Two Monte Carlo-based simulators for imaging-system modeling and projection simulation of flat-panel X-ray source

The advantages of a flat-panel X-ray source(FPXS)make it a promising candidate for imaging applications.Accurate imaging-system modeling and projection simulation are critical for analyzing imaging performance and resolving overlapping projection issues in FPXS.The conventional analytical ray-tracing approach is limited by the number of patterns and is not applicable to FPXS-projection calculations.However,the computation time of Monte Carlo(MC)simulation is independent of the size of the patterned arrays in FPXS.This study proposes two high-efficiency MC projection simulators for FPXS:a graphics processing unit(GPU)-based phase-space sampling MC(gPSMC)simulator and GPU-based fluence sampling MC(gFSMC)simulator.The two simulators comprise three components:imaging-system modeling,photon initialization,and physical-interaction simulations in the phantom.Imaging-system modeling was performed by modeling the FPXS,imaging geometry,and detector.The gPSMC simulator samples the initial photons from the phase space,whereas the gFSMC simulator performs photon initialization from the calculated energy spectrum and fluence map.The entire process of photon interaction with the geometry and arrival at the detector was simulated in parallel using multiple GPU kernels,and projections based on the two simulators were calculated.The accuracies of the two simulators were evaluated by comparing them with the conventional analytical ray-tracing approach and acquired projections,and the efficiencies were evaluated by comparing the computation time.The results of simulated and realistic experiments illustrate the accuracy and efficiency of the proposed gPSMC and gFSMC simulators in the projection calculation of various phantoms.

Facilitated Prediction of Micropollutant Degradation via UV-AOPs in Various Waters by Combining Model Simulation and Portable Measurement

The degradation of micropollutants in water via ultraviolet(UV)-based advanced oxidation processes(AOPs)is strongly dependent on the water matrix.Various reactive radicals(RRs)formed in UV-AOPs have different reaction selectivities toward water matrices and degradation efficiencies for target micropollutants.Hence,process selection and optimization are crucial.This study developed a facilitated prediction method for the photon fluence-based rate constant for micropollutant degradation(K′_(p,MP))in various UV-AOPs by combining model simulation with portable measurement.Portable methods for measuring the scavenging capacities of the principal RRs(RRSCs)involved in UV-AOPs(i.e.,HO^(·),SO_(4)^(·-),and Cl^(·))using a mini-fluidic photoreaction system were proposed.The simulation models consisted of photochemical,quantitative structure–activity relationship,and radical concentration steady-state approximation models.The RRSCs were determined in eight test waters,and a higher RRSC was found to be associated with a more complex water matrix.Then,by taking sulfamethazine,caffeine,and carbamazepine as model micropollutants,the k′_(p,MP) values in various UV-AOPs were predicted and further verified experimentally.A lower k′_(p,MP) was found to be associated with a higher RRSC for a stronger RR competition;for example,k′_(p,MP) values of 130.9 and 332.5 m^(2) einstein^(–1),respectively,were obtained for carbamazepine degradation by UV/H_(2)O_(2) in the raw water(RRSC=9.47×10^(4) s^(-1))and sand-filtered effluent(RRSC=2.87×10^(4) s^(-1))of a drinking water treatment plant.The developed method facilitates process selection and optimization for UV-AOPs,which is essential for increasing the efficiency and cost-effectiveness of water treatment.

Multi-scenario Simulation and Spatial-temporal Analysis of LUCC in China's Coastal Zone Based on Coupled SD-FLUS Model

Increased human activities in China's coastal zone have resulted in the depletion of ecological land resources.Thus,conducting current and future multi-scenario simulation research on land use and land cover change(LUCC)is crucial for guiding the healthy and sustainable development of coastal zones.System dynamic(SD)-future land use simulation(FLUS)model,a coupled simulation model,was developed to analyze land use dynamics in China's coastal zone.This model encompasses five scenarios,namely,SSP1-RCP2.6(A),SSP2-RCP4.5(B),SSP3-RCP4.5(C),SSP4-RCP4.5(D),and SSP5-RCP8.5(E).The SD model simulates land use demand on an annual basis up to the year 2100.Subsequently,the FLUS model determines the spatial distribution of land use for the near term(2035),medium term(2050),and long term(2100).Results reveal a slowing trend in land use changes in China's coastal zone from 2000–2020.Among these changes,the expansion rate of construction land was the highest and exhibited an annual decrease.By 2100,land use predictions exhibit high accuracy,and notable differences are observed in trends across scenarios.In summary,the expansion of production,living,and ecological spaces toward the sea remains prominent.Scenario A emphasizes reduced land resource dependence,benefiting ecological land protection.Scenario B witnesses an intensified expansion of artificial wetlands.Scenario C sees substantial land needs for living and production,while Scenario D shows coastal forest and grassland shrinkage.Lastly,in Scenario E,the conflict between humans and land intensifies.This study presents pertinent recommendations for the future development,utilization,and management of coastal areas in China.The research contributes valuable scientific support for informed,long-term strategic decision making within coastal regions.

Explosion resistance performance of reinforced concrete box girder coated with polyurea:Model test and numerical simulation

To study the anti-explosion protection effect of polyurea coating on reinforced concrete box girder,two segmental girder specimens were made at a scale of 1:3,numbered as G(without polyurea coating)and PCG(with polyurea coating).The failure characteristics and dynamic responses of the specimens were compared through conducting explosion tests.The reliability of the numerical simulation using LS-DYNA software was verified by the test results.The effects of different scaled distances,reinforcement ratios,concrete strengths,coating thicknesses and ranges of polyurea were studied.The results show that the polyurea coating can effectively enhance the anti-explosion performance of the girder.The top plate of middle chamber in specimen G forms an elliptical penetrating hole,while that in specimen PCG only shows a very slight local dent.The peak vertical displacement and residual displacement of PCG decrease by 74.8% and 73.7%,respectively,compared with those of specimen G.For the TNT explosion with small equivalent,the polyurea coating has a more significant protective effect on reducing the size of fracture.With the increase of TNT equivalent,the protective effect of polyurea on reducing girder displacement becomes more significant.The optimal reinforcement ratio,concrete strength,thickness and range of polyurea coating were also drawn.

Complex adaptive system theory,agent-based modeling,and simulation in dominant technology formation

Dominant technology formation is the key for the hightech industry to“cross the chasm”and gain an established foothold in the market(and hence disrupt the regime).Therefore,a stimulus-response model is proposed to investigate the dominant technology by exploring its formation process and mechanism.Specifically,based on complex adaptive system theory and the basic stimulus-response model,we use a combination of agent-based modeling and system dynamics modeling to capture the interactions between dominant technology and the socio-technical landscape.The results indicate the following:(i)The dynamic interaction is“stimulus-reaction-selection”,which promotes the dominant technology’s formation.(ii)The dominant technology’s formation can be described as a dynamic process in which the adaptation intensity of technology standards increases continuously until it becomes the leading technology under the dual action of internal and external mechanisms.(iii)The dominant technology’s formation in the high-tech industry is influenced by learning ability,the number of adopting users and adaptability.Therein,a“critical scale”of learning ability exists to promote the formation of leading technology:a large number of adopting users can promote the dominant technology’s formation by influencing the adaptive response of technology standards to the socio-technical landscape and the choice of technology standards by the socio-technical landscape.There is a minimum threshold and a maximum threshold for the role of adaptability in the dominant technology’s formation.(iv)The socio-technical landscape can promote the leading technology’s shaping in the high-tech industry,and different elements have different effects.This study promotes research on the formation mechanism of dominant technology in the high-tech industry,presents new perspectives and methods for researchers,and provides essential enlightenment for managers to formulate technology strategies.

Mixed D-vine copula-based conditional quantile model for stochastic monthly streamflow simulation

Copula functions have been widely used in stochastic simulation and prediction of streamflow.However,existing models are usually limited to single two-dimensional or three-dimensional copulas with the same bivariate block for all months.To address this limitation,this study developed a mixed D-vine copula-based conditional quantile model that can capture temporal correlations.This model can generate streamflow by selecting different historical streamflow variables as the conditions for different months and by exploiting the conditional quantile functions of streamflows in different months with mixed D-vine copulas.The up-to-down sequential method,which couples the maximum weight approach with the Akaike information criteria and the maximum likelihood approach,was used to determine the structures of multivariate Dvine copulas.The developed model was used in a case study to synthesize the monthly streamflow at the Tangnaihai hydrological station,the inflow control station of the Longyangxia Reservoir in the Yellow River Basin.The results showed that the developed model outperformed the commonly used bivariate copula model in terms of the performance in simulating the seasonality and interannual variability of streamflow.This model provides useful information for water-related natural hazard risk assessment and integrated water resources management and utilization.

Application of Patient Simulators Combined with Internet plus Scenario Simulation Teaching Models on Intravenous Infusion Nursing Education in China

Objective: To explore the effectiveness of applying patient simulators combined with Internet Plus scenario simulation teaching models on intravenous (IV) infusion nursing education, and to provide scientific evidence for the implementation of advanced teaching models in future nursing education. Methods: Enrolled 60 nurses who took the IV infusion therapy training program in our hospital from January 2022 to December 2023 for research. 30 nurses who were trained in traditional teaching models from January to December 2022 were selected as the control group, and 30 nurses who were trained with simulation-based teaching models with methods including simulated patients, internet, online meetings which can be replayed and scenario simulation, etc. from January to December 2023 were selected as the experimental group. Evaluated the learning outcomes based on the Competency Inventory for Nursing Students (CINS), Problem-Solving Inventory (PSI), comprehensive learning ability, scientific research ability, and proficiency in the theoretical knowledge and practical skills of IV infusion therapy. Nursing quality, the incidence of IV infusion therapy complications and nurse satisfaction with different teaching models were also measured. Results: The scientific research ability, PSI scores, CINS scores, and comprehensive learning ability of the experimental group were better than those of the control group (P 0.05), and their assessment results of practical skills, nursing quality of IV infusion therapy during training, and satisfaction with teaching models were all better than those of the control group with statistical significance (P < 0.05). The incidence of IV infusion therapy complications in the experimental group was lower than that in the control group, indicating statistical significance (P < 0.05). Conclusions: Teaching models based on patient simulators combined with Internet Plus scenario simulation enable nursing students to learn more directly and practice at any time and in any place, and can improve their proficiency in IV infusion theoretical knowledge and skills (e.g. PICC catheterization), core competencies, problem-solving ability, comprehensive learning ability, scientific research ability and the ability to deal with complicated cases. Also, it helps provide high-quality nursing education, improve the nursing quality of IV therapy, reduce the incidence of related complications, and ensure the safety of patients with IV therapy.

Multi-Time Scale Operation and Simulation Strategy of the Park Based on Model Predictive Control

Due to the impact of source-load prediction power errors and uncertainties,the actual operation of the park will have a wide range of fluctuations compared with the expected state,resulting in its inability to achieve the expected economy.This paper constructs an operating simulation model of the park power grid operation considering demand response and proposes a multi-time scale operating simulation method that combines day-ahead optimization and model predictive control(MPC).In the day-ahead stage,an operating simulation plan that comprehensively considers the user’s side comfort and operating costs is proposed with a long-term time scale of 15 min.In order to cope with power fluctuations of photovoltaic,wind turbine and conventional load,MPC is used to track and roll correct the day-ahead operating simulation plan in the intra-day stage to meet the actual operating operation status of the park.Finally,the validity and economy of the operating simulation strategy are verified through the analysis of arithmetic examples.

Novel Sum-of-Sinusoids Simulation Channel Modeling for 6G Multiple-Input Multiple-Output Vehicle-to-Everything Communications

In this paper,a statistical cluster-based simulation channel model with a finite number of sinusoids is proposed for depicting the multiple-input multiple-output(MIMO)communications in vehicleto-everything(V2X)environments.In the proposed sum-of-sinusoids(SoS)channel model,the waves that emerge from the transmitter undergo line-of-sight(LoS)and non-line-of-sight(NLoS)propagation to the receiver,which makes the model suitable for describing numerous V2X wireless communication scenarios for sixth-generation(6G).We derive expressions for the real and imaginary parts of the complex channel impulse response(CIR),which characterize the physical propagation characteristics of V2X wireless channels.The statistical properties of the real and imaginary parts of the complex CIRs,i.e.,autocorrelation functions(ACFs),Doppler power spectral densities(PSDs),cross-correlation functions(CCFs),and variances of ACFs and CCFs,are derived and discussed.Simulation results are generated and match those predicted by the underlying theory,demonstrating the accuracy of our derivation and analysis.The proposed framework and underlying theory arise as an efficient tool to investigate the statistical properties of 6G MIMO V2X communication systems.

Full Dynamic Model for Liquid Sloshing Simulation in Cylindrical Tank Shape

This study presents a comprehensive full dynamic model designed for simulating liquid sloshing behavior within cylindrical tank structures. The model employs a discretization approach, representing the liquid as a network of interconnected spring-damper-mass systems. Key aspects include the adaptation of liquid discretization techniques to cylindrical lateral cross-sections and the calculation of stiffness and damping coefficients. External forces, simulating various vehicle maneuvers, are also integrated into the model. The resulting system of equations is solved using Maple Software with the Runge-Kutta-Fehlberg method. This model enables accurate prediction of liquid displacement and pressure forces, offering valuable insights for tank design and fluid dynamics applications. Ongoing refinement aims to broaden its applicability across different liquid types and tank geometries.

Application of Modelica Based Multi- Domain Modeling and Simulation for Gravity-1

In the R&D phase of Gravity-1(YL-1), a multi-domain modeling and simulation technology based on Modelica language was introduced, which was a recent attempt in the practice of modeling and simulation method for launch vehicles in China. It realizes a complex coupling model within a unified model for different domains, so that technologists can work on one model. It ensured the success of YL-1 first launch mission, supports rapid iteration, full validation, and tight design collaboration.

Hybrid-Vlasov simulation of soft X-ray emissions at the Earth’s dayside magnetospheric boundaries

Solar wind charge exchange produces emissions in the soft X-ray energy range which can enable the study of near-Earth space regions such as the magnetopause,the magnetosheath and the polar cusps by remote sensing techniques.The Solar wind Magnetosphere Ionosphere Link Explorer(SMILE)and Lunar Environment heliospheric X-ray Imager(LEXI)missions aim to obtain soft Xray images of near-Earth space thanks to their Soft X-ray Imager(SXI)instruments.While earlier modeling works have already simulated soft X-ray images as might be obtained by SMILE SXI during its mission,the numerical models used so far are all based on the magnetohydrodynamics description of the space plasma.To investigate the possible signatures of ion-kinetic-scale processes in soft Xray images,we use for the first time a global hybrid-Vlasov simulation of the geospace from the Vlasiator model.The simulation is driven by fast and tenuous solar wind conditions and purely southward interplanetary magnetic field.We first produce global X-ray images of the dayside near-Earth space by placing a virtual imaging satellite at two different locations,providing meridional and equatorial views.We then analyze regional features present in the images and show that they correspond to signatures in soft X-ray emissions of mirrormode wave structures in the magnetosheath and flux transfer events(FTEs)at the magnetopause.Our results suggest that,although the time scales associated with the motion of those transient phenomena will likely be significantly smaller than the integration time of the SMILE and LEXI imagers,mirror-mode structures and FTEs can cumulatively produce detectable signatures in the soft X-ray images.For instance,a local increase by 30%in the proton density at the dayside magnetopause resulting from the transit of multiple FTEs leads to a 12%enhancement in the line-of-sight-and time-integrated soft X-ray emissivity originating from this region.Likewise,a proton density increase by 14%in the magnetosheath associated with mirror-mode structures can result in an enhancement in the soft X-ray signal by 4%.These are likely conservative estimates,given that the solar wind conditions used in the Vlasiator run can be expected to generate weaker soft X-ray emissions than the more common denser solar wind.These results will contribute to the preparatory work for the SMILE and LEXI missions by providing the community with quantitative estimates of the effects of small-scale,transient phenomena occurring on the dayside.

Simulating the evolution of focused waves by a two-layer Boussinesq-type model

Accurate simulation of the evolution of freak waves by the wave phase focusing method requires accurate linear and nonlinear properties,especially in deep-water conditions.In this paper,we analyze the ability to simulate deep-water focused waves of a two-layer Boussinesq-type(BT)model,which has been shown to have excellent linear and nonlinear performance.To further improve the numerical accuracy and stability,the internal wavegenerated method is introduced into the two-layer Boussinesq-type model.Firstly,the sensitivity of the numerical results to the grid resolution is analyzed to verify the convergence of the model;secondly,the focused wave propagating in two opposite directions is simulated to prove the symmetry of the numerical results and the feasibility of the internal wave-generated method;thirdly,the limiting focused wave condition is simulated to compare and analyze the wave surface and the horizontal velocity of the profile at the focusing position,which is in good agreement with the measured values.Meanwhile the simulation of focused waves in very deep waters agrees well with the measured values,which further demonstrates the capability of the two-layer BT model in simulating focused waves in deep waters.

Multi-lump Kinetic Parameter Estimation and Simulation of Trickle-bed Reactor for Ultra-deep Hydrodesulfurization of Diesel

A three-lumping Langmuir-Hinshelwood kinetic model was established based on the structures and reactivities of sulfur compounds.This model described the ultra-deep hydrodesulfurization(UDHDS)performance of diesel,reducing sulfur content from 10000μg/g to less than 10μg/g,with experimental and predicted data showing a discrepancy of less than 10%.The diesel UDHDS reaction was simulated by combining the mass transfer,reaction kinetics model,and physical properties of diesel.The results showed how the concentrations of H2S,hydrogen,and sulfur in the gas,liquid,and solid phases varied along the reactor length.Moreover,the study discussed the effects of each process parameter and impurity concentrations(H2S,basic nitrogen and,non-basic nitrogen)on diesel UDHDS.

Physics-based seismic analysis of ancient wood structure:fault-to-structure simulation

Based on the domain reduction method,this study employs an SEM-FEM hybrid workflow which integrates the advantages of the spectral element method(SEM)for flexible and highly efficient simulation of seismic wave propagation in a three-dimensional(3D)regional-scale geophysics model and the finite element method(FEM)for fine simulation of structural response including soil-structure interaction,and performs a physics-based simulation from initial fault rupture on an ancient wood structure.After verification of the hybrid workflow,a large-scale model of an ancient wood structure in the Beijing area,The Tower of Buddhist Incense,is established and its responses under the 1665 Tongxian earthquake and the 1730 Yiheyuan earthquake are simulated.The results from the simulated ground motion and seismic response of the wood structure under the two earthquakes demonstrate that this hybrid workflow can be employed to efficiently provide insight into the relationships between geophysical parameters and the structural response,and is of great significance toward accurate input for seismic simulation of structures under specific site and fault conditions.

Simulation of Start-Up Process of Turbofan Engine Based on Full-State Characteristics of Fan

Difficulties in obtaining component characteristics in the sub-idle state of rotor constrain the simulation capabilities of ground and windmill start-up processes for turbofan engines.This paper proposes a backbone feature method based on conventional characteristics parameters to derive the full-state characteristics of fan.The application of the fan’s full-state characteristics in component-level model of turbofan engine enables zero-speed iterative simulation for ground start-up process and windmill simulation for windmill start-up process,thereby improving the simulation capability of sub-idle state during turbofan engine start-up.

Simulation of Fracture Process of Lightweight Aggregate Concrete Based on Digital Image Processing Technology

The mechanical properties and failure mechanism of lightweight aggregate concrete(LWAC)is a hot topic in the engineering field,and the relationship between its microstructure and macroscopic mechanical properties is also a frontier research topic in the academic field.In this study,the image processing technology is used to establish a micro-structure model of lightweight aggregate concrete.Through the information extraction and processing of the section image of actual light aggregate concrete specimens,the mesostructural model of light aggregate concrete with real aggregate characteristics is established.The numerical simulation of uniaxial tensile test,uniaxial compression test and three-point bending test of lightweight aggregate concrete are carried out using a new finite element method-the base force element method respectively.Firstly,the image processing technology is used to produce beam specimens,uniaxial compression specimens and uniaxial tensile specimens of light aggregate concrete,which can better simulate the aggregate shape and random distribution of real light aggregate concrete.Secondly,the three-point bending test is numerically simulated.Thirdly,the uniaxial compression specimen generated by image processing technology is numerically simulated.Fourth,the uniaxial tensile specimen generated by image processing technology is numerically simulated.The mechanical behavior and damage mode of the specimen during loading were analyzed.The results of numerical simulation are compared and analyzed with those of relevant experiments.The feasibility and correctness of the micromodel established in this study for analyzing the micromechanics of lightweight aggregate concrete materials are verified.Image processing technology has a broad application prospect in the field of concrete mesoscopic damage analysis.

Spatiotemporal evolution and future simulation of land use/land cover in the Turpan-Hami Basin,China

The Turpan-Hami(Tuha)Basin in Xinjiang Uygur Autonomous Region of China,holds significant strategic importance as a key economic artery of the ancient Silk Road and the Belt and Road Initiative,necessitating a holistic understanding of the spatiotemporal evolution of land use/land cover(LULC)to foster sustainable planning that is tailored to the region's unique resource endowments.However,existing LULC classification methods demonstrate inadequate accuracy,hindering effective regional planning.In this study,we established a two-level LULC classification system(8 primary types and 22 secondary types)for the Tuha Basin.By employing Landsat 5/7/8 imagery at 5-a intervals,we developed the LULC dataset of the Tuha Basin from 1990 to 2020,conducted the accuracy assessment and spatiotemporal evolution analysis,and simulated the future LULC under various scenarios via the Markov-Future Land Use Simulation(Markov-FLUS)model.The results revealed that the average overall accuracy values of our LULC dataset were 0.917 and 0.864 for the primary types and secondary types,respectively.Compared with the seven mainstream LULC products(GlobeLand30,Global 30-meter Land Cover with Fine Classification System(GLC_FCS30),Finer Resolution Observation and Monitoring of Global Land Cover PLUS(FROM_GLC PLUS),ESA Global Land Cover(ESA_LC),Esri Land Cover(ESRI_LC),China Multi-Period Land Use Land Cover Change Remote Sensing Monitoring Dataset(CNLUCC),and China Annual Land Cover Dataset(CLCD))in 2020,our LULC data exhibited dramatically elevated overall accuracy and provided more precise delineations for land features,thereby yielding high-quality data backups for land resource analyses within the basin.In 2020,unused land(78.0%of the study area)and grassland(18.6%)were the dominant LULC types of the basin;although cropland and construction land constituted less than 1.0%of the total area,they played a vital role in arid land development and primarily situated within oases that form the urban cores of the cities of Turpan and Hami.Between 1990 and 2020,cropland and construction land exhibited a rapid expansion,and the total area of water body decreased yet resurging after 2015 due to an increase in areas of reservoir and pond.In future scenario simulations,significant increases in areas of construction land and cropland are anticipated under the business-as-usual scenario,whereas the wetland area will decrease,suggesting the need for ecological attention under this development pathway.In contrast,the economic development scenario underscores the fast-paced expansion of construction land,primarily from the conversion of unused land,highlighting the significant developmental potential of unused land with a slowing increase in cropland.Special attention should thus be directed toward ecological and cropland protection during development.This study provides data supports and policy recommendations for the sustainable development goals of Tuha Basin and other similar arid areas.

Multi-scenario Simulation of the Impact of Land Use Change on the Ecosystem Service Value in the Suzhou-Wuxi-Changzhou Metropolitan Area,China

As the most economically developed metropolitan area in China’s Yangtze River Delta,the rapid changing land use patterns of Suzhou-Wuxi-Changzhou(Su-Xi-Chang) metropolitan area have profound impacts on the ecosystem service value(ESV).Based on the patterns of land use change and the ESV change in Su-Xi-Chang metropolitan area from 2000 to 2020,we set up four scenarios:natural development scenario,urban development scenario,arable land protection scenario and ecological protection scenario,and simulated the impact of land use changes on the ESV in these scenarios.The results showed that:1) the area of built-up land in the Su-XiChang metropolitan area increased significantly from 2000 to 2020,and the area of other types of land decreased.Arable land underwent the highest transfer-out area,and was primarily converted into built-up land.The total ESV of Su-Xi-Chang metropolitan area increased initially then declined from 2000–2020,and the value of almost all individual ecosystem services decreased.2) Population density,GDP per area,night lighting intensity,and road network density can negatively impact the ESV.3) The total ESV loss under the natural development and urban development scenarios was high,and the expansion of the built-up land and the drastic shrinkage of the arable land contributed to the ESV decline under both scenarios.The total ESV under arable land protection and ecological protection scenarios increases,and therefore these scenarios are suitable for future land use optimization in Su-Xi-Chang.This study could provide a certain reference for land use planning and allocation,and offer guidance for the rational allocation of land resources.

Bubble size modeling approach for the simulation of bubble columns

The constant bubble size modeling approach(CBSM)and variable bubble size modeling approach(VBSM)are frequently employed in Eulerian–Eulerian simulation of bubble columns.However,the accuracy of CBSM is limited while the computational efficiency of VBSM needs to be improved.This work aims to develop method for bubble size modeling which has high computational efficiency and accuracy in the simulation of bubble columns.The distribution of bubble sizes is represented by a series of discrete points,and the percentage of bubbles with various sizes at gas inlet is determined by the results of computational fluid dynamics(CFD)–population balance model(PBM)simulations,whereas the influence of bubble coalescence and breakup is neglected.The simulated results of a 0.15 m diameter bubble column suggest that the developed method has high computational speed and can achieve similar accuracy as CFD–PBM modeling.Furthermore,the convergence issues caused by solving population balance equations are addressed.