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. .

Zoning Evaluation of Hourly Precipitation in High-resolution Regional Numerical Models over Hainan Island

This study assesses the performance of three high-resolution regional numerical models in predicting hourly rainfall over Hainan Island from April to October for the years from 2020 to 2022.The rainfall amount,frequency,intensity,duration,and diurnal cycle are examined through zoning evaluation.The results show that the China Meteor-ological Administration Guangdong Rapid Update Assimilation Numerical Forecast System(CMA-GD)tends to forecast a higher occurrence of light precipitation.It underestimates the late afternoon precipitation and the occurrence of short-duration events.The China Meteorological Administration Shanghai Numerical Forecast Model System(CMA-SH9)reproduces excessive precipitation at a higher frequency and intensity throughout the island.It overestimates rainfall during the late afternoon and midnight periods.The simulated most frequent peak times of rainfall in CMA-SH9 are 0-1 hour deviations from the observed data.The China Meteorological Administration Mesoscale Weather Numerical Forecasting System(CMA-MESO)displays a similar pattern to rainfall observations but fails to replicate reasonable structure and diurnal variation of frequency-intensity.It underestimates the occurrence of long-duration events and overestimates related rainfall amounts from midnight to early morning.Notably,significant discrepancies are observed in the predictions of the three models for areas with complex terrain,such as the central,southeastern,and southwestern regions of Hainan Island.

Numerical Models of Higher-Order Boussinesq Equations and Comparisons with Laboratory Measurement

Nonlinear water wave propagation passing a submerged shelf is studied experimentally and numerically. The applicability of two different wave propagation models has been investigated. One is higher-order Boussinesq equations derived by Zou (1999) and the other is the classic Boussinesq equations, Physical experiments are conducted, three different front slopes (1:10, 1:5 and 1:2) of the shelf are set up in the experiment and their effects on wave propagation are investigated. Comparisons of numerical results with test data are made, the model of higher-order Boussinesq equations agrees much better with the measurements than the model of the classical Boussinesq equations, The results show that the higher-order Boussinesq equations can also be applied to the steeper slope case although the mild slope assumption is employed in the derivation of the higher order terms of higher order Boussinesq equations.

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.

Numerical models of earthquake mechanism

The tectonic creep and its variation after particular earthquakes are studied by the Stokes equation.The stress state of the region is modelled according to a hypothesis of plate tectonics in which the lithosphere of the region is laterally compressed across the Eurasian,Indian,and Arabian plates.The 1966 Tashkent(Uzbekistan)earthquake and the 1976 Gazli(Uzbekistan)earthquake are selected as examples to study different models of earthquake focal mechanisms.Based on the specifics of the geodynamic formulation,the three-dimensional equations of moment elasticity and hydromechanics are reduced to twodimensional equations for averaged stresses,displacements,and displacement velocities.The twodimensional equations are solved by boundary integral equations.The stresses can be useful in zoning maps.The vertical velocities obtained from the creep model of the earth’s crust can serve as additional data to Central Asia’s horizontal velocities from GPS measurements.

Assessment of Numerical Models for Live Load Distribution in a Road Slab Bridge

This paper presents comparison of numerical models used in an analysis of a road bridge deck. The models were adapted for computing the live load distribution coefficients in composite concrete bridge deck. The load distribution method was chosen for assessment of the usability of different numerical model in slab bridge deck analysis. The goal of the study is to determine a simplest but still accurate numerical model to estimate live load effects on composite slab bridge. In the analysis, the well-established grillage approach was adapted for representation of the bridge deck as a basic model as well as more sophisticated three-dimensional models which was supposed to better represent the real behavior of the deck under concentrated wheel loads. The bridge deck was effectively modeled using beam and shell elements. The grillage method compares well with the finite-element method. This finding is allowed to establish simplification in numerical modeling of slab bridge decks for live load effect computations.

Design of Roof Cover Structures by Help of Numerical Models Defined in Formian

Numerical models defined by means of a suitably assumed set of parameters make it possible to select the optimal structural solution for the given or assumed conditions. The paper presents examples of applications of numerical models defined in the programming language Formian during the shaping processes of various types of spatial structural systems designed for roof covers. These types of numerical models can be relatively easily adapted to the requirements, which can be frequently changed during the investment process, what makes possible a considerable reducing of costs and time of design of the space structures having even the very complex shapes. The advantageous features of application of numerical models defined in Formian are presented in models determined for selected forms of the roof covers designed also by means of a simple type of a space frame. In the paper, there are some presented visualizations made on bases of these models defining mainly for structural systems developed recently by the author for certain types of the dome covers. The proposed structural systems are built by means of the successive spatial hoops or they are created as unique forms of the geodesic dome structures.

Numerical simulation of microwave-induced cracking and melting of granite based on mineral microscopic models

This study introduces a coupled electromagnetic–thermal–mechanical model to reveal the mechanisms of microcracking and mineral melting of polymineralic rocks under microwave radiation.Experimental tests validate the rationality of the proposed model.Embedding microscopic mineral sections into the granite model for simulation shows that uneven temperature gradients create distinct molten,porous,and nonmolten zones on the fracture surface.Moreover,the varying thermal expansion coefficients and Young's moduli among the minerals induce significant thermal stress at the mineral boundaries.Quartz and biotite with higher thermal expansion coefficients are subjected to compression,whereas plagioclase with smaller coefficients experiences tensile stress.In the molten zone,quartz undergoes transgranular cracking due to theα–βphase transition.The local high temperatures also induce melting phase transitions in biotite and feldspar.This numerical study provides new insights into the distribution of thermal stress and mineral phase changes in rocks under microwave irradiation.

Numerical analysis of high‑speed railway slab tracks using calibrated and validated 3D time‑domain modelling

Concrete slabs are widely used in modern railways to increase the inherent resilient quality of the tracks,provide safe and smooth rides,and reduce the maintenance frequency.In this paper,the elastic performance of a novel slab trackform for high-speed railways is investigated using three-dimensional finite element modelling in Abaqus.It is then compared to the performance of a ballasted track.First,slab and ballasted track models are developed to replicate the full-scale testing of track sections.Once the models are calibrated with the experimental results,the novel slab model is developed and compared against the calibrated slab track results.The slab and ballasted track models are then extended to create linear dynamic models,considering the track geodynamics,and simulating train passages at various speeds,for which the Ledsgard documented case was used to validate the models.Trains travelling at low and high speeds are analysed to investigate the track deflections and the wave propagation in the soil,considering the issues associated with critical speeds.Various train loading methods are discussed,and the most practical approach is retained and described.Moreover,correlations are made between the geotechnical parameters of modern high-speed rail and conventional standards.It is found that considering the same ground condition,the slab track deflections are considerably smaller than those of the ballasted track at high speeds,while they show similar behaviour at low speeds.

A methodology for damage evaluation of underground tunnels subjected to static loading using numerical modeling

We have proposed a methodology to assess the robustness of underground tunnels against potential failure.This involves developing vulnerability functions for various qualities of rock mass and static loading intensities.To account for these variations,we utilized a Monte Carlo Simulation(MCS)technique coupled with the finite difference code FLAC^(3D),to conduct two thousand seven hundred numerical simulations of a horseshoe tunnel located within a rock mass with different geological strength index system(GSIs)and subjected to different states of static loading.To quantify the severity of damage within the rock mass,we selected one stress-based(brittle shear ratio(BSR))and one strain-based failure criterion(plastic damage index(PDI)).Based on these criteria,we then developed fragility curves.Additionally,we used mathematical approximation techniques to produce vulnerability functions that relate the probabilities of various damage states to loading intensities for different quality classes of blocky rock mass.The results indicated that the fragility curves we obtained could accurately depict the evolution of the inner and outer shell damage around the tunnel.Therefore,we have provided engineers with a tool that can predict levels of damages associated with different failure mechanisms based on variations in rock mass quality and in situ stress state.Our method is a numerically developed,multi-variate approach that can aid engineers in making informed decisions about the robustness of underground tunnels.

Numerical analysis of geosynthetic-reinforced embankment performance under moving loads

The performance of geosynthetic-reinforced embankments under traffic moving loads is always a hotspot in the geotechnical engineering field.A three-dimensional(3D)model of a geosynthetic-reinforced embankment without drainage consolidation was established using the finite element software ABAQUS.In this model,the traffic loads were simulated by two moving loads of rectangular pattern,and their amplitude,range,and moving speed were realized by a Fortran subroutine.The embankment fill was simulated by an equivalent linear viscoelastic model,which can reflect its viscoelasticity.The geogrid was simulated by the truss element,and the geocell was simulated by the membrane element.Infinite elements were utilized to weaken the boundary effect caused by the model geometry at the boundaries.Validation of the established numerical model was conducted by comparing the predicted deformations in the cross-section of the geosynthetic-reinforced embankment with those from the existing literature.On this basis,the dynamic stress and strain distribution in the pavement structure layer of the geosynthetic-reinforced embankment under a moving load was also analyzed.Finally,a parametric study was conducted to examine the influences of the different types of reinforcement,overload,and the moving load velocity on the geosynthetic-reinforced embankment.

Progressive fragmentation of granular assemblies within rockslides: Insights from discrete-continuous numerical modeling

Rock fragmentation plays a critical role in rock avalanches,yet conventional approaches such as classical granular flow models or the bonded particle model have limitations in accurately characterizing the progressive disintegration and kinematics of multi-deformable rock blocks during rockslides.The present study proposes a discrete-continuous numerical model,based on a cohesive zone model,to explicitly incorporate the progressive fragmentation and intricate interparticle interactions inherent in rockslides.Breakable rock granular assemblies are released along an inclined plane and flow onto a horizontal plane.The numerical scenarios are established to incorporate variations in slope angle,initial height,friction coefficient,and particle number.The evolutions of fragmentation,kinematic,runout and depositional characteristics are quantitatively analyzed and compared with experimental and field data.A positive linear relationship between the equivalent friction coefficient and the apparent friction coefficient is identified.In general,the granular mass predominantly exhibits characteristics of a dense granular flow,with the Savage number exhibiting a decreasing trend as the volume of mass increases.The process of particle breakage gradually occurs in a bottom-up manner,leading to a significant increase in the angular velocities of the rock blocks with increasing depth.The simulation results reproduce the field observations of inverse grading and source stratigraphy preservation in the deposit.We propose a disintegration index that incorporates factors such as drop height,rock mass volume,and rock strength.Our findings demonstrate a consistent linear relationship between this index and the fragmentation degree in all tested scenarios.

Experimental and numerical investigation on alternatives to sandy gravel

The NATO agreement STANAG 4569 defines the protection levels for the occupants of logistic and light armored vehicle.The Allied Engineering Publication,AEP-55,Volume 2 document outlines the test conditions for underbelly improvised explosive device(IEDs),which must be buried in water-saturated sandy gravel.The use of sandy gravel has some drawbacks,for instance reproducibility,time consumption,and cost.This paper focuses on the investigation of four alternatives to sandy gravel,which could produce similar specific and cumulative impulses:a concrete pot filled with water,a concrete pot filled with quartz sand,a steel pot without filling and a concrete pot filled with glass spheres(diameter 200μm—300μm)and different water contents.The impulses are measured with a ring technology developed at the Fraunhofer EMI.A numerical soil model based on the work of Marrs,2014 and Fi serov a,2006 and considering the soil moisture was used to simulate the experiments with glass spheres at different water contents,showing much better agreement with the experiments than the classical Laine&Sandvik model,even for high saturation levels.These results can be used to create new test conditions at original scale that are more cost-effective,more reproducible and simpler to manage in comparison to the current tests carried out with STANAG sandy gravel.

Understanding the spatial interaction of ultrasounds based on three-dimensional dual-frequency ultrasonic field numerical simulation

A transient 3D model was established to investigate the effect of spatial interaction of ultrasounds on the dual-frequency ultrasonic field in magnesium alloy melt.The effects of insertion depth and tip shape of the ultrasonic rods,input pressures and their ratio on the acoustic field distribution were discussed in detail.Additionally,the spacing,angle,and insertion depth of two ultrasonic rods significantly affect the interaction between distinct ultrasounds.As a result,various acoustic pressure distributions and cavitation regions are obtained.The spherical rods mitigate the longitudinal and transversal attenuation of acoustic pressure and expand the cavitation volume by 53.7%and 31.7%,respectively,compared to the plate and conical rods.Increasing the input pressure will enlarge the cavitation region but has no effect on the acoustic pressure distribution pattern.The acoustic pressure ratio significantly affects the pressure distribution and the cavitation region,and the best cavitation effect is obtained at the ratio of 2:1(P15:P20).

Numerical analysis on seismic performance of underground structures in liquefiable interlayer sites from centrifuge shaking table test

When an underground structure passes through a liquefiable soil layer,the soil liquefaction may pose a significant threat to the structure.A centrifuge shaking table test was performed to research the seismic response of underground structures in liquefiable interlayer sites,and a valid numerical model was obtained through simulation model test.Finally,the calibrated numerical model was used to perform further research on the influence of various distribution characteristics of liquefiable interlayers on the seismic reaction of underground structures.The key findings are as follows.The structure faces the most unfavorable condition once a liquefiable layer is located in the middle of the underground structure.When a liquefiable layer exists in the middle of the structure,the seismic reactions of both the underground structure and model site will increase with the rise of the thickness of the liquefiable interlayer.The inter-story drift of the structure in the non-liquefiable site is much smaller than that in the liquefiable interlayer site.The inter-story drift of the structure is not only associated with the site displacement and the soil-structure stiffness ratio but also closely associated with the slippage of the soil-structure contact interface under the condition of large deformation of the site.

A typhoon-induced storm surge numerical model with GPU acceleration based on an unstructured spherical centroidal Voronoi tessellation grid

Storm surge is often the marine disaster that poses the greatest threat to life and property in coastal areas.Accurate and timely issuance of storm surge warnings to take appropriate countermeasures is an important means to reduce storm surge-related losses.Storm surge numerical models are important for storm surge forecasting.To further improve the performance of the storm surge forecast models,we developed a numerical storm surge forecast model based on an unstructured spherical centroidal Voronoi tessellation(SCVT)grid.The model is based on shallow water equations in vector-invariant form,and is discretized by Arakawa C grid.The SCVT grid can not only better describe the coastline information but also avoid rigid transitions,and it has a better global consistency by generating high-resolution grids in the key areas through transition refinement.In addition,the simulation speed of the model is accelerated by using the openACC-based GPU acceleration technology to meet the timeliness requirements of operational ensemble forecast.It only takes 37 s to simulate a day in the coastal waters of China.The newly developed storm surge model was applied to simulate typhoon-induced storm surges in the coastal waters of China.The hindcast experiments on the selected representative typhoon-induced storm surge processes indicate that the model can reasonably simulate the distribution characteristics of storm surges.The simulated maximum storm surges and their occurrence times are consistent with the observed data at the representative tide gauge stations,and the mean absolute errors are 3.5 cm and 0.6 h respectively,showing high accuracy and application prospects.

Numerical Simulation of Thermocapillary Convection with Evaporation Induced by Boundary Heating

The dynamics of a bilayer system filling a rectangular cuvette subjected to external heating is studied.The influence of two types of thermal exposure on the flow pattern and on the dynamic contact angle is analyzed.In particular,the cases of local heating from below and distributed thermal load from the lateral walls are considered.The simulation is carried out within the frame of a two-sided evaporative convection model based on the Boussinesq approximation.A benzine–air system is considered as reference system.The variation in time of the contact angle is described for both heating modes.Under lateral heating,near-wall boundary layers emerge together with strong convection,whereas the local thermal load from the lower wall results in the formation of multicellular motion in the entire volume of the fluids and the appearance of transition regimes followed by a steady-state mode.The results of the present study can aid the design of equipment for thermal coating or drying and the development of methods for the formation of patterns with required structure and morphology.

Numerical investigation of hydro-morphodynamic characteristics of a cascading failure of landslide dams

A cascading failure of landslide dams caused by strong earthquakes or torrential rains in mountainous river valleys can pose great threats to people’s lives,properties,and infrastructures.In this study,based on the three-dimensional Reynoldsaveraged Navier-Stokes equations(RANS),the renormalization group(RNG)k-εturbulence model,suspended and bed load transport equations,and the instability discriminant formula of dam breach side slope,and the explicit finite volume method(FVM),a detailed numerical simulation model for calculating the hydro-morphodynamic characteristics of cascading dam breach process has been developed.The developed numerical model can simulate the breach hydrograph and the dam breach morphology evolution during the cascading failure process of landslide dams.A model test of the breaches of two cascading landslide dams has been used as the validation case.The comparison of the calculated and measured results indicates that the breach hydrograph and the breach morphology evolution process of the upstream and downstream dams are generally consistent with each other,and the relative errors of the key breaching parameters,i.e.,the peak breach flow and the time to peak of each dam,are less than±5%.Further,the comparison of the breach hydrographs of the upstream and downstream dams shows that there is an amplification effect of the breach flood on the cascading landslide dam failures.Three key parameters,i.e.,the distance between the upstream and the downstream dams,the river channel slope,and the downstream dam height,have been used to study the flood amplification effect.The parameter sensitivity analyses show that the peak breach flow at the downstream dam decreases with increasing distance between the upstream and the downstream dams,and the downstream dam height.Further,the peak breach flow at the downstream dam first increases and then decreases with steepening of the river channel slope.When the flood caused by the upstream dam failure flows to the downstream dam,it can produce a surge wave that overtops and erodes the dam crest,resulting in a lowering of the dam crest elevation.This has an impact on the failure occurrence time and the peak breach flow of the downstream dam.The influence of the surge wave on the downstream dam failure process is related to the volume of water that overtops the dam crest and the erosion characteristics of dam material.Moreover,the cascading failure case of the Xiaogangjian and Lower Xiaogangjian landslide dams has also been used as the representative case for validating the model.In comparisons of the calculated and measured breach hydrographs and final breach morphologies,the relative errors of the key dam breaching parameters are all within±10%,which verify the rationality of the model is applicable to real-world cases.Overall,the numerical model developed in this study can provide important technical support for the risk assessment and emergency treatment of failures of cascading landslide dams.

Numerical simulation of formation mechanism of unloading joints in granitic pluton

The Beishan pluton in Gansu of China was selected as the simulated model.The simulation results indicate that the formation of unloading joints in granite is mainly influenced by the unloading rate of confin-ing pressure.Among the rates tested,the slowest unloading rate 0.025 MPa/s is found to be most conducive to the development of unloading joints.Therefore,a slower unloading rate is favourable for the occurrence of unloading joints.A series of simulations with varying initial depths of uplift ranging from 900 m to 200 m were conducted.The results confirm that when the specimen rises to a depth of 550-500 m,the unloading joints begin to form.The uplift from a depth of 700-500 m,with variations in both vertical and lateral un-loading rates,was simulated.The generation of unloading joints exhibits a negative correlation with vertical unloading and no correlation with lateral unloading,indicating that the unloading joints are mainly controlled by the unloading of vertical pressure.Throughout the simulation process,the vertical joints exhibit irregular and unrealistic regularity,suggesting a more complex formation mechanism than that of the unloading joints.

Numerical Modelling of Coupled Heat and Mass Transfer in Porous Materials: Application to Cinder Block Bricks

In this work, we present numerical modelling of coupled heat and mass transfer within porous materials. Our study focuses on cinder block bricks generally used in building construction. The material is assumed to be placed in air. Moisture content and temperature have been chosen as the main transfer drivers and the equations governing these transfer drivers are based on the Luikov model. These equations are solved by an implicit finite difference scheme. A Fortran code associated with the Thomas algorithm was used to solve the equations. The results show that heat and mass transfer depend on the temperature of the air in contact with the material. As this air temperature rises, the temperature within the material increases, and more rapidly at the material surface. Also, thermal conductivity plays a very important role in the thermal conduction of building materials and influences heat and mass transfer in these materials. Materials with higher thermal conductivity diffuse more heat.