Modeling Of Transport Processes Research Articles

Modeling of plasma facing component erosion, impurity migration, dust transport and melting processes at JET-ILW

An overview of the modeling approaches, validation methods and recent main results of analysis and modeling activities related to the plasma-surface interaction (PSI) in JET-ILW experiments, including the recent H/D/T campaigns, is presented in this paper. Code applications to JET experiments improve general erosion/migration/retention prediction capabilities as well as various physics extensions, for instance a treatment of dust particles transport and a detailed description of melting and splashing of PFC induced by transient events at JET. 2D plasma edge transport codes like the SOLPS-ITER code as well as PSI codes are key to realistic description of relevant physical processes in power and particle exhaust. Validation of the PSI and edge transport models across JET experiments considering various effects (isotope effects, first wall geometry, including detailed 3D shaping of plasma-facing components, self-sputtering, thermo-forces, physical and chemically assisted physical sputtering formation of W and Be hydrides) is very important for predictive simulations of W and Be erosion and migration in ITER as well as for increasing quantitative credibility of the models. JET also presents a perfect test-bed for the investigation and modeling of melt material dynamics and its splashing and droplet ejection mechanisms. We attribute the second group of processes rather to transient events as for the steady state and, thus, treat those as independent additions outside the interplay with the first group.

(Invited) Engineering Porous Electrodes for Redox Flow Batteries – Leveraging Computational and Synthetic Platforms

Porous electrodes are critical components in redox flow batteries where they are responsible for multiple critical functions in the cell, such as providing surfaces for electrochemical reactions, an open structure for fluid flow and mass transport, and the conductive scaffold for electronic and thermal conduction. However, our current portfolio of materials is limited to carbon-fiber-based electrodes which are assembled using various mechanical methods (e.g., paper making, weaving, hydro-entangling) resulting in distinct structures such as papers, cloths, and felts (1). These fabrication methods involve multiple complex subprocessing steps impacting the final product cost and limiting the achievable range of electrode properties, which ultimately restricts device performance (2). Thus, there is a need to develop new material sets with precise control over microstructure and surface composition while employing synthetic methods that are compatible with large-scale manufacturing.In this lecture, I will discuss our efforts to design tailored electrodes for redox flow batteries, which hold promise for long-duration stationary energy storage (3). First, I will introduce a pore network modeling framework that captures electrochemical performance in complex microstructures with low computational requirements (4), and then show the coupling of this framework with a genetic algorithm to enable bottom-up electrode design (5). In our most recent effort, we are building topology optimization models of porous electrodes using multi-scale modeling of redox flow batteries, coupling computational macro- and meso-scale models of transport processes constructed using finite element and finite volume methods. We then couple these approaches with upscaling strategies that enable manufacturability of the structures. Second, I will describe a new approach to synthesizing porous electrodes based on non-solvent induced phase separation (NIPS) (6). NIPS is a simple and versatile fabrication method that can be used to synthesize morphologically-diverse electrode microstructures (e.g., isoporous, pore-size gradients, and multimodal porosity) by tuning simple parameters in the polymer solution, such as polymer concentration, solvent type, and temperature. Using a suite of microscopic, spectroscopic, and electrochemical diagnostic tools, I will present synthesis-property-performance relationships of the NIPS electrodes (7). Third and finally, I will highlight our efforts to functionalize porous electrode interfaces with organic molecules to impart targeted functional properties including hydrophilicity, kinetic activity (8), and selectivity (e.g. H2 evolution suppression). References A. Forner-Cuenca, F. R. Brushett, Curr. Opin. Electrochem. 18, 113–122 (2019).C. Minke, U. Kunz, T. Turek, J. Power Sources. 342, 116–124 (2017).M. L. Perry, K. E. Rodby, F. R. Brushett, ACS Energy Lett. 7, 659–667 (2022).M. van der Heijden, R. van Gorp, M. A. Sadeghi, J. Gostick, A. Forner-Cuenca, J. Electrochem. Soc. 169, 040505 (2022).R. van Gorp, M. van der Heijden, M. A. Sadeghi, J. Gostick, A. Forner-Cuenca, Chem. Eng. J. 455, 139947 (2023).C. T. Wan et al., Adv. Mater. 33, 2006716 (2021).R. R. Jacquemond et al., Cell Reports Phys. Sci. 3, 100943 (2022).E. B. Boz, P. Boillat, A. Forner-Cuenca, ACS Appl. Mater. Interfaces. 14, 41883–41895 (2022).

Giant sediment-wave field and supercritical flows in a distally steepened ramp, Fort Payne Formation (Lower Mississippian), Kentucky–Tennessee, U.S.A.

ABSTRACT Sediment waves are common in confined to unconfined settings on modern marine slopes and basin floors worldwide. Their morphology and stratal patterns show that many of them migrate upslope and upflow, a characteristic thought to record Froude-supercritical flow conditions associated with sediment gravity flows and density cascades. Few sediment waves of this type have been observed in the ancient rock record. This study reports the discovery of a giant (> 20,000 km2) sediment-wave field in Lower Mississippian carbonates and shales of the Fort Payne Formation in Tennessee and Kentucky, U.S.A. Sediment waves are present in the clinothem slopes and basin floor of a distally steepened ramp as seismic-scale bedforms ranging from 100 to 700 m long and 15 to 50 m high. Dominant facies include crinoidal shales, packstones, and rudstones. Many of the beds are sharp-based and graded, indicating sediment-gravity-flow deposition. Upslope-inclined rudstones (backsets) and wavy beds with upflow and downflow laminae are common and indicate supercritical flow conditions. These observations and interpretations are in stark contrast to previous interpretations of crinoidal bioherms and Waulsortian-type mounds. Basin physiography, a cool-water heterozoan carbonate factory and coastal upwelling were key factors in establishing a rapidly prograding ramp characterized by high rates of sediment production and basinward shedding. Sediment gravity flows and density cascades transported crinoidal grains downslope and entrained crinoids that inhabited the slope. Flows frequently reached Fr-supercritical flow conditions that led to the formation of sediment waves similar to those on modern marine slopes. This sediment-wave field is one of the first to be documented in the ancient rock record, and its extent is enormous. The near absence of other reported ancient examples must be due to misinterpretation (mounds, slumps) and the problem of observational scale and resolution. Sediment waves are often larger than outcrops. Lack of recognition of sediment waves in subsurface seismic sections is probably due to misinterpretation and insufficient resolution. Perhaps this study demonstrates the need for revisiting and updating existing facies models of carbonate-sediment transport and depositional processes across slopes and basin floors.

Hybrid and coupled modeling for the design of fixed and suspended biomass reactors treating sanitary landfill leachates

This paper deals with an approach for hybrid and coupled modeling of the design of fixed and suspended biomass reactors for organic matter removal from sanitary landfill leachates. Five bioreactors, comprising Rotating Biological Contactors, Trickling Filter, Upflow Anaerobic Sludge Blanket, Upflow Anaerobic Filter in Two Separated Stages (UAF-2SS) and Upflow Anaerobic Filter in Three Separated Stages (UAF-3SS) were evaluated by treating the organic matter contained in the leachates produced in two sanitary landfills. With respect to the hybrid and coupled models, the best performance in the approximation of the measured values in the Se/Si ratio to the predicted results of models were the equations for UAF-2SS and UAF-3SS reactors. Hybrid models were made up of a combination of mass conservation law and equations for estimating transformation process. Coupled models consisted of a combination of transport process models and transformation models based on the substrate utilization rate by the microorganisms.

Joint inversion of induced polarization and hydraulic tomography data for hydraulic conductivity imaging

Summary For accurate modeling of groundwater flow and transport processes within an aquifer, precise knowledge about hydraulic conductivity K and its small-scale heterogeneities is fundamental. Methods based on pumping tests, such as hydraulic tomography (HT), allow for retrieving reliable K-estimates, but are limited in their ability to image structural features with high resolution, since the data from time-consuming hydraulic tests are commonly sparse. In contrast, geophysical methods like induced polarization (IP) can potentially yield structural images of much higher resolution, but depend on empirical petrophysical laws that may introduce significant uncertainties to the K-estimation. Therefore, this paper presents a joint inversion procedure for both HT and IP data, which allows for combining the complementary abilities of both methods. Within this approach, a travel time inversion is applied to the HT data, while the IP inversion is based on a full-decay time-domain forward response, as well as a re-parameterization of the Cole-Cole model to invert for K directly. The joint inversion is tested on a synthetic model mimicking horizontally layered sediments, and the results are compared with the individual HT and IP inversions. It is shown that jointly inverting both data sets consistently improves the results by combining the complementary sensitivities of the two methods, and that the inversion is more robust against changes in the experimental setups. Furthermore, we illustrate how a joint inversion approach can correct biases within the petrophysical laws by including reliable K-information from hydraulic tests and still preserving the high-resolution structural information from IP. The different inversion results are compared based on the structural similarity index (SSIM), which underlines the robustness of the joint inversion compared to using the data individually. Hence, the combined application of HT and IP within field surveys and a subsequent joint inversion of both data sets may improve our understanding of hydraulically relevant subsurface structures, and thus the reliability of groundwater modeling results.

Sensitivity of transport object control quality for measuring the inaccuracy of state variables

This work analyzes the sensitivity functions and optimum control of a transport and logistics process model. It explains the fundamental model of controlling safe ship movement as a differential game, and optimizing control algorithms through multi-matrix game and multi-stage positioning game. The sensitivity features for controlling safe ship in actual collision scenario are described in relation to inaccurate information of process position and variations in its varables, based on the determination of computer simulation algorithms in Matlab/Simulink software.

Analysis of world experience in the use of artificial intelligence in traffic control systems at various levels

When operating automated traffic control systems and their transformation into intelligent transport systems, modern requirements are imposed on the overall parameter safety, which characterizes the quality and efficiency of road traffic, especially when organizing high-speed loaded traffic of motor vehicles. The article discusses the use of various mathematical methods for these purposes when modeling transport processes and systems, including taking into account the development of artificial intelligence algorithms, so that when making decisions on traffic control, one can have reliable forecast indicators obtained from adequate models. A comparison of the models is made and recommendations are given on their applicability and the results obtained for traffic management purposes.

MALTA: A Zonally Averaged Global Atmospheric Transport Model for Long‐Lived Trace Gases

AbstractWe present a two‐dimensional, zonally averaged global model of atmospheric transport named MALTA: Model of Averaged in Longitude Transport in the Atmosphere. It aims to be accessible to a broad community of users, with the primary function of quantifying emissions of greenhouse gases and ozone depleting substances. The model transport is derived from meteorological reanalysis data and flux‐gradient experiments using a three‐dimensional transport model. Atmospheric sinks are prescribed loss frequency fields. The zonally averaged model simulates important large‐scale transport features such as the influence on trace gas concentrations of the quasi‐biennial oscillation and variations in inter‐hemispheric transport rates. Stratosphere‐troposphere exchange is comparable to a three‐dimensional model and inter‐hemispheric transport is faster by up to 0.3 years than typical transport times of three‐dimensional models, depending on the metric used. Validation of the model shows that it can estimate emissions of CFC‐11 from an incorrect a priori emissions field well using three‐dimensional (3D) mole fraction fields generated using a different 3D model than which the flux gradient relationships were derived. The model is open source and is expected to be applicable to a wide range of studies requiring a fast, simple model of atmospheric transport and chemical processes for estimating associated emissions or mole fractions.

Modeling of transportation and technological processes in automated systems

The purpose of the study is to create a problem-oriented model of transport and technological processes in automated systems. To achieve this goal, it is necessary to develop methodological aspects of creating an automated modeling system. The content of the basic principles of problem-oriented modeling in the study of an integrated automated system for managing stocks and transport and technological processes is revealed in the paper. At the same time, methodological aspects of creating automated modeling systems, namely, a conceptual mathematical model for the analysis and standardization of technical and economic indicators are considered. The functioning of logistics systems, namely, system modeling (supply — transport) is also considered. The problems of interaction and relationships, optimization of resource flows, and increasing the efficiency of management decisions making have been solved. It is shown that modeling resource flows involves adjustments through iterative redistribution of interregional and intraregional supplies among suppliers and consumers. Combining product items into one delivery leads to savings in stocks formation costs by reducing the number of orders. To create effective automated control systems, it is necessary to study in detail the primary object — the logistics and technical support system itself. The creation of applied mathematical and software is a promising direction for solving this problem and developing it as an automated modeling system. In this regard, when creating such automated control systems, it is most advisable to use a model-oriented approach, which is based on the principles of system analysis, standardization, classification and modularity. Thus, it is shown that the use of the problem-oriented approach to creating an automated modeling system makes it possible to reduce the labor intensity of its development and implementation, to provide the opportunity to unify algorithms for solving a problem, but also to apply standard methods for processing experimental results.

Enhancing hydro-epidemiological modelling of nearshore coastal waters with source-receptor connectivity study

Faecal Indicator Organism (FIO) concentrations in nearshore coastal waters may lead to significant public health concerns and economic loss. A three-dimensional numerical source-receptor connectivity study was conducted to improve the modelling of FIO transport and decay processes and identify major FIO sources impacting sensitive receptors (source apportionment). The study site was Swansea Bay, UK and the effects of wind, density, and tracer microbe (surrogate FIO) decay models were investigated by comparing the model simulations to microbial tracer field studies. The relevance of connectivity tests to source apportionment was demonstrated by hindcasting FIO concentration in Swansea Bay with the identified FIO source and the Impulse Response Function (IRF) in Control System theory. This is the first time the IRF approach has been applied for FIO modelling in bathing waters. Results show the importance of density, widely ignored in fully mixed water bodies, and the potential for biphasic decay models to improve prediction accuracy. The microbe-carrying riverine freshwater, having a smaller hydrostatic pressure, could not intrude on the heavier seawater and remained in the nearshore areas. The freshwater and the associated tracer microbes then travelled along the shoreline and reached bathing water sites. This effect cannot be faithfully modelled without the inclusion of the density effect. Biphasic decay models improved the agreement between measured and modelled microbe concentrations. The IRF hindcasted and measured FIO concentrations for Swansea Bay agreed reasonably, demonstrating the importance of connectivity tests in identifying key FIO sources. The findings of this study, namely enhancing hydro-epidemiological modelling and highlighting the effectiveness of connectivity studies in identifying key FIO sources, directly benefit hydraulics and water quality modellers, regulatory authorities, water resource managers and policy.

Features of transport flow modeling in projects of sustainable development in urban areas

The paper highlights the problems of modern Russian cities that significantly affect their socio-economic development. Most of the problems are related to the transport and logistics system due to the historical design of urban neighborhoods, chaotic and point development, and the increasing importance of road transport. All this supports the need to develop comprehensive projects for the development of urban areas. It is impossible without the use of specialized software tools, which are based on all aspects of the territory being modernized. The use of a set of methods, based on structural analysis and simulation modeling, allowed us to obtain formal models of transport processes associated with Yeniseyskaya Street in the city of Moscow. Based on the obtained models, examples of created scenarios for forecasting changes in the processes of the object of study over time during the modernization of its individual elements are presented.

Consistent Modeling of Transport Processes and Travel Times—Coupling Soil Hydrologic Processes With StorAge Selection Functions

AbstractUnderstanding the transport processes and travel times of pollutants in the subsurface is crucial for an effective management of drinking water resources. Transport processes and soil hydrologic processes are inherently linked to each other. In order to account for this link, we couple the process‐based hydrologic model RoGeR with StorAge Selection (SAS) functions. We assign to each hydrological process a specific SAS function (e.g., power law distribution function). To represent different transport mechanisms, we combined a specific set of SAS functions into four transport model structures: complete‐mixing, piston flow, advection‐dispersion and advection‐dispersion with time‐variant parameters. In this study, we conduct modeling experiments at the Rietholzbach lysimeter, Switzerland. All modeling experiments are benchmarked with HYDRUS‐1D. We compare our simulations to the measured hydrologic variables (percolation and evapotranspiration fluxes and soil water storage dynamics) and the measured water stable isotope signal (18O) in the lysimeter seepage for a period of ten years (1997–2007). An additional virtual bromide tracer experiment was used to benchmark the models. Additionally, we carried out a sensitivity analysis and provided Sobol indices for hydrologic model parameters and SAS parameters. Our results indicate that the advection‐dispersion transport model produces the best results. And thus, advective‐dispersive transport processes play a dominant role at Rietholzbach lysimeter. Our modeling approach provides the capability to test hypotheses of different transport mechanisms and to improve process understanding and predictions of transport processes. Overall, the combined model allows a very effective simulation of combined flux and transport processes at various temporal and spatial scales.

(Invited) Model-Predictive Design of Low Pt Loaded PEMFC Catalyst Layers

Proton exchange membrane fuel cells (PEMFCs) are a promising means to decarbonize the global vehicle fleet, but commercialization is limited by costly Pt catalysts, among other challenges. PEMFC designs with low Pt loading typically suffer anomalous performance losses. Previous studies have agreed that poor device performance is linked to complex physiochemical processes in the cathode catalyst layer (CL) [1]. More specifically, poor performance with low Pt-loading is attributed to sluggish proton and/or oxygen transport through the nano-thin Nafion ionomer in the CL. Previous studies have also identified that the properties of the Nafion thin films in the CL vary from those previously measured for thicker membranes. However, research has not yet definitively connected CL polymer properties with PEMFC limitations in low Pt-loaded cells, nor found a means to address the limitations for low cost, higher-performance PEMFCs.In this presentation, we will describe efforts to quantify structure-property relationships for thin-film Nafion and incorporate these relationships into PEMFC numerical simulations to identify advantageous PEMFC catalyst layer designs. We model nm-scale transport in thin-film Nafion to develop structure-property relationships for thin-film Nafion, based on in situ neutron reflectometry [2], and conductivity measurements [3] on thin film Nafion. These result in a model that calculates the conductivity as a function of temperature, local water uptake, film thickness, and underlying substrate (Pt or carbon). Incorporating these structure-property models into a continuum-scale PEMFC cathode half-cell model to locally resolve proton conductivity and O2 diffusion improves model fits to PEMFC data with varying Pt loading [4]. The fits provide new insights into the coupling between kinetic, mass transport, and Ohmic losses in low-Pt-loaded PEMFC cathodes and show that Ohmic losses in thin film Nafion play a key limiting role in low-Pt loaded cells. We conclude with a parametric study of PEMFC CL design parameters with low Pt loading. Incorporating multi-scale modelling of Nafion transport processes enhances the predictive model capabilities and unlocks new insights into CL design. We will present a detailed analysis of how best to manage coupled limiting phenomena in PEM fuel cells, and identify functionally graded catalyst layer designs that could significantly improve PEMFC power density with low Pt loading [4]. Weber, A. and Kusoglu, A. Mater. Chem. A. 2014. DOI: 10.1039/c4ta02952fDeCaluwe, S.C. et al. Nano Energy 2018. DOI: 10.1016/j.nanoen.2018.01.008Paul, D.K. et al. Electrochem. Soc. 2014. DOI: 10.1149/2.0571414jesRandall, C.R. and DeCaluwe, S.C., Electrochem. Soc. 2022. DOI: 10.1149/1945-7111/ac8cb4

Critical Review of Transport Properties of HCl, KOH, and NaOH in High Temperature Water and Correlations for Transport Properties of H3O+ and OH−

High-temperature tracer diffusion coefficients for H3O+ and OH− are important parameters in the modeling of diffusion-controlled reaction kinetics and mass transport processes under hydrothermal conditions, and these tracer diffusion coefficients are directly related to the ionic electrical conductivities in the limit of infinite dilution through the Nernst–Einstein relationship. The limiting conductivity of H3O+ and OH− in water is controlled by two separate mechanisms of ionic movement: (i) the bulk ionic diffusion and (ii) proton hopping, also known as “Grotthuss” mechanism and/or “prototropic transfer.” This work reports a critical assessment of the limiting electrical conductivity data (Λ°) for aqueous HCl, KOH, and NaOH measured above room temperature. The initial assessed dataset included temperatures from 273.15 K up to 873.15 K and water densities from 1000 kg m−3 down to 270 kg m−3 and was reduced down to a final critically evaluated dataset spanning temperatures between 273.15 and 678.15 K and densities between 346 and 1006 kg m−3. The results were used to derive values for the excess conductivity due to prototropic transfer, λE°, of H3O+ and OH− using correlations previously reported for aqueous KCl. Simple empirical correlations of water viscosity and density were derived for Λ°(HCl), Λ°(KOH), Λ°(NaOH), λE°(H3O+), and λE°(OH−). Tests using the λE°(OH−) correlation and a previously reported function for Λ°(NaCl) show that the NaOH data can be accurately reproduced to within the estimated uncertainties. The reported correlations provide a means to model more accurately the tracer diffusion coefficients for H3O+ and OH− to supercritical conditions.

Numerical Simulation of Palm Biodiesel Droplet Evaporation at Various Temperatures and Pressures

This study uses numerical simulations to determine the evaporation characteristics of palm biodiesel droplets under normal gravity at temperatures ranging from 473 to 873 K and pressures ranging from 0.2 to 5 bar. A transient, two-phase, axisymmetric volume of fluid (VOF) model is employed to model transport processes across phases. The palm methyl ester is modelled as a single-component fuel with temperature- and pressure-dependent thermophysical properties. The study compares the obtained evaporation rates with those available in the literature and presents the effects of external parameters in experimental setups. Additionally, the study investigates the effects of changing the oxygen/nitrogen composition of the environment at elevated temperatures. The results show that elevated temperatures enhance the evaporation rate at all pressures and oxygen contents due to significantly enhanced thermal conductivity and droplet surface temperatures, while elevated pressures decrease the evaporation rates. Across the pressure range, evaporation rates decrease by 219%, 213%, and 196% for temperatures of 473, 673, and 873 K, respectively. Furthermore, increasing oxygen concentration in the environment can also increase the evaporation rate; however, the effect is less noticeable with a 6.4% increase at 473 K and more significant with a 27.8% increase at 873 K across the selected oxygen composition range.

Prediction of the absolute hydraulic conductivity function from soil water retention data

Abstract. For modeling flow and transport processes in the soil–plant–atmosphere system, knowledge of the unsaturated hydraulic properties in functional form is mandatory. While much data are available for the water retention function, the hydraulic conductivity function often needs to be predicted. The classical approach is to predict the relative conductivity from the retention function and scale it with the measured saturated conductivity, Ks. In this paper we highlight the shortcomings of this approach, namely, that measured Ks values are often highly uncertain and biased, resulting in poor predictions of the unsaturated conductivity function. We propose to reformulate the unsaturated hydraulic conductivity function by replacing the soil-specific Ks as a scaling factor with a generally applicable effective saturated tortuosity parameter τs and predicting total conductivity using only the water retention curve. Using four different unimodal expressions for the water retention curve, a soil-independent general value for τs was derived by fitting the new formulation to 12 data sets containing the relevant information. τs was found to be approximately 0.1. Testing of the new prediction scheme with independent data showed a mean error between the fully predicted conductivity functions and measured data of less than half an order of magnitude. The new scheme can be used when insufficient or no conductivity data are available. The model also helps to predict the saturated conductivity of the soil matrix alone and thus to distinguish between the macropore conductivity and the soil matrix conductivity.

Dispersion of tracer particles by wave turbulence

We have investigated the dispersion of tracer particles by numerically simulating ensemble nonlinear gravity waves on the surface of an infinitely deep fluid. Using the concepts of passive Lagrangian markers and insights from weak wave turbulence theory, we validated fundamental predictions for particle kinematics associated with scaling laws and probability density functions. These results improve the understanding of wave-driven transport phenomena that depart far from equilibrium and the development of the high-fidelity models of transport processes in geophysical systems.

Thermodynamically consistent stochastic models for active transmembrane transport processes.

Simulating the full transport cycle of an active transporter driven an ionic electrochemical transmembrane gradient with atomistic detail has been challenging because full cycle completions occur on typical time scales ranging from milliseconds to seconds, out of reach of typical molecular dynamic (MD) simulations. Instead, multiscaling approaches have been developed that break the cycle into elementary steps for which kinetic and equilibrium parameters can be obtained from MD. These parameters are combined in a stochastic kinetic model whose master equation is solved under varying external conditions such as ion concentrations and membrane potential. We developed two improvements for this well-known approach: (1) We introduce the multibind algorithm to derive thermodynamically consistent state free energies and rates from input free energy differences and rates; without such a step, a kinetic model is not guaranteed to obey the laws of thermodynamics and may produce nonsensical results. We also show how the resulting model can be used for parameter inference of microscopic parameters from macroscopic experimental measurements. (2) As an alternative to the numerical solution of the steady state problem, one can exactly solve it using Hill's diagrammatic approach. Our Kinetic Diagram Analysis (KDA) implementation of Hill's method yields symbolic rational expressions for arbitrary kinetic graphs that can be analytically manipulated and directly evaluated. We demonstrate the kinetic graph multiscale approach for sodium/proton antiporters.

Non-Overlapping Schwarz Waveform-Relaxation for Nonlinear Advection-Diffusion Equations

Nonlinear advection-diffusion equations often arise in the modeling of transport processes. We propose for these equations a non-overlapping domain decomposition algorithm of Schwarz waveform-relaxation (SWR) type. It relies on nonlinear zeroth-order (or Robin) transmission conditions between the sub-domains that ensure the continuity of the converged solution and of its normal flux across the interface. We prove existence of unique iterative solutions and the convergence of the algorithm. We then present a numerical discretization for solving the SWR problems using a forward Euler discretization in time and a finite volume method in space, including a local Newton iteration for solving the nonlinear transmission conditions. Our discrete algorithm is asymptotic preserving, i.e., robust in the vanishing viscosity limit. Finally, we present numerical results that confirm the theoretical findings, in particular the convergence of the algorithm. Moreover, we show that the SWR algorithm can be successfully applied to two-phase flow problems in porous media as paradigms for evolution equations with strongly nonlinear advective and diffusive fluxes.

Three-dimensional cleat scale modelling of gas transport processes in deformable fractured coal reservoirs

To understand the flow processes in naturally fractured coal reservoirs, a 3D numerical model for coupled gas flow, adsorption and deformation at the scale of coal cleat and matrix blocks is presented in this study. A discrete fracture matrix (DFM) modelling approach has been adopted where flow patterns in fractures and matrices are described separately and explicitly. Different from previous studies in which constant diffusion coefficient, equilibrium adsorption and lumped deformation of matrix and fracture are assumed, in this study, adsorbed gases are treated as an independent phase and the mass exchange process between free phase and adsorbed phase is described using the Langmuir kinetic model. Different gas transport mechanisms in a porous coal matrix are considered for both phase gas transport. Particularly, an equivalent poroelastic continuum model is applied to represent deformation of fracture-matrix system, in which impacts of fracture deformation on the bulk matrix-fracture deformation is accounted for. The hybrid dimensional elements have been employed to discretize the governing equations where fractures are discretized using lower-dimensional interface elements. The accuracy of developed model is validated against experimental results collected from literatures. The simulation results indicate that the gas diffusion process in coal matrices is pressure dependent, surface diffusion of adsorbed gas can contribute to the bulk gas diffusion in coal matrices. Individual cleat initially exhibits a slight opening, followed by significant closure due to adsorption-induced swelling. Ignoring the effect of fracture on bulk deformation, the aperture change is overestimated.