A combined method using Lattice Boltzmann Method(LBM)and Finite Volume Method(FVM)to simulate geothermal reservoirs in Enhanced Geothermal System(EGS)

With the development of industrial activities,global warming has accelerated due to excessive emission of CO_(2).Enhanced Geothermal System(EGS)utilizes deep geothermal heat for power generation.Although porous medium theory is commonly employed to model geothermal reservoirs in EGS,Hot Dry Rock(HDR)presents a challenge as it consists of impermeable granite with zero porosity,potentially distorting the physical interpretation.To address this,the Lattice Boltzmann Method(LBM)is employed to simulate CO_(2)flow within geothermal reservoirs and the Finite Volume Method(FVM)to solve the energy conservation equation for temperature distribution.This combined method of LBM and FVM is imple-mented using MATLAB.The results showed that the Reynolds numbers(Re)of 3,000 and 8,000 lead to higher heat extraction rates from geothermal reservoirs.However,higher Re values may accelerate thermal breakthrough,posing challenges to EGS operation.Meanwhile,non-equilibrium of density in fractures becomes more pronounced during the system's life cycle,with non-Darcy's law becoming significant at Re values of 3,000 and 8,000.Density stratification due to buoyancy effects significantly impacts temperature distribution within geothermal reservoirs,with buoyancy effects at Re=100 under gravitational influence being noteworthy.Larger Re values(3,000 and 8,000)induce stronger forced convection,leading to more uniform density distribution.The addition of proppant negatively affects heat transfer performance in geothermal reservoirs,especially in single fractures.Practical engineering considerations should determine the quantity of proppant through detailed numerical simulations.

Numerical Solution of the Rotating Shallow Water Flows with Topography Using the Fractional Steps Method

The two-dimensional nonlinear shallow water equations in the presence of Coriolis force and bottom topography are solved numerically using the fractional steps method. The fractional steps method consists of splitting the multi-dimensional matrix inversion problem into an equivalent one dimensional problem which is successively integrated in every direction along the characteristics using the Riemann invariant associated with the cubic spline interpolation. The height and the velocity field of the shallow water equations over irregular bottom are discretized on a fixed Eulerian grid and time-stepped using the fractional steps method. Effects of the Coriolis force and the bottom topography for particular initial flows on the velocity components and the free surface elevation have been studied and the results are plotted.

Efficient Preparation and Electrochemical Properties of BiOCl/Graphite by One-step Solvothermal Method

We used the surface-pretreated graphite paper(Gp)as a carrier and loaded BiOCl with high selectivity to Cl^(-)on its surface by solvothermal method to form BiOCl@Gp electrode.The morphology,structure,and composition of the materials were characterized by scanning electron microscopy and nitrogen adsorption/desorption,and the results showed that the spherical BiOCl particles were uniformly dispersed on the surface of the Gp,forming a mesoporous BiOCl@Gp composite with a specific surface area of 22.82 m^(2)/g and a pore volume of 0.043 cm3/g.Furthermore,cyclic voltammetry and electrochemical impedance spectroscopy were used to test the electrochemical properties of the composites,and the stability of BiOCl and the high conductivity of Gp were synergistic,the BiOCl@Gp exhibited a specific capacitance of 30.2 F·g^(-1) at a current density of 0.5 A·g^(-1),and the selectivity of the BiOCl@Gp materials for Cl^(-)was significantly higher than that of SO_(4)^(2-),NO_(2)^(-),and HCO_(3)^(-).Therefore,BiOCl@Gp composite electrode materials can be used for the selective adsorption of Cl^(-)in wastewater,in order to achieve efficient wastewater recycling.

Chebyshev polynomial-based Ritz method for thermal buckling and free vibration behaviors of metal foam beams

This study presents the Chebyshev polynomials-based Ritz method to examine the thermal buckling and free vibration characteristics of metal foam beams.The analyses include three models for porosity distribution and two scenarios for thermal distribution.The material properties are assessed under two conditions,i.e.,temperature dependence and temperature independence.The theoretical framework for the beams is based on the higher-order shear deformation theory,which incorporates shear deformations with higher-order polynomials.The governing equations are established from the Lagrange equations,and the beam displacement fields are approximated by the Chebyshev polynomials.Numerical simulations are performed to evaluate the effects of thermal load,slenderness,boundary condition(BC),and porosity distribution on the buckling and vibration behaviors of metal foam beams.The findings highlight the significant influence of temperature-dependent(TD)material properties on metal foam beams'buckling and vibration responses.

Preparation of α-High Strength Gypsum from Flue Gas Desulfurization Gypsum Pretreated by Hydrothermal-aging Method

The synthesis of α-calcium sulfate hemihydrate (α-CSH) from flue gas desulfurization (FGD)gypsum is a good way to realize the comprehensive utilization of FGD gypsum. To obtainα-CSH with the satisfactory performances, a facile hydrothermal-aging pretreatment process for FGD gypsum raw materials was proposed, where FGD gypsum was firstly hydrothermally converted to α-CSH whiskers, and α-CSH whiskers were further hydrated to synthesize CaSO4·2H2O (CSD) by aging under the regulation of N,N'-methylenebisacrylamide (MBA). The effects of aging time, MBA addition, aging temperature, and pH on the morphology of the synthesized CSD were investigated. The synthesized CSD crystals exhibit highly uniform prismatic morphology with the length of ca 100μm and the whiteness of 91.56%. The regulation mechanism of MBA was also illustrated. The synthesized CSD crystals with prismatic morphology were further used as raw materials to synthesize the short columnar α-CSH. The absolute dry compressive strength of paste prepared from the short columnar α-CSH is 40.85 MPa, which reaches α40 strength grade.

A Study of EM Algorithm as an Imputation Method: A Model-Based Simulation Study with Application to a Synthetic Compositional Data

Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.

Application of the “Three Threes” Method in Clinical Teaching of Internal Jugular Vein Puncture

Objective: To clarify the role of the “Three Threes” method in clinical teaching of internal jugular vein puncture and explore improvements in teaching methods. Methods: A doctor was assigned to the induction room of the Second Affiliated Hospital of Naval Medical University (Shanghai Changzheng Hospital) for two months. The time required for catheterization, the first puncture success rate, and occurrence of puncture-related complications were compared before and after learning the “Three Threes” method. Results: Using the “Three Threes” method reduced the catheterization time by 43%, increased the first puncture success rate by 17%, and led to fewer puncture-related complications. Conclusion: The application of the “Three Threes” method not only improves the success rate of internal jugular vein puncture but also reduces complications, making it easier for students to master the technique.

Drilling-based measuring method for the c-φ parameter of rock and its field application

The technology of drilling tests makes it possible to obtain the strength parameter of rock accurately in situ. In this paper, a new rock cutting analysis model that considers the influence of the rock crushing zone(RCZ) is built. The formula for an ultimate cutting force is established based on the limit equilibrium principle. The relationship between digital drilling parameters(DDP) and the c-φ parameter(DDP-cφ formula, where c refers to the cohesion and φ refers to the internal friction angle) is derived, and the response of drilling parameters and cutting ratio to the strength parameters is analyzed. The drillingbased measuring method for the c-φ parameter of rock is constructed. The laboratory verification test is then completed, and the difference in results between the drilling test and the compression test is less than 6%. On this basis, in-situ rock drilling tests in a traffic tunnel and a coal mine roadway are carried out, and the strength parameters of the surrounding rock are effectively tested. The average difference ratio of the results is less than 11%, which verifies the effectiveness of the proposed method for obtaining the strength parameters based on digital drilling. This study provides methodological support for field testing of rock strength parameters.

Implementation of a particle-in-cell method for the energy solver in 3D spherical geodynamic modeling

The thermal evolution of the Earth’s interior and its dynamic effects are the focus of Earth sciences.However,the commonly adopted grid-based temperature solver is usually prone to numerical oscillations,especially in the presence of sharp thermal gradients,such as when modeling subducting slabs and rising plumes.This phenomenon prohibits the correct representation of thermal evolution and may cause incorrect implications of geodynamic processes.After examining several approaches for removing these numerical oscillations,we show that the Lagrangian method provides an ideal way to solve this problem.In this study,we propose a particle-in-cell method as a strategy for improving the solution to the energy equation and demonstrate its effectiveness in both one-dimensional and three-dimensional thermal problems,as well as in a global spherical simulation with data assimilation.We have implemented this method in the open-source finite-element code CitcomS,which features a spherical coordinate system,distributed memory parallel computing,and data assimilation algorithms.

A Hierarchical Method for Locating the Interferometric Fringes of Celestial Sources in the Visibility Data

In source detection in the Tianlai project,locating the interferometric fringe in visibility data accurately will influence downstream tasks drastically,such as physical parameter estimation and weak source exploration.Considering that traditional locating methods are time-consuming and supervised methods require a great quantity of expensive labeled data,in this paper,we first investigate characteristics of interferometric fringes in the simulation and real scenario separately,and integrate an almost parameter-free unsupervised clustering method and seeding filling or eraser algorithm to propose a hierarchical plug and play method to improve location accuracy.Then,we apply our method to locate single and multiple sources’interferometric fringes in simulation data.Next,we apply our method to real data taken from the Tianlai radio telescope array.Finally,we compare with unsupervised methods that are state of the art.These results show that our method has robustness in different scenarios and can improve location measurement accuracy effectively.

Numerical Investigations on the Resonance Errors of Multiscale Discontinuous Galerkin Methods for One-Dimensional Stationary Schrödinger Equation

In this paper,numerical experiments are carried out to investigate the impact of penalty parameters in the numerical traces on the resonance errors of high-order multiscale discontinuous Galerkin(DG)methods(Dong et al.in J Sci Comput 66:321–345,2016;Dong and Wang in J Comput Appl Math 380:1–11,2020)for a one-dimensional stationary Schrödinger equation.Previous work showed that penalty parameters were required to be positive in error analysis,but the methods with zero penalty parameters worked fine in numerical simulations on coarse meshes.In this work,by performing extensive numerical experiments,we discover that zero penalty parameters lead to resonance errors in the multiscale DG methods,and taking positive penalty parameters can effectively reduce resonance errors and make the matrix in the global linear system have better condition numbers.

The Cumulative Method for Multiplication and Division

This paper provides a method of the process of computation called the cumulative method, it is based upon repeated cumulative process. The cumulative method is being adapted to the purposes of computation, particularly multiplication and division. The operations of multiplication and division are represented by algebraic formulas. An advantage of the method is that the cumulative process can be performed on decimal numbers. The present paper aims to establish a basic and useful formula valid for the two fundamental arithmetic operations of multiplication and division. The new cumulative method proved to be more flexible and made it possible to extend the multiplication and division based on repeated addition/subtraction to decimal numbers.

Efficient method to calculate the eigenvalues of the Zakharov–Shabat system

A numerical method is proposed to calculate the eigenvalues of the Zakharov–Shabat system based on Chebyshev polynomials. A mapping in the form of tanh(ax) is constructed according to the asymptotic of the potential function for the Zakharov–Shabat eigenvalue problem. The mapping can distribute Chebyshev nodes very well considering the gradient for the potential function. Using Chebyshev polynomials, tanh(ax) mapping, and Chebyshev nodes, the Zakharov–Shabat eigenvalue problem is transformed into a matrix eigenvalue problem. This method has good convergence for the Satsuma–Yajima potential and the convergence rate is faster than the Fourier collocation method. This method is not only suitable for simple potential functions but also converges quickly for a complex Y-shape potential. It can also be further extended to other linear eigenvalue problems.

On the spreading behavior of a droplet on a circular cylinder using the lattice Boltzmann method

The study of a droplet spreading on a circular cylinder under gravity was carried out using the pseudo-potential lattice Boltzmann high-density ratios multiphase model with a non-ideal Peng–Robinson equation of state. The calculation results indicate that the motion of the droplet on the cylinder can be divided into three stages: spreading, sliding, and aggregating.The contact length and contact time of a droplet on a cylindrical surface can be affected by factors such as the wettability gradient of the cylindrical wall, the Bond number, and droplet size. Furthermore, phase diagrams showing the relationship between Bond number, cylinder wall wettability gradient, and contact time as well as maximum contact length for three different droplet sizes are given. A theoretical foundation for additional research into the heat and mass transfer process between the droplet and the cylinder can be established by comprehending the variable rules of maximum contact length and contact time.

Application of the finite analytic numerical method to a flowdependent variational data assimilation

An anisotropic diffusion filter can be used to model a flow-dependent background error covariance matrix,which can be achieved by solving the advection-diffusion equation.Because of the directionality of the advection term,the discrete method needs to be chosen very carefully.The finite analytic method is an alternative scheme to solve the advection-diffusion equation.As a combination of analytical and numerical methods,it not only has high calculation accuracy but also holds the characteristic of the auto upwind.To demonstrate its ability,the one-dimensional steady and unsteady advection-diffusion equation numerical examples are respectively solved by the finite analytic method.The more widely used upwind difference method is used as a control approach.The result indicates that the finite analytic method has higher accuracy than the upwind difference method.For the two-dimensional case,the finite analytic method still has a better performance.In the three-dimensional variational assimilation experiment,the finite analytic method can effectively improve analysis field accuracy,and its effect is significantly better than the upwind difference and the central difference method.Moreover,it is still a more effective solution method in the strong flow region where the advective-diffusion filter performs most prominently.

Stability and Time-Step Constraints of Implicit-Explicit Runge-Kutta Methods for the Linearized Korteweg-de Vries Equation

This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.

Simplified quantitative analysis method and its application in the insitu synthesized copper-based azide chips

Copper-based azide(Cu(N_(3))2 or CuN_(3),CA)chips synthesized by in-situ azide reaction and utilized in miniaturized explosive systems has become a hot research topic in recent years.However,the advantages of in-situ synthesis method,including small size and low dosage,bring about difficulties in quantitative analysis and differences in ignition capabilities of CA chips.The aim of present work is to develop a simplified quantitative analysis method for accurate and safe analysis of components in CA chips to evaluate and investigate the corresponding ignition ability.In this work,Cu(N_(3))2 and CuN_(3)components in CA chips were separated through dissolution and distillation by utilizing the difference in solubility and corresponding content was obtained by measuring N_(3)-concentration through spectrophotometry.The spectrophotometry method was optimized by studying influencing factors and the recovery rate of different separation methods was studied,ensuring the accuracy and reproducibility of test results.The optimized method is linear in range from 1.0-25.0 mg/L,with a correlation coefficient R^(2)=0.9998,which meets the requirements of CA chips with a milligram-level content test.Compared with the existing ICP method,component analysis results of CA chips obtained by spectrophotometry are closer to real component content in samples and have satisfactory accuracy.Moreover,as its application in miniaturized explosive systems,the ignition ability of CA chips with different component contents for direct ink writing CL-20 and the corresponding mechanism was studied.This study provided a basis and idea for the design and performance evaluation of CA chips in miniaturized explosive systems.

Numerical Simulation of the Seismic Response of a Horizontal Storage Tank Based on a SPH-FEM Coupling Method

A coupled numerical calculation method combining smooth particle hydrodynamics(SPH)and the finite element method(FEM)was implemented to investigate the seismic response of horizontal storage tanks.Anumericalmodel of a horizontal storage tank featuring a free liquid surface under seismic action was constructed using the SPH–FEM coupling method.The stored liquid was discretized using SPH particles,while the tank and supports were discretized using the FEM.The interaction between the stored liquid and the tank was simulated by using the meshless particle contact method.Then,the numerical simulation results were compared and analyzed against seismic simulation shaking table test data to validate the method.Subsequently,a series of numerical models,considering different liquid storage volumes and seismic effects,were constructed to obtain time history data of base shear and top center displacement,which revealed the seismic performance of horizontal storage tanks.Numerical simulation results and experimental data showed good agreement,with an error rate of less than 18.85%.And this conformity signifies the rationality of the SPH-FEM coupling method.The base shear and top center displacement values obtained by the coupled SPH-FEM method were only 53.3% to 69.1% of those calculated by the equivalent mass method employed in the current code.As the stored liquid volume increased,the seismic response of the horizontal storage tank exhibited a gradual upward trend,with the seismic response increasing from 73% to 388% for every 35% increase in stored liquid volume.The maximum von Mises stress of the tank and the supports remained below the steel yield strength during the earthquake.The coupled SPH-FEM method holds certain advantages in studying the seismic problems of tanks with complex structural forms,particularly due to the representation of the flow field distribution during earthquakes by involving reservoir fluid participation.

A hybrid contact approach for modeling soil-structure interaction using the material point method

The grid-based multi-velocity field technique has become increasingly popular for simulating the Material Point Method(MPM)in contact problems.However,this traditional technique has some shortcomings,such as(1)early contact and contact penetration can occur when the contact conditions are unsuitable,and(2)the method is not available for contact problems involving rigid-nonrigid materials,which can cause numerical instability.This study presents a new hybrid contact approach for the MPM to address these limitations to simulate the soil and structure interactions.The approach combines the advantages of point-point and point-segment contacts to implement contact detection,satisfying the impenetrability condition and smoothing the corner contact problem.The proposed approach is first validated through a disk test on an inclined slope.Then,several typical cases,such as granular collapse,bearing capacity,and deformation of a flexible retaining wall,are simulated to demonstrate the robustness of the proposed approach compared with FEM or analytical solutions.Finally,the proposed method is used to simulate the impact of sand flow on a deformable structure.The results show that the proposed contact approach can well describe the phenomenon of soil-structure interaction problems.

Research on the Generation Mechanism and Suppression Method of Aerodynamic Noise in Expansion Cavity Based on Hybrid Method

The expansion chamber serves as the primary silencing structure within the exhaust pipeline.However,it can also act as a sound-emitting structure when subjected to airflow.This article presents a hybrid method for numerically simulating and analyzing the unsteady flow and aerodynamic noise in an expansion chamber under the influence of airflow.A fluid simulation model is established,utilizing the Large Eddy Simulation(LES)method to calculate the unsteady flow within the expansion chamber.The simulation results effectively capture the development and changes of the unsteady flow and vorticity inside the cavity,exhibiting a high level of consistency with experimental observations.To calculate the aerodynamic noise sources within the cavity,the flow field results are integrated using the method of integral interpolation and inserted into the acoustic grid.The acoustic analogy method is then employed to determine the aerodynamic noise sources.An acoustic simulation model is established,and the flow noise source is imported into the sound field grid to calculate the sound pressure at the far-field response point.The calculated sound pressure levels and resonance frequencies show good agreement with the experimental results.To address the issue of airflow regeneration noise within the cavity,perforated tubes are selected as a means of noise suppression.An experimental platformfor airflow regeneration noise is constructed,and experimental samples are processed to analyze and verify the noise suppression effect of perforated tube expansion cavities under different airflow velocities.The research findings indicate that the perforated tube expansion cavity can effectively suppress low-frequency aerodynamic noise within the cavity by impeding the formation of strong shear layers.Moreover,the semi-perforated tube expansion cavity demonstrates the most effective suppression of aerodynamic noise.