follow the same scaling behavior of gas-liquid systems where the non-wetting phase is much less viscous than the wetting phase. Finally, we investigate the impact that relative permeabilities have on heat transfer rates at two-phase flow conditions and the scaling of mass and energy transmissibility and thermal properties of the mixture. An estimation of the exergy carried by the two-phase water-steam mixture is also included.

42 ENGINEERING↗

DOE OSTI2022

CFD Simulation of Biomass Pyrolysis Vapor Upgrading over a Pt/TiO 2 Catalyst in Fixed and Moving Beds

This report presents a comprehensive computational fluid dynamics (CFD) study of the biomass pyrolysis vapor phase upgrading and the catalyst regeneration in different reactors under various operational conditions. This study used the open-source software Multiphase Flow with Interphase eXchanges (MFiX), developed at National Energy Technology Laboratory (NETL) for simulating hydrodynamics, heat transfer, and chemical reactions in multiphase systems. This simulation solved the conservation of mass, momentum, energy, species for gas and solid phases with chemical reactions.

09 BIOMASS FUELS↗

DOE OSTI2021

Feature Analysis, Tracking, and Data Reduction: An Application to Multiphase Reactor Simulation MFiX-Exa for In-Situ Use Case

As we enter the exascale computing regime, powerful supercomputers continue to produce much higher amounts of data than what can be stored for offline data processing. To utilize such high compute capabilities on these machines, much of the data processing needs to happen in situ, when the full high-resolution data is available at the supercomputer memory. In this article, we discuss our MFiX-Exa simulation, which models multiphase flow by tracking a very large number of particles through the simulation domain. In one of the use cases, the carbon particles interact with air to produce carbon dioxide bubbles from the reactor. These bubbles are of primary interest to the domain experts for these simulations. For this particle-based simulation, we propose a streaming technique that can be deployed in situ to efficiently identify the bubbles, track them over time, and use them to down-sample the data with minimal loss in these features.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Fault-related CO 2 degassing, geothermics, and fluid flow in southern California basins---Physiochemical evidence and modeling

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Development of machine learning framework for interface force closures based on bubble tracking data

Interfacial force closures in the two-fluid model play a critical role for the predictive capabilities of void fraction distribution. However, the practices of interfacial force modeling have long been challenged by the inherent physical complexity of the two-phase flows. The rapidly expanding computational capabilities in the recent years have made high-fidelity data from the interface-captured direct numerical simulation become more available, and hence potential for data-driven interfacial force modeling has prevailed. In this work, we established a data-driven modeling framework integrated to the HZDR multiphase Eulerian-Eulerian framework for computational fluid dynamics simulations. The data-driven framework is verified in a benchmark problem, where a feedforward neural network managed to capture the non-linear mapping between bubble Reynolds number and drag coefficient and reproduce the void distribution resulting from the baseline model in the test case. The second focus is on utilizing the bubble tracking data set to form a closure for the bubble drag in the turbulent bubbly flow, in which the drag coefficient is set to be correlated with the bubble Reynolds number and the Eötvös number. Pseudo-steady state filtering in the Frenet Frame was carried out to obtain the drag coefficient from the turbulent bubbly flow data. The performance of the data-driven drag model is also examined through a case study, where improvement of model’s prediction near-wall is regarded necessary. In conclusion, discussion and further plans of investigation are provided.

42 ENGINEERING↗

DOE OSTI2020

Fast Computational Algorithms for Partial Differential Equations and Uncertainty Quantifications

This project concerned the construction, testing and analysis of computational algorithms for solving parameterized and stochastic partial differential equations. The study and understanding of equations of this type is of fundamental importance in numerous engineering and scientific applications. Examples include simulation of plasma dynamics in models of electric propulsion and nuclear fusion, simulation of multiphase flows, such as the flow of water, gas and oil in reservoirs, and structural analysis of the dependence of structures on materials. Parametrization is used in such settings when properties of the models such as viscosity of fluids or electric resistivity of materials are not precisely understood and instead are treated as random variables. The resulting solutions are themselves random, and having such solutions will enable engineers to use probabilistic methods to assess the likelihood of events, for example, whether a pollutant in a liquid will exceed a limit, and to use such analyses to develop ways to ensure positive outcomes. Construction of accurate (high resolution) computational solutions is expensive, requiring significant computer time and computational resources, and there is need to reduce computational cost to make simulation useful and effective. The aim of the project was to construct algorithms to efficiently compute surrogate solutions to parameterized problems to allow for efficient and accurate simulation. The technical approach used focused on two related strategies, based on rank-reduction methods and reduced-order models. These methods construct surrogate solutions of parameter-dependent models by projection or interpolation into low-dimensional approximation spaces. Cost savings are achieved if the low-dimensional spaces can be identified and constructed efficiently and if the resulting low-dimensional algebraic systems can be solved cheaply. Accomplishments include: Theoretical and empirical demonstration of the effectiveness of fast multigrid solution strategies for computing low-rank representations of parameter-dependent solutions to discrete partial differential equations, including the first proof establishing so-called textbook convergence properties for low-rank methods. Development of efficient solution algorithms for solving nonlinear parameter-dependent partial differential equations used in models of fluid dynamics. Developent of efficient algorithms for low-rank representation of solutions of time-dependent simulations of fluid dynamics using multi-dimensional tensor representations of solutions.

97 MATHEMATICS AND COMPUTING↗