Source-sink Terms Research Articles

Macroscopic modeling of urban flood inundation through areal-averaged Shallow-Water-Equations

An areal-averaged form of classical Shallow-Water-Equations is developed in conjunction with Finite-Volume-Method for capturing sub-grid bed variation. The averaging mechanism treats sub-grid obstacles through depth-dependent-area-averaged porosity at the macroscopic level. This porosity assumes a binary distribution (0,1) for a resolution fine enough to treat bed-variation separately, resulting in convergence of the developed framework to classical form. An attempt has been made to incorporate the unresolved fine-scale flow-information (e.g., micro-scale and cross-scale interaction components) in terms of the macroscopic variables through a non-linear closure model. An augmented approximated Riemann solver incorporates varying source–sink terms within interfacial fluxes along with discontinuous porosity and bed variation. The model is applied to three test-cases ranging from wave-interaction with trapezoidal porous block to dam-break flows through obstacle(s) with varying grid configurations. The coarse-scale formulation, along with closure, produces a reasonably accurate solution with minimal computational overhead.

Transient prediction method for flow temperature at wellbore bottom

For the issue of an increase in the flow temperature at the bottom of the wellbore during the production in ultra-deep gas wells, the current completion design, the strength checks of tubing strings, the selection and combination of downhole tools, and theoretical prediction research do not take into account the micro-scale thermal effects of the formation. Thus, by coupling the temperature and pressure fields of the formation and the wellbore through source sink terms, a transient prediction model of the flow temperature at the bottom of the wellbore is established based on the Darcy seepage mechanism and the micro-scale thermal effects. Then, the influences of formation parameters on the flow temperature and the mechanical behavior of tubing strings are assessed. The results indicate that the gas production rate has the largest influence on the flow temperature, followed by the reservoir height, the initial formation pressure, and the initial formation temperature. Due to the influence of the micro-scale thermal effects, the flow temperature can be increased to 34 ℃ at a gas production rate of 400 × 104 m3/day, which is significantly higher than the rated working temperature of downhole tools. The safety factor of tubing strings is lower than the traditional design of tubing strings when the micro-scale thermal effects are taken into account. Finally, the research presented in this paper provides a theoretical prediction tool for a change in the flow temperature due to the influence of the micro-scale thermal effects.

Granular media deformation and fluid flow as overlapping, concurrent, coupled multilayered depth-averaged framework

A novel coupled depth-averaged formulation for the combination of multilayered fluid and monolayer granular flows as a set of interpenetrating continua has been developed in this study. Granular and fluid phases are coupled through an interaction force pair comprised of fluid stresses, and drag forces. Fluid phase is discretized in the vertical direction through a set N of virtual layer interfaces to obtain a variation of flow properties along depth. A novel algorithm for mass and momentum exchange between fluid layers for flow through and over porous media has been proposed. Eigenstructure analysis of the coupled system shows that the system may be discretized in N+1 separate yet coupled Riemann problems. An improved version of well-known HLL method is developed for solution of the model (Finite Volume Method) in a regular grid. The resistive source–sink terms are embedded implicitly within the interfacial flux. Based on the choices of state variables and layer-interface porosity, four variants of the coupled system are developed. A set of benchmark experimental test-cases and a representative test involving both rigid and deformable granular media has been simulated using the four variants to establish the robustness of the model and the coupling procedure.

Rational Allocation of Water Resources in the Arid Area of Northwestern China Based on Numerical Simulations

Adding a series of surface-water transfer projects still cannot solve the current water shortages in the arid area of northwestern China. Selecting a rational allocation plan for the water resources is the key to coordinating water use for the national economy and ecological environment. In this study, taking the Wuwei Basin as the study area, long-term data of source-sink terms from 2007 to 2018 were analyzed. Following the calibration and validation of the numerical simulation model of the groundwater system, the data was highly fitted. Based on this model, the groundwater system balance, water level variations, and suitable ecological water level area in 2050 under four water resource allocation plans were compared. Under plan 4, the groundwater resources change from an average decrease of 7656.4 × 104 m3·yr−1 from 2007 to 2018, to an increase of 4624.6 × 104 m3·yr−1 in 2050, which means the groundwater systems are almost in a positive balance state. Compared with 2018, the water level with small groundwater depth drops by 2.2–5.7 m, while that with large groundwater depths steadily rises by 2.7–8.6 m. In addition, it can maintain the 9 km2 natural oasis wetland area and the 116 km2 well-growing natural vegetation area, which can effectively promote the benign evolution and efficient, balanced sustainable development of the regional water resources, economy, and ecological environment.

Migration mechanism of pollutants in karst groundwater system of tailings impoundment and management control effect analysis: Gold mine tailing impoundment case

Tailing impoundments are sources of high-risk pollution due to the accumulation of mining tailings and wastewater. As a result of thin karst overburden as well as actions of precipitation leaching and scouring, pollutants in the tailing impoundment can easily enter the karst aquifer through sinkholes, corrosion fissures and other channels, causing pollution to groundwater and is not conducive to the utilization of groundwater resources. Through the analysis of hydrogeological conditions, the boundary condition, aquifer structure, source-sink term, and hydraulic characteristics of groundwater are generalized, the groundwater flow model and solute migration model were established, and the migration mechanism of the characteristic pollutant (arsenic ions) was analyzed. The research results show that with the passage of time, the area of high-concentration polluted areas showed a decreasing trend, and the area of low-concentration polluted areas showed a decreasing trend; Under the influence of groundwater flow and the pollutant concentration difference, the pollution plume presents an elliptical shape with the long axis along the direction of water flow; The migration law of pollutants is controlled by the direction of groundwater flow, the concentration difference of pollutants and the permeability of the aqueous medium; The direction of groundwater flow determines the migration direction of pollutants, the concentration difference of pollutants determines the diffusion range of pollutants, and the permeability of aqueous media determines the migration speed of pollutants; Through the prediction of the pollutant control effect, it can be found that a reasonable number of pumping wells that do not interfere with each other are arranged around the groundwater flow channel, which can effectively control the migration of pollutants to the target area. The above research reveals the migration mechanism of pollutants in karst groundwater and main control factors, and also provides a scientific basis for the protection of groundwater resources in karst areas.

Hydrogen separation from synthesis gas using silica membrane: CFD simulation

In the present article, an axisymmetric two-dimensional (2D) computational fluid dynamic (CFD) model was adapted to predict the efficiency of the silica membrane for hydrogen (H2) separation as a renewable energy source. In this model, continuum flows on the shell and tube sides are defined through the Navier-Stokes and transport of chemical species equations. Components transfer through the silica membrane is characterized by introducing source-sink terms based on activating transport mechanisms. To validate the presented model results related to H2 molar fraction at the retentate and permeate sides were compared with experimental data. The CFD model prognosticates the local information of velocity distribution and the molar fraction of the components. Finally, considering the effects of temperature, pressure difference, gas flow rate, and inner radius of the module on the H2 molar fraction, silica membrane performance was investigated. Moreover, it has been shown that with increasing working temperature from 323 to 473 K, H2 molar fraction at the shell side decreases from 59% to 28.4%, and in the tube side, it rises from 78.8% to 82.8%. On the shell side, it could be seen that H2 permeates better for a low gas flow rate. At the tube side, this parameter has a positive effect on H2 purification. The result of the impact of pressure differences at shell and tube sides was used to indicate the variation in the H2 molar fraction. An increase in pressure difference causes a decrease of H2 molar fraction at the tube side. At the shell side, H2 molar fraction would be decreased with an addition in pressure difference from 1 to 3 bar. Any further pressure difference rise from 3 to 4 bar, make this trend ascending. Likewise, at the shell and tube sides, by enhancing the inner radius of the module, the molar fraction of H2 increases.

A single-column ocean biogeochemistry model (GOTM–TOPAZ) version 1.0

Abstract. Recently, Earth system models (ESMs) have begun to consider the marine ecosystem to reduce errors in climate simulations. However, many models are unable to fully represent the ocean-biology-induced climate feedback, which is due in part to significant bias in the simulated biogeochemical properties. Therefore, we developed the Generic Ocean Turbulence Model–Tracers of Phytoplankton with Allometric Zooplankton (GOTM–TOPAZ), a single-column ocean biogeochemistry model that can be used to improve ocean biogeochemical processes in ESMs. This model was developed by combining GOTM, a single-column model that can simulate the physical environment of the ocean, and TOPAZ, a biogeochemical module. Here, the original form of TOPAZ has been modified and modularized to allow easy coupling with other physical ocean models. To demonstrate interactions between ocean physics and biogeochemical processes, the model was designed to allow ocean temperature to change due to absorption of visible light by chlorophyll in phytoplankton. We also added a module to reproduce upwelling and the air–sea gas transfer process for oxygen and carbon dioxide, which are of particular importance for marine ecosystems. The simulated variables (e.g., chlorophyll, oxygen, nitrogen, phosphorus, silicon) of GOTM–TOPAZ were evaluated by comparison against observations. The temporal variability in the observed upper-ocean (0–20 m) chlorophyll is well captured by the GOTM–TOPAZ with a correlation coefficient of 0.53 at point 107 in the Sea of Japan. The surface correlation coefficients among GOTM–TOPAZ oxygen, nitrogen, phosphorus, and silicon are 0.47, 0.31, 0.16, and 0.19, respectively. We compared the GOTM–TOPAZ simulations with those from MOM–TOPAZ and found that GOTM–TOPAZ showed relatively lower correlations, which is most likely due to the limitations of the single-column model. Results also indicate that source–sink terms may contribute to the biases in the surface layer (<60 m), while initial values are important for realistic simulations in the deep sea (>250 m). Despite this limitation, we argue that our GOTM–TOPAZ model is a good starting point for further investigation of key biogeochemical processes and is also useful to couple complex biogeochemical processes with various oceanic global circulation models.

Semi-analytical method for matrix diffusion in heterogeneous and fractured systems with parent-daughter reactions

A semi-analytical/numerical method for modeling matrix diffusion in heterogeneous and fractured groundwater systems is developed. This is a significant extension of the Falta and Wang (2017) method that only applied to diffusion in an aquitard of infinite thickness. The current solution allows for the low permeability matrix to be embedded within a numerical gridblock, having finite average thickness, a specified volume fraction and a specified interfacial area with the high permeability domain. The new formulation also allows for coupled parent-daughter decay reactions with multiple species that each have independent retardation factors, decay rates, and yield coefficients in both the high and low permeability parts of the system. The method uses a fitting function to approximate the transient concentration profile in the low permeability part of each gridblock so that the matrix diffusion flux into the high permeability part of the gridblock can be computed as a concentration dependent source-sink term. This approach is efficient because the only unknowns in each gridblock are the concentrations in the high permeability domain, so there is practically no increase in computational effort compared to a conventional transport simulation. The method is shown to compare favorably with an analytical solution for matrix diffusion in fractured media with parallel fractures, with an analytical solution for matrix diffusion with parent-daughter decay reactions, with laboratory experiments of matrix diffusion in a layered system, with a laboratory experiment involving lens shaped inclusions, and with fine grid numerical simulations of transport in highly heterogeneous systems.

A multiscale numerical algorithm for heat transfer simulation between multidimensional CFD and monodimensional system codes

Nowadays the rapidly-increasing computational power allows scientists and engineers to perform numerical simulations of complex systems that can involve many scales and several different physical phenomena. In order to perform such simulations, two main strategies can be adopted: one may develop a new numerical code where all the physical phenomena of interest are modelled or one may couple existing validated codes. With the latter option, the creation of a huge and complex numerical code is avoided but efficient methods for data exchange are required since the performance of the simulation is highly influenced by its coupling techniques. In this work we propose a new algorithm that can be used for volume and/or boundary coupling purposes for both multiscale and multiphysics numerical simulations. The proposed algorithm is used for a multiscale simulation involving several CFD domains and monodimensional loops. We adopt the overlapping domain strategy, so the entire flow domain is simulated with the system code. We correct the system code solution by matching averaged inlet and outlet fields located at the boundaries of the CFD domains that overlap parts of the monodimensional loop. In particular we correct pressure losses and enthalpy values with source-sink terms that are imposed in the system code equations. The 1D-CFD coupling is a defective one since the CFD code requires point-wise values on the coupling interfaces and the system code provides only averaged quantities. In particular we impose, as inlet boundary conditions for the CFD domains, the mass flux and the mean enthalpy that are calculated by the system code. With this method the mass balance is preserved at every time step of the simulation. The coupling between consecutive CFD domains is not a defective one since with the proposed algorithm we can interpolate the field solutions on the boundary interfaces. We use the MED data structure as the base structure where all the field operations are performed, allowing the algorithm to be used with all the numerical codes where a MED duplicate of the field solution can be created. The MEDmem libraries come with the Salome platform and include basic methods for handling meshes and fields. We provide results that show the consistency of the proposed algorithm.

Numerical inversion of heat exchange coefficient and source sink term for a thermal-fluid coupled model in porous medium

In this paper, we focus on three inverse problems for a coupled model from temperature-seepage field in high-dimensional spaces. These inverse problems aim to determine an unknown heat transfer coefficient and a source sink term in seepage continuity equation with specified initial-boundary conditions and additional measurements. Some finite difference schemes of coupled equations are presented and analyzed.Three algorithms for these inverse problems are proposed. Some numerical experiments are provided to assert the accuracy and efficiency of proposed algorithms.

High-order scheme for the source-sink term in a one-dimensional water temperature model.

The source-sink term in water temperature models represents the net heat absorbed or released by a water system. This term is very important because it accounts for solar radiation that can significantly affect water temperature, especially in lakes. However, existing numerical methods for discretizing the source-sink term are very simplistic, causing significant deviations between simulation results and measured data. To address this problem, we present a numerical method specific to the source-sink term. A vertical one-dimensional heat conduction equation was chosen to describe water temperature changes. A two-step operator-splitting method was adopted as the numerical solution. In the first step, using the undetermined coefficient method, a high-order scheme was adopted for discretizing the source-sink term. In the second step, the diffusion term was discretized using the Crank-Nicolson scheme. The effectiveness and capability of the numerical method was assessed by performing numerical tests. Then, the proposed numerical method was applied to a simulation of Guozheng Lake (located in central China). The modeling results were in an excellent agreement with measured data.

An Inverse Method to Estimate the Root Water Uptake Source-Sink Term in Soil Water Transport Equation under the Effect of Superabsorbent Polymer.

The widespread use of superabsorbent polymers (SAPs) in arid regions improves the efficiency of local land and water use. However, SAPs’ repeated absorption and release of water has periodic and unstable effects on both soil’s physical and chemical properties and on the growth of plant roots, which complicates modeling of water movement in SAP-treated soils. In this paper, we proposea model of soil water movement for SAP-treated soils. The residence time of SAP in the soil and the duration of the experiment were considered as the same parameter t. This simplifies previously proposed models in which the residence time of SAP in the soil and the experiment’s duration were considered as two independent parameters. Numerical testing was carried out on the inverse method of estimating the source/sink term of root water uptake in the model of soil water movement under the effect of SAP. The test results show that time interval, hydraulic parameters, test error, and instrument precision had a significant influence on the stability of the inverse method, while time step, layering of soil, and boundary conditions had relatively smaller effects. A comprehensive analysis of the method’s stability, calculation, and accuracy suggests that the proposed inverse method applies if the following conditions are satisfied: the time interval is between 5 d and 17 d; the time step is between 1000 and 10000; the test error is ≥ 0.9; the instrument precision is ≤ 0.03; and the rate of soil surface evaporation is ≤ 0.6 mm/d.

A soil diffusion–reaction model for surface COS flux: COSSM v1

Abstract. Soil exchange of carbonyl sulfide (COS) is the second largest COS flux in terrestrial ecosystems. A novel application of COS is the separation of gross primary productivity (GPP) from concomitant respiration. This method requires that soil COS exchange is relatively small and can be well quantified. Existing models for soil COS flux have incorporated empirical temperature and moisture functions derived from laboratory experiments but not explicitly resolved diffusion in the soil column. We developed a mechanistic diffusion–reaction model for soil COS exchange that accounts for COS uptake and production, relates source–sink terms to environmental variables, and has an option to enable surface litter layers. We evaluated the model with field data from a wheat field (Southern Great Plains (SGP), OK, USA) and an oak woodland (Stunt Ranch Reserve, CA, USA). The model was able to reproduce all observed features of soil COS exchange such as diurnal variations and sink–source transitions. We found that soil COS uptake is strongly diffusion controlled and limited by low COS concentrations in the soil if there is COS uptake in the litter layer. The model provides novel insights into the balance between soil COS uptake and production: a higher COS production capacity was required despite lower COS emissions during the growing season compared to the post-senescence period at SGP, and unchanged COS uptake capacity despite the dominant role of COS emissions after senescence. Once there is a database of soil COS parameters for key biomes, we expect the model will also be useful to simulate soil COS exchange at regional to global scales.

An Eulerian Vlasov code for plasma-wall interactions

In this work we present a new Eulerian kinetic 1D3V code devoted to the study of plasma-wall interactions and sheath structure. The code solves the Vlasov-Poisson system for two or more kinetic species on a one-dimensional spatial grid between two limiting plates, in the presence of a uniform magnetic field tilted with respect to the normal to the plates. A source-sink term in the Vlasov equation leads to a stationary solution comprising a magnetic and a collisional presheath, as well as the usual Debye sheath in front of the wall. Thanks to a nonuniform spatial grid the sheath structure can be resolved accurately. Several advection schemes are implemented and the code is parallelized. Here, the code is used to illustrate the problems of a stationary sheath-presheath structure in front of a negatively biased wall, with and without a tilted magnetic field.

Rare Earth Element Distributions and Trends in Natural Waters with a Focus on Groundwater

Systematically varying properties and reactivities have led to focused research of the environmental forensic capabilities of rare earth elements (REE). Increasing anthropogenic inputs to natural systems may permanently alter the natural signatures of REE, motivating characterization of natural REE variability. We compiled and analyzed reported dissolved REE concentration data over a wide range of natural water types (ground-, ocean, river, and lake water) and groundwater chemistries (e.g., fresh, brine, and acidic) with the goal of quantifying the extent of natural REE variability, especially for groundwater systems. Quantitative challenges presented by censored data were addressed with nonparametric distributions and regressions. Reported measurements of REE in natural waters range over nearly 10 orders of magnitude, though the majority of measurements are within 2-4 orders of magnitude, and are highly correlated with one another. Few global correlations exist among dissolved abundance and bulk solution properties in groundwater, indicating the complex nature of source-sink terms and the need for care when comparing results between studies. This collection, homogenization, and analysis of a disparate literature facilitates interstudy comparison and provides insight into the wide range of variables that influence REE geochemistry.

Modeling of oxygen permeation through a LSCF ion transport membrane

The oxyfuel combustion characteristics have been investigated numerically for stagnation flow conditions inside a membrane reactor. The effect of combustion in the permeate side on the oxygen permeation through a La0.6Sr0.4Co0.2Fe0.8O3−δ (LSCF-6428) ionic ceramic membrane is presented. The membrane reactor has a simple symmetric design allowing the reduction of the number of coordinates to 2D without reducing the accuracy of the calculations. The results of the present model were validated through comparison with the available literature data. The membrane separates oxygen from oxygen containing stream (typically air). The oxygen transports to a downstream permeate side containing methane, with CO2 as an inert carrier gas. The membrane area is 8cm×8cm and both streams are at 800°C. The numerical simulations were performed using CFD software FLUENT 6.3 with the aid of Gambit 2.2 to construct the mesh. A source sink term has been added to the conservation equations through a series of user defined functions compiled and incorporated to fluent in order to account for the transfer of oxygen across the membrane surface. The simulations were carried out over a wide range of mass fluxes of feed side and permeate side considering the n-type flux equation transport mechanisms and oxidation reaction kinetics (real finite rate combustion of hydrocarbon versus no reaction or cold combustion). It was found that the oxygen permeation flux increases as the permeate side flux increases as a result of reduced partial pressure of O2. Also, it was found that the combustion in the permeate side has a great effect on the oxygen permeation flux. This is due to the increase in the temperature in the permeate side due to combustion which enhances oxygen diffusion and the reduction in the oxygen partial pressure in the permeation side due to the consumption of oxygen in the combustion process. In addition, increasing the partial pressure of oxygen in the air side has a great effect on oxygen permeation flux and overall combustion process. The membrane temperature in all simulations was found to be very close to the inlet flow temperature which should be controlled within the operating temperature of the membrane.

CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. III. MULTIGROUP RADIATION HYDRODYNAMICS

We present a formulation for multigroup radiation hydrodynamics that is correct to order $O(v/c)$ using the comoving-frame approach and the flux-limited diffusion approximation. We describe a numerical algorithm for solving the system, implemented in the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically-rectangular variable-sized grids with simultaneous refinement in both space and time. In our multigroup radiation solver, the system is split into three parts, one part that couples the radiation and fluid in a hyperbolic subsystem, another part that advects the radiation in frequency space, and a parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem and the frequency space advection are solved explicitly with high-order Godunov schemes, whereas the parabolic part is solved implicitly with a first-order backward Euler method. Our multigroup radiation solver works for both neutrino and photon radiation.

Integrated numerical model for vegetated surface and saturated subsurface flow interaction

The construction of an integrated numerical model is presented in this paper to deal with the interactions between vegetated surface and saturated subsurface flows. A numerical model is built by integrating the previously developed quasi-three-dimensional (Q3D) vegetated surface flow model with a two-dimensional (2D) saturated groundwater flow model. The vegetated surface flow model is constructed by coupling the explicit finite volume solution of 2D shallow water equations (SWEs) with the implicit finite difference solution of Navier-Stokes equations (NSEs) for vertical velocity distribution. The subsurface model is based on the explicit finite volume solution of 2D saturated groundwater flow equations (SGFEs). The ground and vegetated surface water interaction is achieved by introducing source-sink terms into the continuity equations. Two solutions are tightly coupled in a single code. The integrated model is applied to four test cases, and the results are satisfactory.

CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. II. GRAY RADIATION HYDRODYNAMICS

We describe the development of a flux-limited gray radiation solver for the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically-rectangular variable-sized grids with simultaneous refinement in both space and time. The gray radiation solver is based on a mixed-frame formulation of radiation hydrodynamics. In our approach, the system is split into two parts, one part that couples the radiation and fluid in a hyperbolic subsystem, and another parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem is solved explicitly with a high-order Godunov scheme, whereas the parabolic part is solved implicitly with a first-order backward Euler method.

Study on Release and Pollution of Waste Pollutants under the Condition of Rainfall

To study the release law of waste pollutant comprehensively and systematically, and analyze transporting law ofpollutant and predict its distribution scientifically, the main pollutants of waste leachate were studies, includingthe release mechanism of COD, Cl-, SO42-, and total hardness, etc. by the dynamic dissolution experiment,according to the practical rainfall of Fuxin city. The results showed that Cl- and COD have the most fast andslow transporting speed. The simulation was carried out by combining the COD decreasing curve fittingequations, which was considered as source sink term, and the established underground water dissolutiontransporting mathematical model. The result showed that, in the center of landfill, the simulated curve is accordwith the COD experiment curve, and the result faithfully reflects the transporting law of pollutants. The modelcan provide the theoretical basis for the prediction of pollution of underground water by waste pollutant and itsprevention and control.