Numerical Models and Methods of Atmospheric Parameters Originating in the Formation of the Earth’s Climatic Cycle

Atmospheric models are physical equations based on the ideal gas law. Applied to the atmosphere, this law yields equations for water, vapor (gas), ice, air, humidity, dryness, fire, and heat, thus defining the model of key atmospheric parameters. The distribution of these parameters across the entire planet Earth is the origin of the formation of the climatic cycle, which is a normal climatic variation. To do this, the Earth is divided into eight (8) parts according to the number of key parameters to be defined in a physical representation of the model. Following this distribution, numerical models calculate the constants for the formation of water, vapor, ice, dryness, thermal energy (fire), heat, air, and humidity. These models vary in complexity depending on the indirect trigonometric direction and simplicity in the sum of neighboring models. Note that the constants obtained from the equations yield 275.156˚K (2.006˚C) for water, 273.1596˚K (0.00963˚C) for vapor, 273.1633˚K (0.0133˚C) for ice, 0.00365 in/s for atmospheric dryness, 1.996 in2/s for humidity, 2.993 in2/s for air, 1 J for thermal energy of fire, and 0.9963 J for heat. In summary, this study aims to define the main parameters and natural phenomena contributing to the modification of planetary climate. .

3D random Voronoi grain-based models for simulation of brittle rock damage and fabric-guided micro-fracturing

A grain-based distinct element model featuring three-dimensional （3D） Voronoi tessellations （randompoly-crystals） is proposed for simulation of crack damage development in brittle rocks. The grainboundaries in poly-crystal structure produced by Voronoi tessellations can represent flaws in intact rockand allow for numerical replication of crack damage progression through initiation and propagation ofmicro-fractures along grain boundaries. The Voronoi modelling scheme has been used widely in the pastfor brittle fracture simulation of rock materials. However the difficulty of generating 3D Voronoi modelshas limited its application to two-dimensional （2D） codes. The proposed approach is implemented inNeper, an open-source engine for generation of 3D Voronoi grains, to generate block geometry files thatcan be read directly into 3DEC. A series of Unconfined Compressive Strength （UCS） tests are simulated in3DEC to verify the proposed methodology for 3D simulation of brittle fractures and to investigate therelationship between each micro-parameter and the model＇s macro-response. The possibility of numericalreplication of the classical U-shape strength curve for anisotropic rocks is also investigated innumerical UCS tests by using complex-shaped （elongated） grains that are cemented to one another alongtheir adjoining sides. A micro-parameter calibration procedure is established for 3D Voronoi models foraccurate replication of the mechanical behaviour of isotropic and anisotropic （containing a fabric） rocks. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Numerical study on residual current and its impact on mass transport in the Hangzhou Bay and the Changjiang Estuary I. A3-D joint model of the Hangzhou Bay and the Changjiang Estuary

A 3-D numerical model is set up in a large domain covering the Hangzhou Bay and the Changjiang Estuary based on the ECOM model in orthogonal curvilinear coordinates.The numerical schemes for baroclinic pressure gradient (BPG)terms and convective terms are improved in the paper according to the characteristics of velocity field and mass transport in the area.The model is validated by the simulations of residual current and salinity transport in the Hangzhou Bay and the Changjiang Estuary.

Benchmarking of two three-dimensional numerical models in time/space domain to predict railway-induced ground vibrations

In the last 30 years,the scientific community has developed and proposed different models and numerical approaches for the study of vibrations induced by railway traffic.Most of them are formulated in the frequency/wave number domain and with a 2.5D approach.Three-dimensional numerical models formulated in the time/space domain are less frequently used,mainly due to their high computational cost.Notwithstanding,these models present very attractive characteristics,such as the possibility of considering nonlinear behaviors or the modelling of excess pore pressure and non-homogeneous and non-periodic geometries in the longitudinal direction of the track.In this study,two 3D numerical approaches formulated in the time/space domain are compared and experimentally validated.The first one consists of a finite element approach and the second one of a finite difference approach.The experimental validation in an actual case situated in Carregado(Portugal)shows an acceptable fitting between the numerical results and the actual measurements for both models.However,there are some differences among them.This study therefore includes some recommendations for their use in practical soil dynamics and geotechnical engineering.

Quasi-3D Numerical Simulation of Tidal Hydrodynamic Field

Based on the 2D horizontal plane numerical model, a quasi-3D numerical model is established for coastal regions of shallow water. The characteristics of this model are that the velocity profiles;can be obtained at the same time when the equations of the value of difference between the horizontal current velocity and its depth-averaged velocity in the vertical direction are solved and the results obtained are consistent with the results of the 2D, model. The circulating flow in the rectangular area induced by wind is simulated and applied to the tidal flow field of the radial sandbanks in the South Yellow Sea. The computational results from this quasi-3D model are in good agreement with analytical results and observed data. The solution of the finite difference equations has been found to be stable, and the model is simple, effective and practical.

Real-time 3-D space numerical shake prediction for earthquake early warning

In earthquake early warning systems, real-time shake prediction through wave propagation simulation is a promising approach. Compared with traditional methods, it does not suffer from the inaccurate estimation of source parameters. For computation efficiency, wave direction is assumed to propagate on the 2-D surface of the earth in these methods. In fact, since the seismic wave propagates in the 3-D sphere of the earth, the 2-D space modeling of wave direction results in inaccurate wave estimation. In this paper, we propose a 3-D space numerical shake pre- diction method, which simulates the wave propagation in 3-D space using radiative transfer theory, and incorporate data assimilation technique to estimate the distribution of wave energy. 2011 Tohoku earthquake is studied as an example to show the validity of the proposed model. 2-D space model and 3-D space model are compared in this article, and the prediction results show that numerical shake prediction based on 3-D space model can estimate the real-time ground motion precisely, and overprediction is alleviated when using 3-D space model.

A three-dimensional numerical study on the effect of geometric asymmetry on arcjet thruster performance

In an arcjet thruster,the cathode and constrictor degrade with time,and the electrical arc discharge may become unsymmetrical.In this work,a three-dimensional numerical model of a hydrogen plasma arcjet is developed and validated to study the effect of unsymmetrical electric arc discharge on thruster performance.The unsymmetrical arc discharge is realized by introducing a radial shift of the cathode so that the cathode tip offset is 80μm(25%of the constrictor radius).Simulations are conducted for both axially centered cathode(coaxial)and off-centered cathode(non-coaxial)configurations with identical propellant flow rates and input current.Simulations show asymmetrical arc discharge in the non-coaxial cathode configuration,resulting in azimuthally asymmetric Joule heating,species concentrations,and velocity field.This asymmetry continues as the plasma expands in the divergent section of the nozzle.Temperature,species concentrations,and axial velocity exhibit asymmetric radial distribution at the nozzle exit.The computed Joule heating was found to reduce with cathode shift,and consequently,the thrust and specific impulse of the thruster was decreased by about 6.6%.In the case of the non-coaxial cathode,geometric asymmetry also induces a small side thrust.

Meshing effects of the 3-D FEM numerical modeling in seismo-electromagnetics:An application in selectivity of seismic electric signal (SES)

We investigated how density and quality of mesh around interest domain affect electromagnetic （EM） responses of 3D Earth layered media using finite element method （FEM）. Effect of different mesh shapes was also investigated using a method of mixing structured and unstructured mesh. As a case study, we estimated the effects of meshing on selectivity phenomenon of seismic electric signal （SES）. Our results suggest that the relative errors resulting from mesh effects may not be negligible, which may lead to some unconvincing explanation of the SES selectivity based on the numerical modeling results.

Temperature Distributions in Single Cell of Polymer Electrolyte Fuel Cell Simulated by an 1D Multi-plate Heat-Transfer Model and a 3D Numerical Simulation Model

The purpose of this study is to verify an 1D multi-plate heat-transfer model estimating the temperature distribution on the interface between polymer electrolyte membrane and catalyst layer at cathode in single cell of polymer electrolyte fuel cell, which is named as reaction surface in this study, with a 3D numerical simulation model solving many governing equations on the coupling phenomena in the cell. The results from both models/simulations agreed well. The effects of initial operation temperature, flow rate, and relative humidity of supply gas on temperature distribution on the reaction surface were also investigated. It was found in both 1D and 3D simulations that, the temperature rise （i.e., Treact-Tini） of the reaction surface from initial operation temperature at 70℃ was higher than that at 80℃ irrespective of flow rate of supply gas. The effect of relative humidity of supply gas on Treact- Tini near the inlet of the cell was small. Compared to the previous studies conducted under the similar operation conditions, the Treact - Tini calculated by 1D multi-plate heat-transfer model in this study as well as numerical simulation using 3D model was reasonable.

Runout prediction of potential landslides based on the multi-source data collaboration analysis on historical cases

Long runout landslides involve a massive amount of energy and can be extremely hazardous owing to their long movement distance,high mobility and strong destructive power.Numerical methods have been widely used to predict the landslide runout but a fundamental problem remained is how to determine the reliable numerical parameters.This study proposes a framework to predict the runout of potential landslides through multi-source data collaboration and numerical analysis of historical landslide events.Specifically,for the historical landslide cases,the landslide-induced seismic signal,geophysical surveys,and possible in-situ drone/phone videos(multi-source data collaboration)can validate the numerical results in terms of landslide dynamics and deposit features and help calibrate the numerical(rheological)parameters.Subsequently,the calibrated numerical parameters can be used to numerically predict the runout of potential landslides in the region with a similar geological setting to the recorded events.Application of the runout prediction approach to the 2020 Jiashanying landslide in Guizhou,China gives reasonable results in comparison to the field observations.The numerical parameters are determined from the multi-source data collaboration analysis of a historical case in the region(2019 Shuicheng landslide).The proposed framework for landslide runout prediction can be of great utility for landslide risk assessment and disaster reduction in mountainous regions worldwide.

Numerical Si mulation of Transportation of SPMfrom the Yellow River to the Bohai Sea

A 3D diagnostic model including a suspended sediment transport module, ECOMSED, driven by the monthly discharge and sediment load of the Yellow River in 1983 ～ 1984, was applied to the Bohai Sea. The simulation of the temporal-spatial variation of SPM （Suspended Particular Matter） concentration, sediment flux, and deposition rate was carfled out. It could be seen that, the SPM concentration exhibited distinct seasonal variation, and the variation characteristic was similar for two years. Some of the fine sediment of the Yellow River extended to the western bank of the Liaodong Bay, but most of the sediment deposited around the estuary of the Yellow River, the deposition flux rapidly decreasing with the increasing distance to the estuary. The deposition rate kept at 0.05 ～ 0.1 mm/a for most area, close to the insitu data. There were two areas of high SPM concentration in the Bohai Sea, one of which could be attributed to the Yellow River discharge, and another one, located at the seas with intensive resuspension power, to the tidal current energy. The sediment from the Yellow River was transported mainly along the track of the, Lagrangian residual cireulations. In one word, the suspended load transport was basically attributed to the wind-driven and tidal-induced Lagrangian residual circulations. The resuspenslon flux was related to the bottom currents： the larger the current speed, the more the sediment resuspended.

Approach of moving boundary and its application in 3D tidal current simulation of Changjiang (Yangtze) River Estuary based on ECOMSED model

Considering three-dimensional model ECOMSED can not simulate wetting-drying of shoal with its fixed boundary, an approach to represent moving boundary in the model is introduced here. This approach smoothly joints the internal and external mode by making use of wetting and drying technique and is verified by a numerical test which presents a good agreement with the previous test results obtained by other researchers. A three dimensional numerical model is established to simulate the hydrodynamics in spring tide in the Changjiang （Yangtze） River estuary by this modified ECOMSED model which is also validated through the observed field data, the simulation presents a good periodic tidal change. It also successfully simulates the tidal current of computational areas and reproduces the tidal flat intermittent appearance.

Numerical verification of similar Cam-clay model based on generalized potential theory

From the mathematical principles, the generalized potential theory can be employed to create constitutive model of geomaterial directly. The similar Cam-clay model, which is created based on the generalized potential theory, has less assumptions,clearer mathematical basis, and better computational accuracy. Theoretically, it is more scientific than the traditional Cam-clay models. The particle flow code PFC3 D was used to make numerical tests to verify the rationality and practicality of the similar Cam-clay model. The verification process was as follows: 1) creating the soil sample for numerical test in PFC3 D, and then simulating the conventional triaxial compression test, isotropic compression test, and isotropic unloading test by PFC3D; 2)determining the parameters of the similar Cam-clay model from the results of above tests; 3) predicting the sample's behavior in triaxial tests under different stress paths by the similar Cam-clay model, and comparing the predicting results with predictions by the Cam-clay model and the modified Cam-clay model. The analysis results show that the similar Cam-clay model has relatively high prediction accuracy, as well as good practical value.

Simulation of subcritical flow pattern in 180° uniform and convergent open-channel bends using SSIIM 3-D model

In meandering rivers, the flow pattern is highly complex, with specific characteristics at bends that are not observed along straight paths. A numerical model can be effectively used to predict such flow fields. Since river bends are not uniform-some are divergent and others convergent-in this study, after the SSIIM 3-D model was calibrated using the result of measurements along a uniform 180° bend with a width of 0.6 m, a similar but convergent 180v bend, 0.6 m to 0.45 m wide, was simulated using the SSI1M 3-D numerical model. Flow characteristics of the convergent 180° bend, including lengthwise and vertical velocity profiles, primary and secondary flows, lengthwise and widtbwise slopes of the water surface, and the helical flow strength, were compared with those of the uniform 180° bend. The verification results of the model show that the numerical model can effectively simulate the flow field in the uniform bend. In addition, this research indicates that, in a convergent channel, the maximum velocity path at a plane near the water surface crosses the channel＇s centerline at about a 30° to 40° cross-section, while in the uniform bend, this occurs at about the 50° cross-section. The varying range of the water surface elevation is wider in the convergent channel than in the uniform one, and the strength of the helical flow is generally greater in the uniform channel than in the convergent one. Also, unlike the uniform bend, the convergent bend exhibits no rotational cell against the main direction of secondary flow rotation at the 135° cross-section.

A Higher-Efficient Three-Dimensional Numerical Model for Small Amplitude Free Surface Flows

A higher-efficient three-dimensional non-hydrostatic model is developed to simulate small amplitude free surface flows based on a staggered unstructured grid. In this model, a fractional step algorithm is adopted to solve the Navier-Stokes equations in two major steps. A top-layer pressure method is proposed to minimize the number of vertical layers and subsequently the computational cost. Three classical examples of small amplitude free surface flows are used to demonstrate the capability and efficiency of the model. The satisfactory results demonstrated the capability and efficiency of modelling a range of small amplitude free surface flows with only a small number of vertical layers.

Numerical Study on Instantaneous Discharge of Unsorted Particle Cloud in Cross Flow

The mixing characteristics of particles such as dredged sediment of variable size discharged into cross flow are studied by a 3D numerical modal, which is developed to model the particle-fluid two-phase flow. The Eulerian method with the modified k- ε parameterization of turbulence for the fluid phase is used to solve fluid phase, while a Lagrangian method for the sohd phase （particles）, both the processes are coupled through the momentmn sources. In the model the wake turbulence induced by particles has been included as additional source term in the k - ε model; and the variable drift velocities of the particles are treated efficiently by the Lagrangian method in which the particles are tracked explicitly and the diffusion process is approximated by a random walk model. The hydrodynamic behavior of dumping a cloud of particles is governed by the total buoyancy of the cloud, the drag force on each particle and the velocity of cross-flow. The computed results show a roughly linear relationship between the displacement of the frontal position and the longitudi- nal width of the particle cloud. The particle size in the cloud and the velocity of cross flow dominate the flow behavior. The computed results are compared with the results of laboratory experiments and satisfactory agreement is obtained.

Influence of complex topography on magnetotelluric-observed data using threedimensional numerical simulation:A case from Guangxi area,China

Fully recognize various problems in the observed magnetotelluric(MT)data is the precondition of inverse solutions.In the paper,according to the geomorphological conditions of the observational MT stations in the Guangxi area,we constructed several different kinds of models to conduct a three-dimensional forward simulation of the MT fi eld using the vector fi nite element method(FEM).First,the variation rule and differences of apparent resistivityρxy andρyx in the xy and yx modes were studied and analyzed,and then the geoelectric information refl ected by the change of apparent resistivityρxx andρyy were discussed.Final,the responses of typical geological structures that cause a static shift problem were presented.The synthetic examples showed thatρxy andρyx were relevant to the layout of the survey line,for instance,ρxy had different values along the west-east profi le compared with that of the southnorth profi le,Moreover,ρxx andρyy could subtly show the abnormal body-host rock interface,which could be used to restrict the anomalous domain in the inversion process.In addition to the scale and depth of the top surface of the anomalous body,the widespread rivers and hills,can simulate static shift.Hence,to reduce the infl uence of static shift on MT data,a reasonable distance between a station and rivers or hills should be considered in accordance with the scale of rivers or hills.

Modeling and simulation of solvent behavior and temperature distribution within long stick propellants with large web thickness undergoing drying

Drying is a complicated physical process which involves simultaneous heat and mass transfer in the removal of solvents inside propellants.Inappropriate drying techniques may result in the formation of a hard skin layer near the surface to block the free access of most solvent through for long stick propellants with large web thickness,which lead to lower drying efficiency and worse drying quality.This study aims to gain a comprehensive understanding of drying process and clarify the mechanism of the blocked layer near the propellant surface.A new three-dimensional coupled heat and mass transfer(3D-CHMT)model was successfully developed under transient conditions.The drying experiment results show that the 3DCHMT model could be applied to describe the drying process well since the relative error of the content of solvent between simulation and experiment values is only 5.5%.The solvent behavior simulation demonstrates that the mass transfer process can be divided into super-fast(SF)and subsequent minorfast(MF)stages,and the SF stage is vital to the prevention of the blocked layer against the free access for solvent molecules inside propellant grains.The effective solvent diffusion coefficient(Deff)of the propellant surface initially increases from 3.4×10^(-6)to 5.3×10^(-6)m^(2)/s as the temperature increases,and then decreases to 4.1×10^(-8)m^(2)/s at 60-100 min.The value of Deffof surface between 0-1.4 mm has a unique trend of change compared with other regions,and it is much lower than that of the internal at100 min under simulation conditions.Meanwhile,the temperature of the propellant surface increases rapidly at the SF stage(0-100 min)and then very slowly thereafter.Both the evolution of Deffand temperature distribution demonstrate that the blocked layer near the propellant surface has been formed in the time period of approximately 0-100 min and its thickness is about 1.4 mm.To mitigate the formation of blocked layer and improve its drying quality of finial propellant products effectively,it should be initially dried at lower drying temperature(30-40℃)in 0-100 min and then dried at higher drying temperature(50-60℃)to reduce drying time for later drying process in double base gun propellants.The present results can provide theoretical guidance for drying process and optimization of drying parameters for long stick propellants with large web thickness.

A model study of influence of circulation on the pollutant transport in the Zhujiang River Estuary and adjacent coastal waters

A tracer model with random diffusion coupled to the hydrodynamic model for the Zhujiang River Estuary (Pearl River Estuary, PRE) is to examine the effect of circulations on the transport of completely conservative pollutants. It is focused on answering the following questions: (1) What role does the estuarine plume front in the winter play in affecting the pollutants transport and its distribution in the PRE ? (2) What effect do the coastal currents driven by the monsoon have on the pollutants transport? The tracer experiment results show that: (1) the pollutant transport paths strongly depend on the circulation structures and plume frontal dynamics of the PRE and coastal waters; (2) during the summer when a southwesterly monsoon prevails, the pollutants from the four easterly river inlets and those from the bottom layer of offshore stations will greatly influence the water quality in Hong Kong waters, however, the pollutants released from the four westerly river-inlets will seldom affect the water qual

Contrasted continental rifting via plume-craton interaction： Applications to Central East African Rift

The East African Rift system （EARS） provides a unique system with the juxtaposition of two contrasting yet simultaneously formed rift branches, the eastern, magma-rich, and the western, magma-poor, on either sides of the old thick Tanzanian craton embedded in a younger lithosphere. Data on the pre-rifr, syn-rift and post-rift far-field volcanic and tectonic activity show that the EARS formed in the context of the interaction between a deep mantle plume and a horizontally and vertically heterogeneous lithosphere under far-field tectonic extension. We bring quantitative insights into this evolution by implementing high-resolution 3D thermo-mechanical numerical deformation models of a lithosphere of realistic rheology. The models focus on the central part of the EARS. We explore scenarios of plumelithosphere interaction with plumes of various size and initial position rising beneath a tectonically pre-stretched lithosphere. We test the impact of the inherited rheological discontinuities （suture zones） along the craton borders, of the rheological structure, of lithosphere plate thickness variations, and of physical and mechanical contrasts between the craton and the embedding lithosphere. Our experiments indicate that the ascending plume material is deflected by the cratonic keel and preferentially channeled along one of its sides, leading to the formation of a large rift zone along the eastern side of the craton, with significant magmatic activity and substantial melt amount derived from the mantle plume material. We show that the observed asymmetry of the central EARS, with coeval amagmatic （western） and magmatic （eastern） branches, can be explained by the splitting of warm material rising from a broad plume head whose initial position is slightly shifted to the eastern side of the craton. In that case, neither a mechanical weakness of the contact between the craton and the embedding lithosphere nor the presence of second plume are required to produce simulations that match observations. This result reconciles the passive and active rift models and demonstrates the possibility of development of both magmatic and amagmatic rifts in identical geotectonic environments.