Macro-scale Model Research Articles

Macroscale Modeling of Geochemistry Influence on Polymer and Low-Salinity Waterflooding in Carbonate Oil Reservoirs.

The enhancement of oil recovery (EOR) through low-salinity waterflooding (LSWF) and the emerging hybrid with a polymer (LSP) has proven to be effective at microscale investigations and cost-effective with ease of operation at field-scale tests. Their application in carbonate oil reservoirs, which typically occur oil-wet, presents a particularly essential capacity given that over half of the global oil reserves are hosted in carbonate formation. However, modeling the mechanisms involved to predict and evaluate the performance of low salinity-based EOR at a large scale is complex and requires the integration of geochemistry in reservoir simulation to upscale the interfacial interactions of crude oil, brine, and rock observed at the micrometer scale. This study presents an integrated approach that combines MRST's polymer model with PHREEQC geochemical modeling to simulate LSWF at the reservoir scale. Using single-phase and multiphase experimental flooding data for validation, the coupled model was shown to accurately predict effluent ionic and oil recovery profiles. The simulation of LSWF and LSP both exhibited additional tertiary oil recovery, with LSWF and LSP showing 3 and 2%, respectively, which are consistent with previously reported field and core flooding results. Furthermore, the sequential application of formation water (FW), LSWF, and LSP flooding in secondary mode showed a high increase in oil recovery, with oil recovery percentages of 61, 20, and 19%, respectively. However, the FW results were 50% lower compared to regular core flooding due to upscaling limitations. The modeling of vertical and anisotropic permeability heterogeneity effects showed a positive synergy with low-salinity floodings, resulting in a 4% drop and 3 and 1% increase in FW, LSWF, and LSP, respectively. These findings demonstrate the potential of the coupled MRST-PHREEQC model in accurately simulating hydrogeochemical interactions during LSWF/LSP at the reservoir scale, providing valuable insights for the optimization of low salinity-based EOR strategies in carbonate reservoirs.

Environmental performance of eco‐design strategies applied to the building sector

AbstractThe application of eco‐design principles in the building sector is considered a promising way to mitigate its substantial environmental impacts. However, quantitative evidence for this mitigation potential is lacking. The objective of this study was to quantify the environmental performance of diverse eco‐design strategies when applied to the building sector. A macroscale model capable of simulating the future demand for housing and related material flows within the urban building stock was developed based on an existing building stock model. These material flows were used to build inventories for a consequential life cycle assessment and, in turn, to quantify the potential environmental consequences of introducing eco‐design strategies in the building sector, assessed across 16 impact categories. Model outputs have a high level of uncertainty but are still useful for decision‐making, given the model's simplicity and transparency. The main results show that impact reductions can be obtained from specific uses of wood and wooden products, for example, when used for the walls in high‐rise buildings, whereas using hempcrete for partition walls increases the impact. Although the use of adaptability or disassembly strategies can reduce impacts, this pay‐off can only be obtained after a long period of implementation. In summary, the present study provides new quantitative insights into the ability of eco‐design strategies to mitigate environmental impacts in the building sector.

Study on the Melt Rheological Characterization of Micro-Tube Gas-Assisted Extrusion Based on the Cross-Scale Viscoelastic Model.

In the micro-tube gas-assisted extrusion process, flow theories ignoring cross-scale viscoelastic variations fail to effectively characterize the rheological state of the melt. To investigate the impact of cross-scale viscoelastic variation on the quality of the micro-tube gas-assisted extrusion, a 3D multiphase flow extrusion model incorporating a double gas-assisted layer was developed. Subsequently, we modified the DCPP constitutive equations based on the cross-scale factor model. Both the traditional and gas-assisted extrusions were simulated under macroscale and cross-scale models using the Ansys Polyflow. Finally, using the established gas-assisted extrusion platform, extrusion experiments were conducted. The results indicate that, owing to the reduced melt viscosity under the cross-scale model, the deformation behavior of the melt is more pronounced than in the macroscale model. The cross-scale model's numerical results more closely match the experimental outcomes under the same parameters, thereby confirming the feasibility of the theoretical analysis and numerical simulation. Moreover, the predictive capability of the cross-scale model for the micro-tube gas-assisted extrusion is further validated through numerical and experimental analyses with varying parameters. It is demonstrated that the cross-scale viscoelastic variation is a critical factor that cannot be overlooked in the gas-assisted extrusion.

Correction: Homogenized Macroscale Model and Morphological Microscale Model to Understand the Varying Mechanical Properties of Scar Tissue of Hip Capsule Ligaments Grown Around Different Implant Materials

Correction: Homogenized Macroscale Model and Morphological Microscale Model to Understand the Varying Mechanical Properties of Scar Tissue of Hip Capsule Ligaments Grown Around Different Implant Materials

Multiscale Computational and Artificial Intelligence Models of Linear and Nonlinear Composites: A Review

Herein, state‐of‐the‐art multiscale modeling methods have been described. This research includes notable molecular, micro‐, meso‐, and macroscale models for hard (polymer, metal, yarn, fiber, fiber‐reinforced polymer, and polymer matrix composites) and soft (biological tissues such as brain white matter [BWM]) composite materials. These numerical models vary from molecular dynamics simulations to finite‐element (FE) analyses and machine learning/deep learning surrogate models. Constitutive material models are summarized, such as viscoelastic hyperelastic, and emerging models like fractional viscoelastic. Key challenges such as meshing, data variability and material nonlinearity‐driven uncertainty, limitations in terms of computational resources availability, model fidelity, and repeatability are outlined with state‐of‐the‐art models. Latest advancements in FE modeling involving meshless methods, hybrid ML and FE models, and nonlinear constitutive material (linear and nonlinear) models aim to provide readers with a clear outlook on futuristic trends in composite multiscale modeling research and development. The data‐driven models presented here are of varying length and time scales, developed using advanced mathematical, numerical, and huge volumes of experimental results as data for digital models. An in‐depth discussion on data‐driven models would provide researchers with the necessary tools to build real‐time composite structure monitoring and lifecycle prediction models.

Multiscale modeling of smectite illitization in bentonite buffer of engineered barrier system

With the increasing usage of nuclear energy, how to properly dispose nuclear waste becomes a critical issue. In this study, a multiscale modeling approach combining the experimental findings is presented to address the illitization process, its impact on transport properties, and system behavior of bentonite buffer in engineered barrier systems (EBS). Through the pore-scale modeling, reactive transport properties such as illite generation rate and effective diffusion coefficient of potassium ion as a function of porosity and temperature are quantified by employing the findings of hydrothermal reaction experiments of Bentonil-WRK. The capability of pore-scale modeling has been developed based on the Darcy-Brinkmann-Stokes equation, involving the processes of smectite illitization and clay swelling. Obtained reactive transport properties are utilized as input parameters for the macroscale modeling to predict the long-term behavior of bentonite buffer in EBS. As such, this study involves the whole workflow of quantifying the reaction parameters of smectite illitization through the hydrothermal reaction experiments, and numerically modeling the reactive transport process of smectite illitization in bentonite buffer of EBS from pore-scale to macroscale. The presented multiscale modeling findings are expected to provide reliable solution for safe nuclear waste disposal with EBS.

DLP printed 3D gyroid structure: Mechanical response at meso and macro scale

Rapid prototyping (RP) technology enables the fabrication of complex geometries, making lattice structures increasingly popular. Lattice structures, known as cellular materials, have garnered significant attention over the past two decades due to their ability to optimise mass distribution in components. These structures excel in mechanical properties, catering to energy absorption (bending-dominated structures) and structural performance (stretch-dominated structures). In this paper, we investigate the behaviour of stretch-dominated lattice structures using periodic surface models, specifically focusing on sheet-based Gyroid cells, to allow for a more efficient macroscale modelling. We study cells and scaffolds of different sizes, considering various triply periodic minimal surface thicknesses and relative densities ranging from approximately 0.2 to 0.65. We explore load applications in directions different from the unit cell's principal axes and analyse the strain rate effect on both bulk and cellular material. The lattice structures are manufactured using epoxy resin and digital light processing (DLP) technology. In the range of relative density investigated, both in quasi-static and dynamic conditions, a linear trend is observed for Young's modulus and compression yield strength. To extend the quasi-static results to the dynamic regime, we employ a more generalized normalization technique. This approach divides Young's modulus and compression yield strength by the behaviour of the base material at a specific strain rate, facilitating the correlation of mechanical properties across the two loading regimes. Based on experimental findings, we implemented and calibrated a bi-linear material model for describing, in macroscale, triply periodic minimal surface (TPMS) Gyroid structures. The model coefficients are parameterized with respect to relative density. In addition, the presented material law was compared with that proposed by Gibson-Ashby. Furthermore, we evaluated the anisotropy of both the base material and the unit cell. The first one is done by testing the 3D printed samples in directions different from the printing one, the latter by using the Zener factor. The anisotropy evaluation confirmed the isotropic behaviour of the unit cell within the range of relative density and test conditions investigated. Finally, we perform linear elastic 3D macroscopic and mesoscopic model simulations for combined shear-compression tests using the implemented bi-linear material model and the anisotropic stiffness matrix (obtained through the homogeneous formulation) for the macroscale, and the base material for the mesoscopic one. The results demonstrate the suitability of the proposed equivalent material model for studying the TPMS Gyroid structure in the elastic regime, both in quasi-static and dynamic states. This allows for an efficient FE modelling process of complex lattice structures.

Impact of a nanodroplet on liquid surfaces

The present study investigates impact of nanodroplets on liquid films with varied film thicknesses over hydrophilic to hydrophobic surfaces via molecular dynamics simulations. A new crown pattern, hollow crown, is observed on medium liquid films for nanodroplets, whereas it is not reported for millimeter-sized droplets. Holes (or hollows) are attributed to capillary vibration of a nanometer-thick liquid film. The occurrence of holes is inhibited effectively for deep liquid films because the cavity thickness is much larger than the amplitude of capillary vibration. Surface wettability has a significant influence on thin and medium liquid films for nanodroplets, whereas it only affects thin liquid films for macrodroplets because the range of solid–liquid intermolecular forces is comparable to the size of droplets when the size of droplets reduces to the nanoscale. Subsequently, the accuracies of the existing macroscale models for predicting the time-dependent crown radius of nanodroplets are tested by simulated results. The results show that the macroscale models cannot capture the time-dependent crown radius of nanodroplets. On the basis of energetics analysis, we prove that the failure of macroscale models is attributed to the distinct difference in viscous dissipation mechanisms between macroscale and nanoscale droplets.

Global Evaluation of Simulated High and Low Flows from 23 Macroscale Models

Abstract Macroscale hydrological/land surface models are important tools for assessing historical and predicting future characteristics of extreme hydrological events, yet quantitative understandings of how these large-scale models perform in simulating extreme hydrological characteristics remain limited. Here we evaluate simulated high and low flows from 23 macroscale models within three modeling experiments (i.e., 14 climate models from CMIP6, 6 global hydrological models from ISIMIP2a, and 3 land surface models from GLDAS) against observation in 633 unimpaired catchments globally over 1971–2010. Our findings reveal limitations in simulating extreme flow characteristics by these models. Specifically, we find that (i) most models overestimate high-flow magnitudes (bias range: from +15% to +70%) and underestimate low-flow magnitudes (bias range: from −80% to −20%); (ii) interannual variability in high and low flows is reasonably reproduced by ISIMIP2a and GLDAS models but poorly reproduced by CMIP6 models; (iii) no model consistently replicates the observed trend direction in high and low flows in over two-thirds of the catchments, and most models overestimate high-flow trends and underestimate low-flow trends; and (iv) CMIP6 and GLDAS models show timing biases, with early high flows and late low flows, while ISIMIP2a models exhibit the opposite pattern. Furthermore, all models performed better in more humid environments and noncold regions, with model structure and parameterization contributing more to uncertainties than climatic forcings. Overall, our results demonstrate that extreme flow characteristics simulated from current state-of-the-art macroscale models still contain large uncertainties and provide important guidance regarding the robustness of assessing extreme hydrometeorological events based on these modeling outputs. Significance Statement Macroscale hydrological and land surface models represent crucial tools for assessing historical trends and making predictions about future hydrological changes. Nevertheless, our current understanding of the quantitative performance of these large-scale models in simulating extreme hydrological characteristics remains limited. Here, we evaluate simulated high and low flows from 23 state-of-the-art macroscale models against observation in 633 unimpaired catchments globally over 1971–2010. Our results reveal important limitations in the extreme flow characteristics simulated from these models and provide important guidance regarding the robustness of assessing extreme hydrometeorological events based on these modeling outputs. The model evaluation performed herein serves as a pivotal, offering valuable insights to inform the development of the next generation of macroscale hydrological and land surface models.

Scaling from global to regional river flow with global hydrological models: Choice matters

High-resolution global flow discharge datasets are critical to understand the terrestrial water cycle and river ecosystem services. Recently, a number of global hydrological models have been developed to capture global river flow dynamics at locally relevant scales. However, the relative accuracy of these simulated flow discharges is largely unknown. In this paper, using the largest observed streamflow datasets from > 26,000 gauging stations, we evaluated the performance of monthly and sub-monthly flow variation (1980–2014) generated from five major global hydrological models, Catchment-based Macro-scale Floodplain model (CaMa-Flood), Global Flood Awareness System (GloFAS-reanalysis), Global Reach-level Flood Reanalysis (GRFR), PCRaster GLOBal Water Balance model (PCR-GLOBWB), and Water Global Assessment and Prognosis (WaterGAP). Significant spatial heterogeneity in model performance was identified. We found that estimates by all five discharge datasets have a relatively high correlation with the observations (medians > 0.6). But none of them showed adequate correlations between simulated and observed flows for systems in Southwest or Central U.S.A., South Africa, or South Australia. Across all models, overestimation of monthly mean flow was more common than underestimation and high flows at a sub-monthly scale were more accurately characterized than low flows. Performance of all models was poor in Africa and Oceania. No single model performed universally best at all gauging stations, but GRFR showed the best estimate at around 40 % of the locations. None of the models provided satisfying estimates for rivers and streams in arid regions. We also found a significant negative effect of flow regulation on the predictive accuracy of all models. Our study highlights the importance of thorough evaluation of global discharge datasets before their local and regional application and provides guidance for future enhancement of global hydrological models.

Hybrid modeling of a circulating fluidized bed boiler for development of a prediction and prescription system for power plant operation

A novel hybrid modeling system of a circulating fluidized bed boiler was developed in this study. The proposed approach combines a computational fluid dynamics model, practice-oriented macro-scale models, and a data-driven reduced order model to capture both the physical and empirical behaviors of the boiler. The application of various modeling strategies allowed for capturing features of the simulated process at various scales and for developing a fast and accurate prediction system. The use of the computational fluid dynamics model improved the predictions of the practice-oriented macro-scale models providing more detailed flow information and the use of the reduced order model allowed for reducing the computation time by a factor of 1350. The hybrid model and its submodels were validated against real measurement data. The validation confirmed good accuracy in predicting key process variables. The developed model is used as a prediction and prescription system to enable operators to optimize the boiler operation and prevent abnormal events. The hybrid system is used for a supercritical, once-through boiler in Łagisza power plant in Poland, however, the presented modeling strategy can be applied in other power plants, which can improve efficiency, reduce emissions, enhance boiler availability, and ultimately contribute to more sustainable energy systems.

Ballistic impact modeling of woven composites using the microplane triad model with meso-scale damage mechanisms

Existence of undulating fill and warp yarns in woven composite laminae introduces complex unit cell geometries and multi-scale interactions among the constituents. Due to these, the failure process involves various meso-scale constituent-level failure modes under complex loading scenarios such as ballistic impact. This can be challenging to model via conventional macro-scale damage tensor-based models. This challenge is tackled here via the adaptation of the previously developed multi-scale microplane triad model to ballistic impact of woven composites. The model can resolve meso-scale constituent level details (including yarn undulations) and predict not only the elastic constants of a woven lamina but also its fracturing behavior. In the present adaptation, only two damage laws are formulated, one for the fibers and one for the matrix. This enables the model to embody the correct values of the intralaminar mode I and II fracture energies of the woven lamina. The model is calibrated using constituent and lamina level test data, and then used to predict the ballistic impact behavior of a single plain-woven lamina under a wide range of projectile impact velocities. The model is demonstrated to predict very well the projectile residual (rebound and exit) velocities, the energy dissipation, the major failure modes of the lamina and the corresponding extent of damage, as well as the ballistic limit and deformation cone wave propagation speeds. The model’s simple, conceptually clear architecture, and computational efficiency represent a major advantage compared to existing damage tensor-based models. The model is also extended to multi-layer thick section woven laminate impact, where the analyses consider both intralaminar and interlaminar failures. The predictions are found to be comparable to those from MAT162, a commercially available material model in LS-Dyna, with much better computational efficiency. Via detailed sensitivity studies, it is demonstrated that the mode I and II intralaminar fracture energies of the lamina are a crucial model input, necessary for accurate predictions of ballistic impact. Not knowing these can introduce significant uncertainty and therefore, their characterization is an absolute must. Finally, the optimal meshing considerations as well as the advantages and limitations of the microplane triad model are discussed.

Mesoscale modeling of woven composite twisted structures combining digital element embedded model and affine transform

The mesoscale model with realistic yarn geometries could improve the accuracy of property prediction of woven composite structures. This paper aims to propose a novel mesoscale modeling method for the woven composite twisted structures. Firstly, the torsional deformation of the yarns in the unit cell model is simulated with high-fidelity using digital element fibers embedded into the matrix solid meshes. Then, the solid geometry model of the twisted composite structures is reconstructed from the digital element deformation model by combining the affine transforms. Finally, the elastic responses of the twisted composite structure under cantilever loading are predicted by assigning the element information of the established mesoscale model to the macroscale model. It is shown that the geometric morphology and predicted mechanical responses of the high-fidelity model are consistent with the experimental results. Furthermore, the effect of twist angles on the stiffness properties of the twisted composite structures is analyzed using the presented numerical method. The proposed digital modeling method could provide a guide for the early design of woven composite structures.

Analysis of coupled thermo-mechanical response and damage behaviour of curved ramp bridge deck pavement using a 3D multiscale method

A three-dimensional (3D) multiscale modelling approach was developed in this study, which considers a two-way coupling of material properties and mechanical responses between macroscale (pavement level) and mesoscale (mixture level) finite element (FE) models. Both thermal and mechanical properties at the two scales were linked through a homogenisation method, and the boundary response was transferred from the macroscopic target element to the mesoscale model using a mapping procedure. The results show that seasonal temperature variations have a significant effect on the coupled thermo-mechanical response within bridge deck pavement. In winter, the deck pavement is subject to tensile stresses, the maximum values of which mainly occur at the tire edges and the dual-tire clearance centre; while the deck pavement experiences compressive stresses in summer, and the stress difference within the asphalt concrete layer increases with the temperature.

Flow Mechanics in Ablative Thermal Protection Systems

Ablative thermal protection systems have experienced renewed interest in the past decade owing to the retirement of NASA's Space Shuttle fleet and the US presidential mandate to develop technologies that enable humans to explore space beyond low Earth orbit. Blunt body architecture for spacecraft and the use of ablators for thermal protection systems returned as the primary choice in mission planning. This review addresses current progress in modernizing predictive tools for ablative material response. Current theory development leverages progress made in the theory of flows in porous media. This development, combined with progress in experimental techniques and high-end computing, is enabling the development of 3D macroscale models with realistic closure coefficients derived from direct numerical simulations of 3D microscale geometries of actual materials. While flight data quantifying ablative material response remain sparse, the next decade will be one of exploration in which heatshield instrumented spacecraft will provide crucial flight data for refining and validating closure models.

Homogenization of a coupled electrical and mechanical bidomain model for the myocardium

We propose a coupled electrical and mechanical bidomain model for the myocardium tissue. The structure that we investigate possesses an elastic matrix with embedded cardiac myocytes. We are able to apply the asymptotic homogenization technique by exploiting the length scale separation that exists between the microscale where we see the individual myocytes and the overall size of the heart muscle. We derive the macroscale model which describes the electrical conductivity and elastic deformation of the myocardium driven by the existence of a Lorentz body force. The model comprises balance equations for the current densities and for the stresses, with the novel coefficients accounting for the difference in the electric potentials and elastic properties at different points in the microstructure. The novel coefficients of the model are to be computed by solving the periodic cell differential problems arising from application of the asymptotic homogenization technique. By combining both the mechanical and electrical behaviors, we obtain a macroscale model that highlights how the elastic deformation of the heart tissue is influenced and driven by the difference in the electric potentials at various points in the material.

Unlocking Efficiency in Radio-Frequency Heating: Eigenfrequency Analysis for Resonance Identification and Propagation Enhancement in Nigerian Tar Sands.

Nigerian bituminous tar sands are among the world's largest deposits of bitumen and heavy oil. They are estimated to contain 38-40 billion barrels of heavy oil and bitumen, spanning approximately 120 km in length and 4-6 km in breadth. With global commitments to net zero emissions and various energy transition plans, improvements in the recovery methods for heavy oil and bitumen are being sought. To address this, renewable energy electrothermal enhanced oil recovery is considered an eco-friendly alternative. In our study, we introduce a novel Reservoir-Waveguide-Debye model. This model explores the enhancement of penetration for radio-frequency electromagnetic (EM) waves, which can be generated from renewable energy sources. These waves facilitate the viscosity reduction of heavy oil and bitumen. Through a comprehensive 2D numerical simulation employing the bulk properties of bituminous tar sands, we assess the propagation of EM fields within porous media. We utilize the industrial heating radio-frequency bandwidth of 1-60 MHz to conduct frequency domain investigations. Our analysis delves into propagation modes using eigenfrequency analysis, pinpointing the EM resonance of the tar sands. Furthermore, we investigate the impact of mesh refinement on the EM eigenfrequencies of porous media at both the microscale (400 μm) and macroscale (100 m in radial distance). Our results demonstrate the occurrence of resonance phenomena at complex eigenfrequencies around 27.12 and 54.24 MHz in both the microscale and macroscale models of the bituminous sands. This breakthrough research offers promising insights into harnessing renewable energy-driven EM waves for efficient thermal recovery processes in the Nigerian bituminous tar sands, thus fostering sustainable and eco-friendly energy solutions.

Multiphysics-Lattice Discrete Particle Model: possible strategies for upscaling

The optimization of civil infrastructure maintenance and management is a challenging task, littered of open issues requiring the synergic development of effective structural health monitoring systems and reliable models to be addressed. Relevant to concrete structures, models cannot disregard the multi-physics nature of the problem: moisture and heat transport phenomena in uncracked and cracked conditions, the ingress of aggressive agents, and the ensuing chemical reactions - that the latter may trigger - heavily affect the mechanical performance. Most of the mentioned processes happen at a scale typically smaller than the structural one. Then, it is also necessary to perform multiscale analysis, capable of adapting structural models to the insights resulting from lower scale analyses. In the last decade, Multiphysics-Lattice Discrete Particle Model (M-LDPM) has been successfully adopted to model a wide range of phenomena in civil engineering involving concrete structural members: ageing, environment-induced degradation, shrinkage, creep, and usage of advanced construction materials. Furthermore, the discrete nature of the model has shown the capability of predicting the cracking patterns accurately. However, such a comprehensive and accurate model simulates the material at the mesoscale, and the path towards the exploitation of the insights resulting from lower-scale modelling at the structural level is paved of computational and theoretical burdens. In this work, a review of the state-of-the-art concepts that allow upscaling M-LDPM is presented. The aim is to explore alternatives for the formulation of computationally efficient macroscale models that leverage on both the predictive quality of M-LDPM in capturing and predicting the material constitutive behaviour, and the computational affordability that features the classical Finite Element Method for the structural analysis of complex systems.

Multiscale Analysis of Composite Structures with Artificial Neural Network Support for Micromodel Stress Determination.

Structures made of heterogeneous materials, such as composites, often require a multiscale approach when their behavior is simulated using the finite element method. By solving the boundary value problem of the macroscale model, for previously homogenized material properties, the resulting stress maps can be obtained. However, such stress results do not describe the actual behavior of the material and are often significantly different from the actual stresses in the heterogeneous microstructure. Finding high-accuracy stress results for such materials leads to time-consuming analyses in both scales. This paper focuses on the application of machine learning to multiscale analysis of structures made of composite materials, to substantially decrease the time of computations of such localization problems. The presented methodology was validated by a numerical example where a structure made of resin epoxy with randomly distributed short glass fibers was analyzed using a computational multiscale approach. Carefully prepared training data allowed artificial neural networks to learn relationships between two scales and significantly increased the efficiency of the multiscale approach.

Recent advances in well-posed Eulerian models for polydisperse multiphase flows

The current state-of-the-art for computational modeling of polydisperse multiphase flows is reviewed and future research directions are discussed. Physics-based computational models at three distinct levels of abstraction: the microscale, mesoscale and macroscale; are discussed and compared. Special emphasis is placed on the relationship between the models at different scales and on how information from the finer scales is used to provide closures at the coarser scales. For disperse multiphase flows, it is argued that the passage from a direct-numerical simulation at the microscale to the kinetic description at the mesoscale is the crucial step for ensuring the validity of the macroscale model. In particular, the passage from the microscale to the mesoscale requires physics-based closures, while the passage from the mesoscale to the macroscale requires mathematical closures. The choices made in the physical and mathematical closures of the spatial fluxes and coupling terms will determine whether the Eulerian model is well-posed. In addition, the use of quadrature-based moment methods for polydisperse particles is presented as an efficient macroscale closure when dealing with a distribution of particle sizes. Examples of monodisperse and polydisperse multiphase flows are provided for cases where the fluid phase is compressible (high speed) and incompressible (low speed).