A Well Productivity Model for Multi-Layered Marine and Continental Transitional Reservoirs with Complex Fracture Networks

Using the typical characteristics of multi-layered marine and continental transitional gas reservoirs as a basis,a model is developed to predict the related well production rate.This model relies on the fractal theory of tortuous capillary bundles and can take into account multiple gas flow mechanisms at the micrometer and nanometer scales,as well as the flow characteristics in different types of thin layers(tight sandstone gas,shale gas,and coalbed gas).Moreover,a source-sink function concept and a pressure drop superposition principle are utilized to introduce a coupled flow model in the reservoir.A semi-analytical solution for the production rate is obtained using a matrix iteration method.A specific well is selected for fitting dynamic production data,and the calculation results show that the tight sandstone has the highest gas production per unit thickness compared with the other types of reservoirs.Moreover,desorption and diffusion of coalbed gas and shale gas can significantly contribute to gas production,and the daily production of these two gases decreases rapidly with decreasing reservoir pressure.Interestingly,the gas production from fractures exhibits an approximately U-shaped distribution,indicating the need to optimize the spacing between clusters during hydraulic fracturing to reduce the area of overlapping fracture control.The coal matrix water saturation significantly affects the coalbed gas production,with higher water saturation leading to lower production.

Recognition and Anticipation of Diabetic Foot Ulcer in Type Ⅱ Diabetic Patients using Multi-layered Fuzzy Model

Diabetes mellitus is associated with foot ulcers,which frequently pave the way to lower-extremity amputation.Neuropathy,trauma,deformity,high plantar pressures,and peripheral vascular disease are the most common underlying causes.Around 15%of diabetic patients are affected by diabetic foot ulcer in their lifetime.64 million people are affected by diabetics in India and 40000 amputations are done every year.Foot ulcers are evaluated and classified in a systematic and thorough manner to assist in determining the best course of therapy.This paper proposes a novel model which predicts the threat of diabetic foot ulcer using independent agents for various input values and a combination of fuzzy expert systems.The proposed model uses a classification system to distinguish between each fuzzy framework and its parameters.Based on the severity levels necessary prevention,treatment,and medication are recommended.Combining the results of all the fuzzy frameworks derived from its constituent parameters,a risk-specific medication is recommended.The work also has higher accuracy when compared to other related models.

Multi-layer perceptron-based data-driven multiscale modelling of granular materials with a novel Frobenius norm-based internal variable

One objective of developing machine learning(ML)-based material models is to integrate them with well-established numerical methods to solve boundary value problems(BVPs).In the family of ML models,recurrent neural networks(RNNs)have been extensively applied to capture history-dependent constitutive responses of granular materials,but these multiple-step-based neural networks are neither sufficiently efficient nor aligned with the standard finite element method(FEM).Single-step-based neural networks like the multi-layer perceptron(MLP)are an alternative to bypass the above issues but have to introduce some internal variables to encode complex loading histories.In this work,one novel Frobenius norm-based internal variable,together with the Fourier layer and residual architectureenhanced MLP model,is crafted to replicate the history-dependent constitutive features of representative volume element(RVE)for granular materials.The obtained ML models are then seamlessly embedded into the FEM to solve the BVP of a biaxial compression case and a rigid strip footing case.The obtained solutions are comparable to results from the FEM-DEM multiscale modelling but achieve significantly improved efficiency.The results demonstrate the applicability of the proposed internal variable in enabling MLP to capture highly nonlinear constitutive responses of granular materials.

A flexible ultra-broadband multi-layered absorber working at 2 GHz-40 GHz printed by resistive ink

A flexible extra broadband metamaterial absorber(MMA)stacked with five layers working at 2 GHz–40 GHz is investigated.Each layer is composed of polyvinyl chloride(PVC),polyimide(PI),and a frequency selective surface(FSS),which is printed on PI using conductive ink.To investigate this absorber,both one-dimensional analogous circuit analysis and three-dimensional full-wave simulation based on a physical model are provided.Various crucial electromagnetic properties,such as absorption,effective impedance,complex permittivity and permeability,electric current distribution and magnetic field distribution at resonant peak points,are studied in detail.Analysis shows that the working frequency of this absorber covers entire S,C,X,Ku,K and Ka bands with a minimum thickness of 0.098λ_(max)(λ_(max) is the maximum wavelength in the absorption band),and the fractional bandwidth(FBW)reaches 181.1%.Moreover,the reflection coefficient is less than-10 dB at 1.998 GHz–40.056 GHz at normal incidence,and the absorptivity of the plane wave is greater than 80%when the incident angle is smaller than 50°.Furthermore,the proposed absorber is experimentally validated,and the experimental results show good agreement with the simulation results,which demonstrates the potential applicability of this absorber at 2 GHz–40 GHz.

采用STAMP-24Model的多组织事故分析

安全生产事故往往由多组织交互、多因素耦合造成,事故原因涉及多个组织。为预防和遏制多组织生产安全事故的发生,基于系统理论事故建模与过程模型(Systems-Theory Accident Modeling and Process,STAMP)、24Model,构建一种用于多组织事故分析的方法,并以青岛石油爆炸事故为例进行事故原因分析。结果显示:STAMP-24Model可以分组织,分层次且有效、全面、详细地分析涉及多个组织的事故原因,探究多组织之间的交互关系;对事故进行动态演化分析,可得到各组织不安全动作耦合关系与形成的事故失效链及管控失效路径,进而为预防多组织事故提供思路和参考。

基于改进24Model-ISM-SNA建筑工人不安全行为关联路径研究

建筑施工现场环境复杂,为有效控制不安全行为发生,基于行为安全“2-4”模型对360份具有代表性的建筑安全事故调查报告进行分析,提取出22个不安全行为的主要影响因素。利用灰色关联分析方法(GRA)改进的集成ISM-SNA模型,将不安全行为风险因素划分为表层、过渡层与深层,然后对风险因素进行可视化分析、中心度分析及凝聚子群分析,揭示了各致因因素间的关联关系和传导路径。结果表明,建筑工人不安全行为影响因素可划分成7级3阶的多级递阶结构,安全意识、现场监管、外部环境是建筑工人不安全行为的关键影响因素,同时现场监管和隐患排查到位能有效降低不安全行为的发生。

基于24Model-D-ISM的地铁站火灾疏散影响因素研究

为预防地铁站火灾事故,深入了解地铁站火灾人员疏散影响因素间的内在联系与层次结构,基于第6版“2-4”模型(24Model)分析63起地铁站火灾疏散事故,充分考虑各个因素之间的交互作用,提取19个影响地铁站人员疏散的关键因素,建立地铁站火灾人员疏散影响因素指标体系;采用算子客观赋权法(C-OWA)改进决策试验与评价实验法(DEMATEL),确定地铁站火灾人员疏散的重要影响因素;在此基础上,采用解释结构模型(ISM)分析各个因素间的层次结构及相互作用路径,构建地铁站火灾人员疏散影响因素的多级递阶结构模型。研究结果表明:疏散引导、恐慌从众行为、人员拥挤为地铁站火灾人员疏散的关键影响因素;地铁站火灾人员疏散受表层因素、中间层因素、深层因素共同作用的影响,其中,疏散教育与培训、设施维护与检查、疏散预案等因素是根源影响因素,重视根源影响因素的改善有利于从本质上预防和控制事故的发生。

Optimizing slope safety factor prediction via stacking using sparrow search algorithm for multi-layer machine learning regression models

The safety factor is a crucial quantitative index for evaluating slope stability.However,the traditional calculation methods suffer from unreasonable assumptions,complex soil composition,and inadequate consideration of the influencing factors,leading to large errors in their calculations.Therefore,a stacking ensemble learning model(stacking-SSAOP)based on multi-layer regression algorithm fusion and optimized by the sparrow search algorithm is proposed for predicting the slope safety factor.In this method,the density,cohesion,friction angle,slope angle,slope height,and pore pressure ratio are selected as characteristic parameters from the 210 sets of established slope sample data.Random Forest,Extra Trees,AdaBoost,Bagging,and Support Vector regression are used as the base model(inner loop)to construct the first-level regression algorithm layer,and XGBoost is used as the meta-model(outer loop)to construct the second-level regression algorithm layer and complete the construction of the stacked learning model for improving the model prediction accuracy.The sparrow search algorithm is used to optimize the hyperparameters of the above six regression models and correct the over-and underfitting problems of the single regression model to further improve the prediction accuracy.The mean square error(MSE)of the predicted and true values and the fitting of the data are compared and analyzed.The MSE of the stacking-SSAOP model was found to be smaller than that of the single regression model(MSE=0.03917).Therefore,the former has a higher prediction accuracy and better data fitting.This study innovatively applies the sparrow search algorithm to predict the slope safety factor,showcasing its advantages over traditional methods.Additionally,our proposed stacking-SSAOP model integrates multiple regression algorithms to enhance prediction accuracy.This model not only refines the prediction accuracy of the slope safety factor but also offers a fresh approach to handling the intricate soil composition and other influencing factors,making it a precise and reliable method for slope stability evaluation.This research holds importance for the modernization and digitalization of slope safety assessments.

Optimization Design of the Multi-Layer Cross-Sectional Layout of An Umbilical Based on the GA-GLM

Marine umbilical is one of the key equipment for subsea oil and gas exploitation,which is usually integrated by a great number of different functional components with multi-layers.The layout of these components directly affects manufacturing,operation and storage performances of the umbilical.For the multi-layer cross-sectional layout design of the umbilical,a quantifiable multi-objective optimization model is established according to the operation and storage requirements.Considering the manufacturing factors,the multi-layering strategy based on contact point identification is introduced for a great number of functional components.Then,the GA-GLM global optimization algorithm is proposed combining the genetic algorithm and the generalized multiplier method,and the selection operator of the genetic algorithm is improved based on the steepest descent method.Genetic algorithm is used to find the optimal solution in the global space,which can converge from any initial layout to the feasible layout solution.The feasible layout solution is taken as the initial value of the generalized multiplier method for fast and accurate solution.Finally,taking umbilicals with a great number of components as examples,the results show that the cross-sectional performance of the umbilical obtained by optimization algorithm is better and the solution efficiency is higher.Meanwhile,the multi-layering strategy is effective and feasible.The design method proposed in this paper can quickly obtain the optimal multi-layer cross-sectional layout,which replaces the manual design,and provides useful reference and guidance for the umbilical industry.

Projecting Wintertime Newly Formed Arctic Sea Ice through Weighting CMIP6 Model Performance and Independence

Precipitous Arctic sea-ice decline and the corresponding increase in Arctic open-water areas in summer months give more space for sea-ice growth in the subsequent cold seasons. Compared to the decline of the entire Arctic multiyear sea ice,changes in newly formed sea ice indicate more thermodynamic and dynamic information on Arctic atmosphere–ocean–ice interaction and northern mid–high latitude atmospheric teleconnections. Here, we use a large multimodel ensemble from phase 6 of the Coupled Model Intercomparison Project(CMIP6) to investigate future changes in wintertime newly formed Arctic sea ice. The commonly used model-democracy approach that gives equal weight to each model essentially assumes that all models are independent and equally plausible, which contradicts with the fact that there are large interdependencies in the ensemble and discrepancies in models' performances in reproducing observations. Therefore, instead of using the arithmetic mean of well-performing models or all available models for projections like in previous studies, we employ a newly developed model weighting scheme that weights all models in the ensemble with consideration of their performance and independence to provide more reliable projections. Model democracy leads to evident bias and large intermodel spread in CMIP6 projections of newly formed Arctic sea ice. However, we show that both the bias and the intermodel spread can be effectively reduced by the weighting scheme. Projections from the weighted models indicate that wintertime newly formed Arctic sea ice is likely to increase dramatically until the middle of this century regardless of the emissions scenario.Thereafter, it may decrease(or remain stable) if the Arctic warming crosses a threshold(or is extensively constrained).

Anisotropic time-dependent behaviors of shale under direct shearing and associated empirical creep models

Understanding the anisotropic creep behaviors of shale under direct shearing is a challenging issue.In this context,we conducted shear-creep and steady-creep tests on shale with five bedding orientations (i.e.0°,30°,45°,60°,and 90°),under multiple levels of direct shearing for the first time.The results show that the anisotropic creep of shale exhibits a significant stress-dependent behavior.Under a low shear stress,the creep compliance of shale increases linearly with the logarithm of time at all bedding orientations,and the increase depends on the bedding orientation and creep time.Under high shear stress conditions,the creep compliance of shale is minimal when the bedding orientation is 0°,and the steady-creep rate of shale increases significantly with increasing bedding orientations of 30°,45°,60°,and 90°.The stress-strain values corresponding to the inception of the accelerated creep stage show an increasing and then decreasing trend with the bedding orientation.A semilogarithmic model that could reflect the stress dependence of the steady-creep rate while considering the hardening and damage process is proposed.The model minimizes the deviation of the calculated steady-state creep rate from the observed value and reveals the behavior of the bedding orientation's influence on the steady-creep rate.The applicability of the five classical empirical creep models is quantitatively evaluated.It shows that the logarithmic model can well explain the experimental creep strain and creep rate,and it can accurately predict long-term shear creep deformation.Based on an improved logarithmic model,the variations in creep parameters with shear stress and bedding orientations are discussed.With abovementioned findings,a mathematical method for constructing an anisotropic shear creep model of shale is proposed,which can characterize the nonlinear dependence of the anisotropic shear creep behavior of shale on the bedding orientation.

Modeling Locking Angle of the Multi-layered Biaxial Weft Knitted Fabric in Shear Deformation

This paper introduces the construction of the multi-layered biaxial weft knitted fabric （MBWK fabric） and studies the locking angle of this kind of fabric. Moreover, a locking angle model of the MBWK fabric is established for the first time according to its unique construction. Two kinds of locking angles are considered under different restraint conditions: the locking angle θ1 controlled by the inserting yarns and the locking angle θ2 controlled by the stitch yarns. It is concluded that the ultimate value of the locking angle θ is the larger one of the two angles.

Geostatistical seismic inversion and 3D modelling of metric flow units,porosity and permeability in Brazilian presalt reservoir

Flow units(FU)rock typing is a common technique for characterizing reservoir flow behavior,producing reliable porosity and permeability estimation even in complex geological settings.However,the lateral extrapolation of FU away from the well into the whole reservoir grid is commonly a difficult task and using the seismic data as constraints is rarely a subject of study.This paper proposes a workflow to generate numerous possible 3D volumes of flow units,porosity and permeability below the seismic resolution limit,respecting the available seismic data at larger scales.The methodology is used in the Mero Field,a Brazilian presalt carbonate reservoir located in the Santos Basin,who presents a complex and heterogenic geological setting with different sedimentological processes and diagenetic history.We generated metric flow units using the conventional core analysis and transposed to the well log data.Then,given a Markov chain Monte Carlo algorithm,the seismic data and the well log statistics,we simulated acoustic impedance,decametric flow units(DFU),metric flow units(MFU),porosity and permeability volumes in the metric scale.The aim is to estimate a minimum amount of MFU able to calculate realistic scenarios porosity and permeability scenarios,without losing the seismic lateral control.In other words,every porosity and permeability volume simulated produces a synthetic seismic that match the real seismic of the area,even in the metric scale.The achieved 3D results represent a high-resolution fluid flow reservoir modelling considering the lateral control of the seismic during the process and can be directly incorporated in the dynamic characterization workflow.

耦合优化蚁群算法与P-Median model的选址模型设计

为节省城建部门对于公共体育设施的投入成本以及提高城市人民生活质量,以运动场所优化选址为例,提出一种新型设施选址模型。该模型主要基于P-Median model(最小化阻抗模型)根据需求点数量从全部候选设施选址中选择设施空间位置,让用户达到离自己最近设施距离成本总和最小的目的,对选址的基本原则和实际情况提出要求,构造目标函数用于优化后蚁群算法求解进行选址工作。优化蚁群算法实现基于Python语言模块,通过改进蚁群原始信息素,提升原有算法的收敛速度,求出目标函数最优解,可以很好地模拟对于运动场所的选址。用二者耦合进行优势互补所设计的选址模型来搜寻研究区蚁群信息素浓度残留最大的栅格像元,从而确定未被已有设施点服务半径覆盖的最佳设施点建立位置。实验结果表明,该新型选址模型相较于最小化阻抗模型与最大化覆盖模型,新增优化设施点使整体服务半径覆盖率分别高出10.42%和6.95%,适合求解较为精确且小规模空间下的选址问题。

A modified stochastic model for LS+AR hybrid method and its application in polar motion short-term prediction

Short-term(up to 30 days)predictions of Earth Rotation Parameters(ERPs)such as Polar Motion(PM:PMX and PMY)play an essential role in real-time applications related to high-precision reference frame conversion.Currently,least squares(LS)+auto-regressive(AR)hybrid method is one of the main techniques of PM prediction.Besides,the weighted LS+AR hybrid method performs well for PM short-term prediction.However,the corresponding covariance information of LS fitting residuals deserves further exploration in the AR model.In this study,we have derived a modified stochastic model for the LS+AR hybrid method,namely the weighted LS+weighted AR hybrid method.By using the PM data products of IERS EOP 14 C04,the numerical results indicate that for PM short-term forecasting,the proposed weighted LS+weighted AR hybrid method shows an advantage over both the LS+AR hybrid method and the weighted LS+AR hybrid method.Compared to the mean absolute errors(MAEs)of PMX/PMY sho rt-term prediction of the LS+AR hybrid method and the weighted LS+AR hybrid method,the weighted LS+weighted AR hybrid method shows average improvements of 6.61%/12.08%and 0.24%/11.65%,respectively.Besides,for the slopes of the linear regression lines fitted to the errors of each method,the growth of the prediction error of the proposed method is slower than that of the other two methods.

Mshpy23:a user-friendly,parameterized model of magnetosheath conditions

Lunar Environment heliospheric X-ray Imager(LEXI)and Solar wind−Magnetosphere−Ionosphere Link Explorer(SMILE)will observe magnetosheath and its boundary motion in soft X-rays for understanding magnetopause reconnection modes under various solar wind conditions after their respective launches in 2024 and 2025.Magnetosheath conditions,namely,plasma density,velocity,and temperature,are key parameters for predicting and analyzing soft X-ray images from the LEXI and SMILE missions.We developed a userfriendly model of magnetosheath that parameterizes number density,velocity,temperature,and magnetic field by utilizing the global Magnetohydrodynamics(MHD)model as well as the pre-existing gas-dynamic and analytic models.Using this parameterized magnetosheath model,scientists can easily reconstruct expected soft X-ray images and utilize them for analysis of observed images of LEXI and SMILE without simulating the complicated global magnetosphere models.First,we created an MHD-based magnetosheath model by running a total of 14 OpenGGCM global MHD simulations under 7 solar wind densities(1,5,10,15,20,25,and 30 cm)and 2 interplanetary magnetic field Bz components(±4 nT),and then parameterizing the results in new magnetosheath conditions.We compared the magnetosheath model result with THEMIS statistical data and it showed good agreement with a weighted Pearson correlation coefficient greater than 0.77,especially for plasma density and plasma velocity.Second,we compiled a suite of magnetosheath models incorporating previous magnetosheath models(gas-dynamic,analytic),and did two case studies to test the performance.The MHD-based model was comparable to or better than the previous models while providing self-consistency among the magnetosheath parameters.Third,we constructed a tool to calculate a soft X-ray image from any given vantage point,which can support the planning and data analysis of the aforementioned LEXI and SMILE missions.A release of the code has been uploaded to a Github repository.

Development and validation of a prediction model for early screening of people at high risk for colorectal cancer

BACKGROUND Colorectal cancer(CRC)is a serious threat worldwide.Although early screening is suggested to be the most effective method to prevent and control CRC,the current situation of early screening for CRC is still not optimistic.In China,the incidence of CRC in the Yangtze River Delta region is increasing dramatically,but few studies have been conducted.Therefore,it is necessary to develop a simple and efficient early screening model for CRC.AIM To develop and validate an early-screening nomogram model to identify individuals at high risk of CRC.METHODS Data of 64448 participants obtained from Ningbo Hospital,China between 2014 and 2017 were retrospectively analyzed.The cohort comprised 64448 individuals,of which,530 were excluded due to missing or incorrect data.Of 63918,7607(11.9%)individuals were considered to be high risk for CRC,and 56311(88.1%)were not.The participants were randomly allocated to a training set(44743)or validation set(19175).The discriminatory ability,predictive accuracy,and clinical utility of the model were evaluated by constructing and analyzing receiver operating characteristic(ROC)curves and calibration curves and by decision curve analysis.Finally,the model was validated internally using a bootstrap resampling technique.RESULTS Seven variables,including demographic,lifestyle,and family history information,were examined.Multifactorial logistic regression analysis revealed that age[odds ratio(OR):1.03,95%confidence interval(CI):1.02-1.03,P<0.001],body mass index(BMI)(OR:1.07,95%CI:1.06-1.08,P<0.001),waist circumference(WC)(OR:1.03,95%CI:1.02-1.03 P<0.001),lifestyle(OR:0.45,95%CI:0.42-0.48,P<0.001),and family history(OR:4.28,95%CI:4.04-4.54,P<0.001)were the most significant predictors of high-risk CRC.Healthy lifestyle was a protective factor,whereas family history was the most significant risk factor.The area under the curve was 0.734(95%CI:0.723-0.745)for the final validation set ROC curve and 0.735(95%CI:0.728-0.742)for the training set ROC curve.The calibration curve demonstrated a high correlation between the CRC high-risk population predicted by the nomogram model and the actual CRC high-risk population.CONCLUSION The early-screening nomogram model for CRC prediction in high-risk populations developed in this study based on age,BMI,WC,lifestyle,and family history exhibited high accuracy.

24Model与LCM原因因素定义对比研究

为探究损失致因模型(LCM)原因因素定义与事故致因“2-4”模型(24Model)存在的异同和优缺点,梳理2个模型各层面原因和结果的定义,对比定义内容及其对事故原因分析等安全实务的指导作用,并以一起瓦斯爆炸事故为例加以实证分析,获得二者分析结果之间的差异。研究结果表明:LCM是首个将管理因素纳入事故致因分析的一维事件序列模型,可明确各层面原因因素的定义和因素间的逻辑关系,但部分定义存在交叉重复的问题,并没有揭示安全工作指导思想等深层次事故致因因素;24Model作为系统性事故致因模型,对各类因素的定义均以组织为主体,描述事件、事故、安全的概念内涵,划分个体安全动作、安全能力和组织安全管理体系的类别并给出含义解析,探究组织安全文化层面的问题并以32个元素体现;2个模型的事故原因分析方法均建立在对各层级原因因素定义的基础上,并适用于模型理论体系本身。

Genetically modified non-human primate models for research on neurodegenerative diseases

Neurodegenerative diseases(NDs)are a group of debilitating neurological disorders that primarily affect elderly populations and include Alzheimer's disease(AD),Parkinson's disease(PD),Huntington's disease(HD),and amyotrophic lateral sclerosis(ALS).Currently,there are no therapies available that can delay,stop,or reverse the pathological progression of NDs in clinical settings.As the population ages,NDs are imposing a huge burden on public health systems and affected families.Animal models are important tools for preclinical investigations to understand disease pathogenesis and test potential treatments.While numerous rodent models of NDs have been developed to enhance our understanding of disease mechanisms,the limited success of translating findings from animal models to clinical practice suggests that there is still a need to bridge this translation gap.Old World nonhuman primates(NHPs),such as rhesus,cynomolgus,and vervet monkeys,are phylogenetically,physiologically,biochemically,and behaviorally most relevant to humans.This is particularly evident in the similarity of the structure and function of their central nervous systems,rendering such species uniquely valuable for neuroscience research.Recently,the development of several genetically modified NHP models of NDs has successfully recapitulated key pathologies and revealed novel mechanisms.This review focuses on the efficacy of NHPs in modeling NDs and the novel pathological insights gained,as well as the challenges associated with the generation of such models and the complexities involved in their subsequent analysis.

Multi-layer analytic solution for k-ωmodel equations via a symmetry approach

Despite being one of the oldest and most widely-used turbulence models in engineering computational fluid dynamics(CFD),the k-ωmodel has not been fully understood theoretically because of its high nonlinearity and complex model parameter setting.Here,a multi-layer analytic expression is postulated for two lengths(stress and kinetic energy lengths),yielding an analytic solution for the k-ωmodel equations in pipe flow.Approximate local balance equations are analyzed to determine the key parameters in the solution,which are shown to be rather close to the empirically-measured values from the numerical solution of the Wilcox k-ωmodel,and hence the analytic construction is fully validated.The results provide clear evidence that the k-ωmodel sets in it a multilayer structure,which is similar to but different,in some insignificant details,from the Navier-Stokes(N-S)turbulence.This finding explains why the k-ωmodel is so popular,especially in computing the near-wall flow.Finally,the analysis is extended to a newlyrefined k-ωmodel called the structural ensemble dynamics(SED)k-ωmodel,showing that the SED k-ωmodel has improved the multi-layer structure in the outer flow but preserved the setting of the k-ωmodel in the inner region.