Multiscale Simulation of Microstructure Evolution during Preparation and Service Processes of Physical Vapor Deposited c-TiAlN Coatings

Physical Vapor Deposited(PVD)TiAlN coatings are extensively utilized as protective layers for cutting tools,renowned for their excellent comprehensive performance.To optimize quality control of TiAlN coatings for cutting tools,a multi-scale simulation approach is proposed that encompasses the microstructure evolution of coatings considering the entire preparation and service lifecycle of PVD TiAlN coatings.This scheme employs phase-field simulation to capture the essential microstructure of the PVD-prepared TiAlN coatings.Moreover,cutting simulation is used to determine the service temperature experienced during cutting processes at varying rates.Cahn-Hilliard modeling is finally utilized to consume the microstructure and service condition data to acquaint the microstructure evolution of TiAlN coatings throughout the cutting processes.This methodology effectively establishes a correlation between service temperature and its impact on the microstructure evolution of TiAlN coatings.It is expected that the present multi-scale numerical simulation approach will provide innovative strategies for assisting property design and lifespan prediction of TiAlN coatings.

Fast compressed sensing spectral measurement with adaptive gradient multiscale resolution

We propose a fast,adaptive multiscale resolution spectral measurement method based on compressed sensing.The method can apply variable measurement resolution over the entire spectral range to reduce the measurement time by over 75%compared to a global high-resolution measurement.Mimicking the characteristics of the human retina system,the resolution distribution follows the principle of gradually decreasing.The system allows the spectral peaks of interest to be captured dynamically or to be specified a priori by a user.The system was tested by measuring single and dual spectral peaks,and the results of spectral peaks are consistent with those of global high-resolution measurements.

An Initial Perturbation Method for the Multiscale Singular Vector in Global Ensemble Prediction

Ensemble prediction is widely used to represent the uncertainty of single deterministic Numerical Weather Prediction(NWP) caused by errors in initial conditions(ICs). The traditional Singular Vector(SV) initial perturbation method tends only to capture synoptic scale initial uncertainty rather than mesoscale uncertainty in global ensemble prediction. To address this issue, a multiscale SV initial perturbation method based on the China Meteorological Administration Global Ensemble Prediction System(CMA-GEPS) is proposed to quantify multiscale initial uncertainty. The multiscale SV initial perturbation approach entails calculating multiscale SVs at different resolutions with multiple linearized physical processes to capture fast-growing perturbations from mesoscale to synoptic scale in target areas and combining these SVs by using a Gaussian sampling method with amplitude coefficients to generate initial perturbations. Following that, the energy norm,energy spectrum, and structure of multiscale SVs and their impact on GEPS are analyzed based on a batch experiment in different seasons. The results show that the multiscale SV initial perturbations can possess more energy and capture more mesoscale uncertainties than the traditional single-SV method. Meanwhile, multiscale SV initial perturbations can reflect the strongest dynamical instability in target areas. Their performances in global ensemble prediction when compared to single-scale SVs are shown to(i) improve the relationship between the ensemble spread and the root-mean-square error and(ii) provide a better probability forecast skill for atmospheric circulation during the late forecast period and for short-to medium-range precipitation. This study provides scientific evidence and application foundations for the design and development of a multiscale SV initial perturbation method for the GEPS.

Multiscale analysis of fine slag from pulverized coal gasification in entrained-flow bed

Fine slag(FS)is an unavoidable by-product of coal gasification.FS,which is a simple heap of solid waste left in the open air,easily causes environmental pollution and has a low resource utilization rate,thereby restricting the development of energy-saving coal gasification technologies.The multiscale analysis of FS performed in this study indicates typical grain size distribution,composition,crystalline structure,and chemical bonding characteristics.The FS primarily contained inorganic and carbon components(dry bases)and exhibited a"three-peak distribution"of the grain size and regular spheroidal as well as irregular shapes.The irregular particles were mainly adsorbed onto the structure and had a dense distribution and multiple pores and folds.The carbon constituents were primarily amorphous in structure,with a certain degree of order and active sites.C 1s XPS spectrum indicated the presence of C–C and C–H bonds and numerous aromatic structures.The inorganic components,constituting 90%of the total sample,were primarily silicon,aluminum,iron,and calcium.The inorganic components contained Si–O-Si,Si–O–Al,Si–O,SO_(4)^(2−),and Fe–O bonds.Fe 2p XPS spectrum could be deconvoluted into Fe 2p_(1/2) and Fe 2p_(3/2) peaks and satellite peaks,while Fe existed mainly in the form of Fe(III).The findings of this study will be beneficial in resource utilization and formation mechanism of fine slag in future.

A Multiscale Reliability-Based Design Optimization Method for Carbon-Fiber-Reinforced Composite Drive Shafts

Carbon fiber composites,characterized by their high specific strength and low weight,are becoming increasingly crucial in automotive lightweighting.However,current research primarily emphasizes layer count and orientation,often neglecting the potential of microstructural design,constraints in the layup process,and performance reliability.This study,therefore,introduces a multiscale reliability-based design optimization method for carbon fiber-reinforced plastic(CFRP)drive shafts.Initially,parametric modeling of the microscale cell was performed,and its elastic performance parameters were predicted using two homogenization methods,examining the impact of fluctuations in microscale cell parameters on composite material performance.A finite element model of the CFRP drive shaft was then constructed,achieving parameter transfer between microscale and macroscale through Python programming.This enabled an investigation into the influence of both micro and macro design parameters on the CFRP drive shaft’s performance.The Multi-Objective Particle Swarm Optimization(MOPSO)algorithm was enhanced for particle generation and updating strategies,facilitating the resolution of multi-objective reliability optimization problems,including composite material layup process constraints.Case studies demonstrated that this approach leads to over 30%weight reduction in CFRP drive shafts compared to metallic counterparts while satisfying reliability requirements and offering insights for the lightweight design of other vehicle components.

The 2022 Extreme Heatwave in Shanghai,Lower Reaches of the Yangtze River Valley:Combined Influences of Multiscale Variabilities

In the summer of 2022,China(especially the Yangtze River Valley,YRV)suffered its strongest heatwave(HW)event since 1961.In this study,we examined the influences of multiscale variabilities on the 2022 extreme HW in the lower reaches of the YRV,focusing on the city of Shanghai.We found that about 1/3 of the 2022 HW days in Shanghai can be attributed to the long-term warming trend of global warming.During mid-summer of 2022,an enhanced western Pacific subtropical high(WPSH)and anomalous double blockings over the Ural Mountains and Sea of Okhotsk,respectively,were associated with the persistently anomalous high pressure over the YRV,leading to the extreme HW.The Pacific Decadal Oscillation played a major role in the anomalous blocking pattern associated with the HW at the decadal time scale.Also,the positive phase of the Atlantic Multidecadal Oscillation may have contributed to regulating the formation of the double-blocking pattern.Anomalous warming of both the warm pool of the western Pacific and tropical North Atlantic at the interannual time scale may also have favored the persistency of the double blocking and the anomalously strong WPSH.At the subseasonal time scale,the anomalously frequent phases 2-5 of the canonical northward propagating variability of boreal summer intraseasonal oscillation associated with the anomalous propagation of a weak Madden-Julian Oscillation suppressed the convection over the YRV and also contributed to the HW.Therefore,the 2022 extreme HW originated from multiscale forcing including both the climate warming trend and air-sea interaction at multiple time scales.

Multiscale confinement nitridation in molybdenum carbide for efficient hydrogen production

The molybdenum carbide(Mo_(2)C)has been regarded as one of the most cost-efficient and stable electrocatalyst for the hydrogen evolution reaction(HER)by the virtue of its Pt-like electronic structures.However,the inherent limitation of high density of empty valence band significantly reduces its catalytic reactivity by reason of strong hydrogen desorption resistance.Herein,we propose a multiscale confinement synthesis method to design the nitrogen-rich Mo_(2)C for modulating the band structure via decomposing the pre-coordination bonded polymer in a pressure-tight tube sealing system.Pre-bonded c/N-Mo in the coordination precursor constructs a micro-confinement space,enabling the homogeneous nitrogenization in-situ happened during the formation of Mo_(2)C.Simultaneously,the evolved gases from the precursor decomposition in tube sealing system establish a macro-confinement environment,preventing the lattice N escape and further endowing a continuous nitridation.Combining the multiscale confinement effects,the nitrogen-rich Mo2C displays as high as 25%N-Mo concentration in carbide lattice,leading to a satisfactory band structure.Accordingly,the constructed nitrogen-rich Mo_(2)C reveals an adorable catalytic activity for HER in both alkaline and acid solution.It is anticipated that the multiscale confinement synthesis strategy presents guideline for the rational design of electrocatalysts and beyond.

Effect of Heat Treatment on Microstructure and Mechanical Properties of Multiscale SiC_p Hybrid Reinforced 6061 Aluminum Matrix Composites

The performance of solid solution aging treatment on aluminum matrix composites prepared by powder metallurgy and reinforced with 6061 aluminum alloy powder as matrix;meanwhile, nano silicon carbide particles(nm Si Cp), submicron silicon carbide particles(1 μm Si Cp) and Ti particles were studied. The Al/Si Cp composite powder was prepared by high-energy ball milling, and then cold-pressed, sintered, hotextruded, and then heat-treated with different solution temperatures and aging times for the extruded composites. Optical microscopy, scanning electron microscopy, energy dispersive X-ray spectroscopy(EDS), X-ray diffractometer(XRD) and extrusion testing were used to analyze and test the microstructure and mechanical properties of aluminum matrix composites. The results show that after the multi-stage solid solution at 530 ℃×2 h+535 ℃×2 h+540 ℃×2 h, the particles are mainly equiaxed grains and uniformly distributed. There is no reinforcement agglomeration, and the surface is dense and the insoluble phase is basically dissolved. In the matrix, the strengthening effect is good, and the hardness and compressive strength are 179.43 HV and 680.42 MPa, respectively. Under this solution process, when the aluminum matrix composites are aged at 170 ℃ for 10 h, the hardness and compressive strength can reach their peaks and increase to 195.82 HV and 721.48 MPa, respectively.

Multiscale and Auto-Tuned Semi-Supervised Deep Subspace Clustering and Its Application in Brain Tumor Clustering

In this paper,we introduce a novel Multi-scale and Auto-tuned Semi-supervised Deep Subspace Clustering(MAS-DSC)algorithm,aimed at addressing the challenges of deep subspace clustering in high-dimensional real-world data,particularly in the field of medical imaging.Traditional deep subspace clustering algorithms,which are mostly unsupervised,are limited in their ability to effectively utilize the inherent prior knowledge in medical images.Our MAS-DSC algorithm incorporates a semi-supervised learning framework that uses a small amount of labeled data to guide the clustering process,thereby enhancing the discriminative power of the feature representations.Additionally,the multi-scale feature extraction mechanism is designed to adapt to the complexity of medical imaging data,resulting in more accurate clustering performance.To address the difficulty of hyperparameter selection in deep subspace clustering,this paper employs a Bayesian optimization algorithm for adaptive tuning of hyperparameters related to subspace clustering,prior knowledge constraints,and model loss weights.Extensive experiments on standard clustering datasets,including ORL,Coil20,and Coil100,validate the effectiveness of the MAS-DSC algorithm.The results show that with its multi-scale network structure and Bayesian hyperparameter optimization,MAS-DSC achieves excellent clustering results on these datasets.Furthermore,tests on a brain tumor dataset demonstrate the robustness of the algorithm and its ability to leverage prior knowledge for efficient feature extraction and enhanced clustering performance within a semi-supervised learning framework.

Automatic Road Tunnel Crack Inspection Based on Crack Area Sensing and Multiscale Semantic Segmentation

The detection of crack defects on the walls of road tunnels is a crucial step in the process of ensuring travel safetyand performing routine tunnel maintenance. The automatic and accurate detection of cracks on the surface of roadtunnels is the key to improving the maintenance efficiency of road tunnels. Machine vision technology combinedwith a deep neural network model is an effective means to realize the localization and identification of crackdefects on the surface of road tunnels.We propose a complete set of automatic inspection methods for identifyingcracks on the walls of road tunnels as a solution to the problem of difficulty in identifying cracks during manualmaintenance. First, a set of equipment applied to the real-time acquisition of high-definition images of walls inroad tunnels is designed. Images of walls in road tunnels are acquired based on the designed equipment, whereimages containing crack defects are manually identified and selected. Subsequently, the training and validationsets used to construct the crack inspection model are obtained based on the acquired images, whereas the regionscontaining cracks and the pixels of the cracks are finely labeled. After that, a crack area sensing module is designedbased on the proposed you only look once version 7 model combined with coordinate attention mechanism (CAYOLOV7) network to locate the crack regions in the road tunnel surface images. Only subimages containingcracks are acquired and sent to the multiscale semantic segmentation module for extraction of the pixels to whichthe cracks belong based on the DeepLab V3+ network. The precision and recall of the crack region localizationon the surface of a road tunnel based on our proposed method are 82.4% and 93.8%, respectively. Moreover, themean intersection over union (MIoU) and pixel accuracy (PA) values for achieving pixel-level detection accuracyare 76.84% and 78.29%, respectively. The experimental results on the dataset show that our proposed two-stagedetection method outperforms other state-of-the-art models in crack region localization and detection. Based onour proposedmethod, the images captured on the surface of a road tunnel can complete crack detection at a speed often frames/second, and the detection accuracy can reach 0.25 mm, which meets the requirements for maintenanceof an actual project. The designed CA-YOLO V7 network enables precise localization of the area to which a crackbelongs in images acquired under different environmental and lighting conditions in road tunnels. The improvedDeepLab V3+ network based on lightweighting is able to extract crack morphology in a given region more quicklywhile maintaining segmentation accuracy. The established model combines defect localization and segmentationmodels for the first time, realizing pixel-level defect localization and extraction on the surface of road tunnelsin complex environments, and is capable of determining the actual size of cracks based on the physical coordinatesystemafter camera calibration. The trainedmodelhas highaccuracy andcanbe extendedandapplied to embeddedcomputing devices for the assessment and repair of damaged areas in different types of road tunnels.

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.

Multiscale evolution mechanism of sandstone under wet-dry cycles of deionized water:From molecular scale to macroscopic scale

Water is the most abundant molecule found on the earth’s surface and is a key factor in multiscale rock destruction.However,given the fine-grained nature of rock and the complexity of its internal structure,the microstructural evolution of rock under the action of water has not yet been elucidated in detail,and little is understood about the relationship between the rock structure and solideliquid unit.A variety of techniques were used in this study to track the mechanical properties,pore and crack characteristics,and mineral structure degradation characteristics of sandstone at different stages under the action of deionized water,and the evolution mechanisms of the microstructure were analyzed at the molecular scale.The results showed that during the watererock interaction process,water was adsorbed onto the surface of dolomite minerals and the hydrophilic surface of clay minerals,forming a high-density hydrogen bond network.However,different mineral surface structures had different water adsorption structures,resulting in the strain of the dense clay mineral aggregates under expansion action.Stress concentrated at crack tips under the capillary force of dolomite minerals(very weak dolomite dissolution).These effects resulted in a substantial increase in the number of small pores and enhancements in poreecrack connectivity,and the rock strength exhibited varying degrees of decline at different stages of wet-dry cycles.In general,the results of this paper will help to further elucidate the internal connections between molecular-scale and macroscale processes in rock science.

A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems

By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability.

A Perspective on the Evolution of Atmospheric Blocking Theories:From Eddy-Mean flow Interaction to Nonlinear Multiscale Interaction

In this paper,we first review the research advancements in blocking dynamics and highlight the merits and drawbacks of the previous theories of atmospheric blocking.Then,the dynamical mechanisms of atmospheric blocking are presented based on a nonlinear multi-scale interaction(NMI)model.Previous studies suggested that the eddy deformation(e.g.,eddy straining,wave breaking,and eddy merging)might lead to the formation and maintenance of atmospheric blocking.However,the results were speculative and problematic because the previous studies,based on the time-mean eddy-mean flow interaction model,cannot identify the causal relationship between the evolution of atmospheric blocking and the eddy deformation.Based on the NMI model,we indicate that the onset,growth,maintenance,and decay of atmospheric blocking is mainly produced by the spatiotemporal evolution of pre-existing upstream synoptic-scale eddies,whereas the eddy deformation is a concomitant phenomenon of the blocking formation.The lifetime of blocking is mainly determined by the meridional background potential vorticity gradient(PVy)because a small PVyfavors weak energy dispersion and strong nonlinearity to sustain the blocking.But the zonal movement of atmospheric blocking is associated with the background westerly wind,PVy,and the blocking amplitude.Using this NMI model,a bridge from the climate change to sub-seasonal atmospheric blocking and weather extremes might be established via examining the effect of climate change on PVy.Thus,it is expected that using the NMI model to explore the dynamics of atmospheric blocking and its change is a new direction in the future.

Multiscale Theories and Applications:From Microstructure Design to Macroscopic Assessment for Carbon Nanotubes Networks

Carbon nanotube(CNT)networks enable CNTs to be used as building blocks for synthesizing novel advanced materials,thus taking full advantage of the superior properties of individual CNTs.Multiscale analyses have to be adopted to study the load transfer mechanisms of CNT networks from the atomic scale to the macroscopic scale due to the huge computational cost.Among them,fully resolved structural features include the graphitic honeycomb lattice(atomic),inter-tube stacking(nano)and assembly(meso)of CNTs.On an atomic scale,the elastic properties,ultimate stresses,and failure strains of individual CNTs with distinct chiralities and radii are obtained under various loading conditions by molecular mechanics.The dependence of the cohesive energies on spacing distances,crossing angles,size and edge effects between two CNTs is analyzed through continuum modeling in nanoscale.The mesoscale models,which neglect the atomic structures of individual CNTs but retain geometrical information about the shape of CNTs and their assembly into a network,have been developed to study the multi-level mechanism of material deformation and microstructural evolution in CNT networks under stretching,from elastic elongation,strengthening to damage and failure.This paper summarizes the multiscale theories mentioned above,which should provide insight into the optimal assembling of CNT network materials for elevated mechanical performance.

Multiscale tensegrity model for the tensile properties of DNA nanotubes

DNA nanotubes(DNTs)with user-defined shapes and functionalities have potential applications in many fields.So far,compared with numerous experimental studies,there have been only a handful of models on the mechanical properties of such DNTs.This paper aims at presenting a multiscale model to quantify the correlations among the pre-tension states,tensile properties,encapsulation structures of DNTs,and the surrounding factors.First,by combining a statistical worm-like-chain(WLC)model of single DNA deformation and Parsegian's mesoscopic model of DNA liquid crystal free energy,a multiscale tensegrity model is established,and the pre-tension state of DNTs is characterized theoretically for the first time.Then,by using the minimum potential energy principle,the force-extension curve and tensile rigidity of pre-tension DNTs are predicted.Finally,the effects of the encapsulation structure and surrounding factors on the tensile properties of DNTs are studied.The predictions for the tensile behaviors of DNTs can not only reproduce the existing experimental results,but also reveal that the competition of DNA intrachain and interchain interactions in the encapsulation structures determines the pre-tension states of DNTs and their tensile properties.The changes in the pre-tension states and environmental factors make the monotonic or non-monotonic changes in the tensile properties of DNTs under longitudinal loads.

Multiscale strain alleviation of Ni-rich cathode guided by in situ environmental transmission electron microscopy during the solid-state synthesis

Ni-rich layered oxides are one of the most promising cathode materials for Li-ion batteries due to their high energy density.However,the chemomechanical breakdown and capacity degradation associated with the anisotropic lattice evolution during lithiation/delithiation hinders its practical application.Herein,by utilizing the in situ environmental transmission electron microscopy(ETEM),we provide a real time nanoscale characterization of high temperature solid-state synthesis of LiNi_(0.8)CO_(0.1)Mn_(0.1)O_(2)(NCM811) cathode,and unprecedentedly reveal the strain/stress formation and morphological evolution mechanism of primary/second ary particles,as well as their influence on electrochemical performance.We show that stress inhomogeneity during solid-state synthesis will lead to both primary/secondary particle pulverization and new grain boundary initiation,which are detrimental to cathode cycling stability and rate performance.Aiming to alleviate this multiscale strain during solid-state synthesis,we introduced a calcination scheme that effectively relieves the stress during the synthesis,thus mitigating the primary/secondary particle crack and the detrimental grain boundaries formation,which in turn improves the cathode structural integrity and Li-ion transport kinetics for long-life and high-rate electrochemical performance.This work remarkably advances the fundamental understanding on mechanochemical properties of transition metal oxide cathode with solid-state synthesis and provides a unified guide for optimization the Ni-rich oxide cathode.

Multiscale Combined Action and Disturbance Characteristics of Pre-summer Extreme Precipitation Events over South China

The dominant frequency modes of pre-summer extreme precipitation events(EPEs)over South China(SC)between1998 and 2018 were investigated.The 67 identified EPEs were all characterized by the 3-8-d(synoptic)frequency band.However,multiscale combined modes of the synoptic and three low-frequency bands[10-20-d(quasi-biweekly,QBW);15-40-d(quasi-monthly,QM);and 20-60-d(intraseasonal)]accounted for the majority(63%)of the EPEs,and the precipitation intensity on the peak wet day was larger than that of the single synoptic mode.It was found that EPEs form within strong southwesterly anomalous flows characterized by either lower-level cyclonic circulation over SC or a deep trough over eastern China.Bandpass-filtered disturbances revealed the direct precipitating systems and their life cycles.Synoptic-scale disturbances are dominated by mid-high latitude troughs,and the cyclonic anomalies originate from downstream of the Tibetan Plateau(TP).Given the warm and moist climate state,synoptic-scale northeasterly flows can even induce EPEs.At the QBW and QM scales,the disturbances originate from the tropical Pacific,downstream of the TP,or mid-high latitudes(QBW only).Each is characterized by cyclonic-anticyclonic wave trains and intense southwesterly flows between them within a region of large horizontal pressure gradient.The intraseasonal disturbances are confined to tropical regions and influence SC by marginal southwesterly flows.It is concluded that low-frequency disturbances provide favorable background conditions for EPEs over SC and synoptic-scale disturbances ultimately induce EPEs on the peak wet days.Both should be simultaneously considered for EPE predictions over SC.

Behaviour of non-ballast pre-stressed and precast track structures in high speed railway based on multiscale finite element model

In order to make further study on the mechanical property of CRTSIII type slab non-ballast track structures,which was self-designed in China,based on the method of the multiscale finite element model(FEM),the traditional FEM of slab non-ballast track structures was improved.The multiscale FEM of CRTSII type slab nonballast track structures was established based on the general finite element program ABAQUs.Then the comparative calculation was made between various FEMs,showing that the high solution precision,fast modelling speed and high solution efficiency could be obtained.Therefore,the multiscale FEM was suitable for the parametric study on mechanical behaviour of CRTSII type slab non-ballast track structures,and then the key influence factor and constructions could be optimized.

A Variational Multiscale Method for Particle Dispersion Modeling in the Atmosphere

A LES model is proposed to predict the dispersion of particles in the atmosphere in the context of Chemical,Biological,Radiological and Nuclear(CBRN)applications.The code relies on the Finite Element Method(FEM)for both the fluid and the dispersed solid phases.Starting from the Navier-Stokes equations and a general description of the FEM strategy,the Streamline Upwind Petrov-Galerkin(SUPG)method is formulated putting some emphasis on the related assembly matrix and stabilization coefficients.Then,the Variational Multiscale Method(VMS)is presented together with a detailed illustration of its algorithm and hierarchy of computational steps.It is demonstrated that the VMS can be considered as a more general version of the SUPG method.The final part of the work is used to assess the reliability of the implemented predictor/multicorrector solution strategy.