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A computationally efficient state estimation method for lithium-ion (Li-ion) batteries is proposed based on a degradation-conscious high-fidelity electrochemical-thermal model for advanced battery management systems. The computational burden caused by the high-dimensional nonlinear nature of the battery model is effectively eased by adopting an ensemble-based state estimator using the singular evolutive interpolated Kalman filter (SEIKF). Unlike the existing schemes, it shows that the proposed algorithm intrinsically ensures mass conservation without imposing additional constraints, leading to a battery state estimator simple to tune and fast to converge. The model uncertainty caused by battery degradation and the measurement errors are properly addressed by the proposed scheme as it adaptively adjusts the error covariance matrices of the SEIKF. The performance of the proposed adaptive ensemble-based Li-ion battery state estimator is examined by comparing it with some well-established nonlinear estimation techniques that have been used previously for battery electrochemical state estimation, and the results show that excellent performance can be provided in terms of accuracy, computational speed, as well as robustness.

Despite the extensive research already done on laminar flows with porous boundaries, polar flows bounded by cylinders have not yet been studied. This paper investigates the polar laminar flow for an incompressible fluid located in a porous annular pipe and driven by suction-injection at the walls. The fluid being confined between the cylinders with zero axial velocity, it is proven that the flow takes place in the polar plane with conservation of mass if an incoming flow exists in the same plane to compensate the mass of fluid extorted by suction. So, one of the cylinders undergoes the suction, and the other the injection. Suitable boundary conditions for both cylinders are then found. The problem depends on the Reynolds number, the pipe gap ratio, and the pore density and surface ratios. The method of solution utilizes the shooting technique including the Runge-Kutta and Newton-Raphson algorithms. Radial flows are found as a possible solution. When the flow is not radial, the patterns of the acceptable streamlines highlight a particular zone in which the fluid is at rest, bounded by two singular streamlines and the downstream cylinder. The flow velocity is determined. Physical understandings of the flow are derived.

To account for partially premixed process in combustion, a novel transported multi-regime flamelet model, which gives local contributions of premixed and non-premixed regimes, is proposed with a theoretical derivation of the governing equation of the premixed weighting coefficient. The model intrinsically ensures mass conservation and physically incorporates transport properties. Thus, it avoids artificial treatment that has to be employed in algebraic multi-regime flamelet models. An ethylene-fueled combustion in a scramjet model combustor is simulated using the transported multi-regime flamelet model. The pressure distribution that characterizes the flame anchoring position and wave distribution is well predicted by the model. It is observed that the premixed regime is distributed mainly in the recirculation zone upstream of the fuel orifice, inside the cavity and close to the lower wall. Besides, there is an apparent instantaneous distribution of the premixed regime in the fuel jet wake, which is attributed to the enhanced premixing by transient vortices. However, the overall contribution of the premixed regime is not as great as that of the non-premixed one, indicating that combustion is non-premixed dominated. The evolution of the OH concentration shows that the OH first emerges close to the cavity ramp. After that, it propagates upstream into the cavity and meanwhile downstream along the lower wall of the expanding section. The isoline of the premixed weighting coefficient used to mark the temperature interface reveals that the premixing can enhance combustion. In contrast, numerical oscillations and a pseudo regime distribution indicating a premixed-dominated combustion that conflicts the physics is observed in a reference simulation using an algebraic multi-regime flamelet model. It is thus demonstrated that the transported multi-regime flamelet model is superior over the algebraic one in the prediction of partially premixed combustion with multi-regimes involved.

Nonlinear contaminant transports through porous media are important in many scientific and engineering applications. In this paper, we develop and analyze fourth-order block-centered compact difference scheme (BCCDS) for the nonlinear contaminant transport equations with adsorption process in porous media. Based on block-centered mesh, a fourth order compact difference scheme of solution and its flux is derived. We prove the mass conservation of the proposed scheme and its unconditional stability. We analyze the convergence and obtain the fourth-order error estimate under the smooth regularity of exact solution. Numerical experiments are presented to show the performance of the schemes.

The Gauss Jordan method is used in this study to equalize chemical reactions using a system of linear equations. One of the most common topics in Chemistry is balancing chemical reaction equations. Students typically struggle with balancing the chemical equation and find it difficult to understand; sometimes teachers struggle as well to balance chemical equations. The results of the equation balancing comply with the law on the conservation of matter and confirm that the existing methods for balance of chemical equations do not contradict each other. To solve the mathematical problem, the Gauss-Jordan method was used. Any chemical reaction can be handled using this method by certain reactants and products. we can add several other features to the python application which can check whether the chemical equation is already balanced or not, we can also categorise the type of the chemical reaction.

We carry out error estimates for a linear, second-order, unconditionally energy stable, semi-discrete time stepping scheme, which is based on the Lagrange Multiplier approach and could also be viewed as a special case of the invariant energy quadratization approach, for the modified phase field crystal equation. At each time step, the proposed scheme only requires solving several linear equations. Rigorous proofs are presented to demonstrate the unique solvability, mass conservation, and unconditional energy stability of the scheme. Various numerical experiments in 2D and 3D are performed to validate the accuracy, unconditional energy stability and mass conservation of the proposed numerical strategy.

In this paper, a methodology for modelling two-phase flows based on a conservative level set method in the framework of finite volume method is presented. The novelty of the interface capturing method used here lies on the advection of level set which is solved with a WENO scheme and is corrected with a novel re-initialisation method for retaining its signed distance function character. The coupling with the volume of fluid method is done with a simple algebraic approach and with the new algorithm the accumulated mass conservation errors remain reasonably low. The paper presents a unique coupling between the level set method and the Eulerian-Lagrangian-Spray-Atomisation approach for modelling spray dispersion in liquid atomisation systems. The method is shown to have good accuracy providing similar results to other numerical codes for the classical tests presented. Preliminary results are also shown for three-dimensional simulations of the primary break-up of a turbulent liquid jet obtaining results comparable to direct numerical simulations. Consequently, the coupled method can be used for simulating various two-phase flow applications offering an accurate representation of the interface dynamics.

Due to the elevated operating temperatures (800–1000 °C) of tubular solid oxide fuel cells (SOFC), severe thermal stresses are produced during their operation. Functionally graded materials (FGMs) are used in anodes and cathodes to reduce the specific thermal stresses. The use of FGMs compensates for the effect of any sudden shift in the coefficient of thermal expansion of these electrodes with respect to the electrolyte. In this study, the tubular SOFC efficiency, performance, and produced thermal stresses were numerically investigated. A 3D numerical model that includes the equations of mass conservation, momentum, charging transport, and electricity was developed. These coupled equations of the electrochemical phenomena were solved using ANSYS 19.1-Fluent Solver. The temperature values that were obtained were sequentially introduced into the structural finite element model as body loads, and the model was solved with ANSYS 19.1-MAPDL Solver. The numerical model was validated against previously published experimental results. For both electrodes, the FGM was identified by a grading index “m.” The use of the FGM for the anode and cathode instead of conventional electrodes increased the tubular SOFC efficiency and reduced the thermal stress. Optimum results were obtained at grading index m = 2.0, with the cell output increased by 8 % and induced thermal stresses well below the yielding levels.

With the development of gas well exploitation, the calculation of wellbore with single-phase state affected by single factor cannot meet the actual needs of engineering. We need to consider the simulation calculation of complex wellbore environment under the coupling of multiphase and multiple factors, so as to better serve the petroleum industry. In view of the problem that the commonly used temperature and pressure model can only be used for single-phase state under complex well conditions, and the error is large. Combined with the wellbore heat transfer mechanism and the calculation method of pipe flow pressure drop gradient, this study analyzes the shortcomings of Ramey model and Hassan & Kabir model through transient analysis. Based on the equations of mass conservation, momentum conservation and energy conservation, and considering the interaction between fluid physical parameters and temperature and pressure, the wellbore pressure coupling model of water-bearing gas well is established, and the Newton Raphael iterative method is used for MATLAB programming. On this basis, the relationship between tubing diameter, gas production, gas–water ratio, and wellbore temperature field and pressure field in high water-bearing gas wells is discussed. The results show that the wellbore temperature pressure coupling model of high water-bearing gas well considering the coupling of gas–liquid two-phase flow wellbore temperature pressure field has higher accuracy than Ramey model and Hassan & Kabir model, and the minimum coefficients of variation of each model are 0.022, 0.037 and 0.042, respectively. Therefore, the model in this study is highly consistent with the field measured data. Therefore, the findings of this study are helpful to better calculate the wellbore temperature and pressure parameters under complex well conditions.

This work is motivated by the industrial process of air (or dry) atomization of slag, where a high-speed jet of air impinges onto a free-falling stream of molten slag and disintegrates it into small droplets. The droplets solidify to form slag powder particles which may be used in applications such as sand blasting, roof shingles, and asphalt. Since different applications require slag powders with different ranges of particle size, controlling the particle size is of essence. A mathematical model is presented for the atomization process, which relates the Sauter Mean Diameter (SMD or $${D}_{32}$$ ) of molten slag droplets to the atomizer design and operating parameters. The model solves a set of non-linear governing equations, including conservation of mass, momentum, and energy, in the integral form using an iterative method. This universal model can be applied to any combination of gas-liquid, and thus the model is validated with existing experimental results for air atomization of a water stream. A strong agreement exists between the calculated and experimentally measured values of $${D}_{32}$$ . It is also found that at a constant air flowrate, the liquid flowrate affects the $${D}_{32}$$ of droplets and the opening angle of the spray; the former is the main output parameter, and the latter is an intermediate parameter.

In the present work a numerical study based on discrete multiphase approach, Lagrangian approach, is proposed to investigate and predict the trajectories of nanoparticles- filled fluid (nanofluid) infiltrated around a staggered microfiber matrix. The trajectory of the nanoparticle has been predicted by integration the force balance on it in a Lagrangian references frame during its motion through the fluid. The governing integral equations for the conservation of mass, momentum and energy have been solved in a segregated numerical fashion by a Control-Volume-Based Finite-Element Method. The nanoparticles trajectories and their interactions with fluid flow and microfiber walls have been predicted showing undesirable sticking tendency of the nanoparticles on the microfiber walls. To avoid this tendency, the contribution of Marangoni shear stress has been introduced coupled with a temperature difference between the fluid flow and the microfiber walls.

Surface texturing is a viable technique to enhance the tribological performance of sliding interacting contacts. Single-scaled surface textures exhibit better tribological performance only at hydrodynamic lubrication regime (fluid film pressure) but not in mixed lubrication regime where fluid film pressure and asperity contact pressure co-exists. In most of the machinery with the increase in load and/or decrease in speed, there is a shift of lubrication regime from hydrodynamic to mixed lubrication. To address this, the present work proposed a multi-scale (a combination of shallow and deep) textures concept. A numerical model is developed to study its effect on the tribological characteristics of parallel sliding contacts by considering mixed lubrication regime and mass-conservative cavitation condition. It has been observed that multi-scaled textures exhibit superior results in comparison with single-scaled textures. Moreover, improved tribological characteristics are observed when shallow surface textures are placed first towards the fluid inlet flow.

Even though the Wurster technology is commonly used in the pharmaceutical industry for applying coating to beads, additional research work is still necessary to fully understand and control the process. Various simulation approaches have been used extensively in the recent years to investigate different fluidized beds, with and without spray application. The Computational Fluid Dynamics- Discrete Element Method (CFD-DEM) coupled approach is especially suitable to simulate the coating process because it resolves both the fluid and granular flow, and provides detailed particle-scale information. This paper primarily highlights the ability of the CFD-DEM coupled code to capture the thermodynamics and water mass loading of the gas phase in the Wurster coating application by directly comparing the experimental results with the CFD-DEM simulation results, for four different experimental runs and unscaled particle size. It also reports on the four specially designed experiments, giving the measurements of the air temperature and humidity at four points in the coater. The code is verified as well, using a simple simulation test case, with the objective of ensuring the energy and mass conservation in the CFD-DEM communication protocol. The paper also presents the time-averaged contour plots of temperature, humidity and particle volume fraction distribution for four different experiment/simulation cases and provides insights into their spatial distribution in the Wurster coater.

The inclined magnetohydrodynamic (MHD) unsteady flow and heat transfer of Casson hybrid nanofluid (HNF) due to porous stretching sheet is investigated. In the present paper we analyze the Casson fluid unsteady flow over permeable flat plate in the presence of inclined magnetic field and heat transfer of fluid with the effect of thermal radiation. The conservation of mass, conservation of momentum and thermal equations are non-dimensional into the system of nonlinear ODEs by taking the suitable similarity transformation. An exact analytical solution is obtained for velocity. The energy equation in the presence of inclined magnetic field and radiation is a differential equation with variable coefficients, which is transformed to an incomplete gamma function using a new variable and using the Rosseland approximation for the radiation. The governing differential equations are solved analytically and the effects of various parameters on velocity profiles, skin friction coefficient, temperature profile and wall heat transfer are presented graphically. There is an enhancement in heat transfer and pressure drop by usage of HNF. The variations in velocity and temperature profiles with respect to different various pertinent physical parameters. An increase of the mass transpiration (suction) parameter intensity increases the skin friction, which consequently improves the heat transfer enhancement and reduces the HNF temperature. Furthermore, the skin friction coefficient increases due to mass suction and MHD in the stretching sheet, whereas the rate of heat transfer decays. The results have possible technological applications in liquid-based systems involving stretchable materials.

This paper presents a new method for modeling rarefied gas flows based on hybridization of direct simulation Monte Carlo (DSMC) and discrete velocity method (DVM)-based quasi-particle representatio...

Laser surface texturing can improve the surface properties of the metallic components. In this work, surface texturing has been carried in a powder bed fusion of Inconel 718 (IN718) rather than material removal process. A 2D finite element method (FEM) has been built to simulate the thermo-fluidic dynamics of surface texturing, incorporating the phase-field method in the preplaced IN718 powder. The temperature and induced velocity fields have been predicted using transient heat transfer and fluid flow based on the conservation of mass, momentum, and energy in the melt pool. Furthermore, the roles of driving forces such as Marangoni force, recoil pressure, and thermal buoyancy force on the melt pool behavior have been evaluated. Micro-textures were developed using laser on the powder bed by using different scanning patterns, such as line, circle, hatch and convex dimple. The effect of process parameters (pitch distance, number of pulses and number of layers) on the surface hydrophobicity were evaluated by measuring the contact angle, where the convex dimple texture exhibited the maximum contact angle. The hydrophobicity was affected by the ripples (2nd level of roughness) on the surface, which increased with an increase in number of pulses.

Acidizing in carbonate formations is an inevitable stimulation treatment method for oil and gas wells. In the limestone, acidizing stimulation makes capillary wormholes to increase fluids flow reservoir production. The pore volume to breakthrough number is one of the main indexes for recognizing the wormhole structure. Therefore, finding the pore volume to breakthrough number is one of the main goals in the limestone acidizing. Obtaining this number is always required for experimental works, which needs time, energy and cost. The purpose of this research is to develop an empirical method to estimate an acceptable result for this number merely by implementing limestone core and acid properties without any experimental work. In order to create a wormhole, an empirical method is developed using the law of conservation of mass considering that the core of limestone as an isolated package and the overall mass is constant in this package in the acidizing period. Also, to develop the mathematical section, the Damkohler number is used. Since this number must be calculated experimentally, a constant number is created in the model to eliminate the Damkohler number. An average accuracy of 92.31% is obtained for the developed empirical model by comparing the results obtained from the other three experimental and numerical works. This study conclusively provides a thoroughly empirical method for estimating a high accuracy of the pore volume to breakthrough number by only using known physical properties limestone core and acid.

To describe the long-term coupled behaviour of landfilled municipal solid waste (MSW), this paper proposes a numerical model based on the theories of the conservation of mass, momentum and energy of porous media over a three-phase solid–liquid–gas system. Compared with currently available coupled models, the proposed model can simultaneously simulate such physical processes as phase change, dissolution of the gas phase, the diffusion of its components, evaporation in the liquid phase and changes in the pH of leachate, as well as its solute migration. The finite-volume method was used to numerically discretise the governing equations, with a sequentially iterative technique used for the numerical model of the solution. The corresponding computer code was formulated on the open-source platform OpenFoam. The model was then used to simulate the famous MSW degradation consolidating anaerobic reactor experiment conducted at Southampton University, where the results generally agreed well with the experimental data. The proposed model was also applied to capture spatial and temporal variations in the skeleton of MSW, leachate and landfill gas in a simplified two-dimensional landfill. Overall, the work here provides a basic coupled framework for simulating the long-term behaviours of landfilled MSW. It can be improved upon in future research by implementing other, more reasonable, constitutive relations of MSW.

This article analyzes existing installations for active ventilation of grain (further in the article:AVG) in containers (bunkers, silos), identifies their main disadvantages. Experimental study has been carried out to assess the technological efficiency of existing installations for AVGduring stationary storage in a container. As a result of the analysis of the obtained results of the experimental study, the cause of the inhomogeneous temperature field inside the grain mound was revealed due to the uneven distribution of the air flow (working agent) in the intergrain space. When designing the air distribution channel of the installation, the need to comply with the law of conservation of mass for a continuous medium, for example, an air flow, was not taken into account. A ventilated bunker with a rational design of an installation for active ventilation of grain has been proposed. The principal difference between the bunker and the existing ones lies in the method of uniform distribution of the air flow inside the grain mound. The installation for the implementation of this method includes two channels designed for injecting air into the mound and removing the exhaust air together with the evaporated moisture when drying the grain using the active ventilation method. The law of conservation of mass is observed due to the cone-shaped design of the air distribution channels, as a result of which a uniform temperature field and humidity are created in the intergrain space of the mound.

Numerical methods that are mass conservative, computationally stable, and efficient are essential for simulating multiphase flow in fractured porous reservoirs. In this paper, a fully mass conservative numerical method that meets these requirements is proposed and analyzed. Unlike in the implicit pressure and explicit saturation (IMPES) method, in this method, the pressure and saturation equations are solved sequentially in each iteration step. In this framework, the calculation of the saturation-related parameters no longer depends on the initial conditions of the current time step, but on the results of the current and previous iterations. Through this treatment, the discontinuities of the saturation and capillary pressure in the pre- and post-two time steps can be overcome to achieve fully mass conservation. Two numerical examples are designed to verify the robustness and efficiency of the presented method. The numerical results indicate that this new method is fully mass conservative, computationally more stable, and more efficient than the IMPES method. Furthermore, the proposed method is suitable not only for reservoirs with homogeneous permeability distributions but also for reservoirs with heterogeneous permeability distributions, which greatly improves the applicability of the new method.

The encapsulation technique of phase change materials in the nanodimension is an innovative approach to improve the heat transfer capability and solve the issues of corrosion during the melting process. This new type of nanoparticle is suspended in base fluids call NEPCMs, nanoencapsulated phase change materials. The goal of this work is to analyze the impacts of pertinent parameters on the free convection and entropy generation in an elliptical-shaped enclosure filled with NEPCMs by considering the effect of an inclined magnetic field. To reach the goal, the governing equations (energy, momentum, and mass conservation) are solved numerically by CVFEM. Currently, to overcome the low heat transfer problem of phase change material, the NEPCM suspension is used for industrial applications. Validation of results shows that they are acceptable. The results reveal that the values of N u ave descend with ascending Ha while N gen has a maximum at Ha = 16 . Also, the value of N T , MF increases with ascending Ha . The values of N u ave and N gen depend on nondimensional fusion temperature where good performance is seen in the range of 0.35 < θ f < 0.6 . Also, Nu ave increases 19.9% and ECOP increases 28.8% whereas N gen descends 6.9% when ϕ ascends from 0 to 0.06 at θ f = 0.5 . Nu ave decreases 4.95% while N gen increases by 8.65% when Ste increases from 0.2 to 0.7 at θ f = 0.35 .

It is well known that the classic Allen-Cahn equation satisfies the maximum bound principle (MBP), that is, the absolute value of its solution is uniformly bounded for all time by certain constant under suitable initial and boundary conditions. In this paper, we consider numerical solutions of the modified Allen-Cahn equation with a Lagrange multiplier of nonlocal and local effects, which not only shares the same MBP as the original Allen-Cahn equation but also conserves the mass exactly. We reformulate the model equation with a linear stabilizing technique, then construct first- and second-order exponential time differencing schemes for its time integration. We prove the unconditional MBP preservation and mass conservation of the proposed schemes in the time discrete sense and derive their error estimates under some regularity assumptions. Various numerical experiments in two and three dimensions are also conducted to verify the theoretical results.

Recently, Zou et al. (2020a) published a theoretical analysis on the radial flow of a Bingham fluid, where they argued that the classical analysis by Dai and Bird (1981) violates the mass conservation. The present discussion aims to clarify this conflict between those two studies. It is noted that Zou et al. (2020a) presumed the gap-wise mass flux is negligible in the mass conservation equation, while Dai and Bird (1981) did not require so in their model, and this is found to be the origin of the conflict. In fact, Dai and Bird (1981)’s model is shown to not violate the mass conservation. Therefore, those two models should be viewed as separate models derived from different perspectives. Details of the major difference between the two models are discussed.

In this paper, we extend the long-wave theory for the free surface dynamics of the thin non-Newtonian second-grade fluid (ANZIAM J 60(2): 249–268, 2018) over the stretching sheet by the inclusion of thermo-capillarity and the variable fluid properties effect in the systematic long-wave theory framework. The two-dimensional flow of non-Newtonian fluid over a non-porous heated stretching sheet is described by the conservation of mass, momentum, and energy equations with free surface and no-slip boundary conditions. From standard long-wave theory expansion technique in terms of the small aspect ratio of the fluid layer, we derive the transient equation systematically to describe the free surface dynamics of the thin-liquid film. We apply the finite volume method with implicit flux discretization for numerical investigation of the effects of thermocapillary forces, non-Newtonian parameter, and variable fluid properties. The investigation reveals that the Newtonian fluid with variable viscosity property exhibits faster thinning in comparison to the second-grade non-Newtonian fluid concerning the prescribed temperature at the sheet and the stretching rate. Furthermore, under constant fluid properties assumptions, the derived non-Newtonian thin-film model decouples from the thermal problem and reduces to the isothermal viscous model of Santra and Dandapat (Z Angew Math Phys 60(4): 688–700, 2009).

In this work, we consider an online enrichment procedure in the context of the Generalized Multiscale Finite Element Method (GMsFEM) for the two-phase flow model in highly heterogeneous porous media. The coefficient of the pressure equation is referred to as the permeability and is the main source of heterogeneity within the model. The elliptic pressure equation is solved using online GMsFEM, which is coupled with a hyperbolic transport equation where local conservation of mass is necessary. To satisfy the conservation property, we aim at constructing conservative fluxes within the space of multiscale basis functions through the use of a postprocessing technique. In order to improve the accuracy of the pressure and velocity solutions in the online GMsFEM, we apply a systematic online enrichment procedure. The increase in pressure accuracy due to the online construction is inherited by the conservative flux fields and the desired saturation solutions from the coupled transport equation. Despite the fact that the coefficient of the pressure equation is dependent on the saturation which may vary in time, we construct an approximation space using the absolute permeability field (λ(S) = 1) and no further basis updates follow. Numerical results corresponding to three different types of heterogeneous permeability coefficients are exhibited to show the performance of the proposed methodology.

A method for infering bed topography beneath glaciers from surface measurements (elevation from altimetry and velocity from InSAR) and sparse thickness measurements is developed and evaluated. The method is based on an original non-isothermal Reduced Uncertainty (RU) version of the Shallow Ice Approximation (SIA) equation that natively incorporates the surface measurements. The flow model has a single dimensionless multi-physics parameter γ. This parameter takes into account the basal slipperiness and the variable vertical rate factor profiles, thus the vertical thermal variations. The inversions are based on three steps involving: an Artificial Neural Network (ANN) and two Variational Data Assimilation (VDA) processes. The ANN-based stage aims at estimating the multi-physics number γ from the thickness measurements; the resulting estimator is remarkably robust. The full inversion method is valid for half-sheared flows (presenting a moderate basal slipperiness): it can be applied to inland ice-sheets areas. Also these estimates connect continuously with estimates from mass conservation only, i.e. with areas of sliding flows. Numerical results are presented for areas of the East Antarctica Ice Sheet where bed elevation can be very uncertain (Bedmap2 values). Estimates are valid for wavelengths longer than $\sim 10 \bar h$ (due to the long wave assumption, shallow flow model) with resolution at $\sim \bar h$ ( $\bar h$ a characteristic thickness value).

Lifetime assessment of hollow cathode (HC) sources is an experimentally demanding process, due to the large amount of hours space qualification requires. In this Paper, we present a one-dimensional...

We present the WRF-GC model v2.0, an online two-way coupling of the Weather Research and Forecasting (WRF) meteorological model (v3.9.1.1) and the GEOS-Chem model (v12.7.2). WRF-GC v2.0 is built on the modular framework of WRF-GC v1.0 and further includes aerosol–radiation interaction (ARI) and aerosol–cloud interaction (ACI) based on bulk aerosol mass and composition, as well as the capability to nest multiple domains for high-resolution simulations. WRF-GC v2.0 is the first implementation of the GEOS-Chem model in an open-source dynamic model with chemical feedbacks to meteorology. In WRF-GC, meteorological and chemical calculations are performed on the exact same 3-D grid system; grid-scale advection of meteorological variables and chemical species uses the same transport scheme and time steps to ensure mass conservation. Prescribed size distributions are applied to the aerosol types simulated by GEOS-Chem to diagnose aerosol optical properties and activated cloud droplet numbers; the results are passed to the WRF model for radiative and cloud microphysics calculations. WRF-GC is computationally efficient and scalable to massively parallel architectures. We use WRF-GC v2.0 to conduct sensitivity simulations with different combinations of ARI and ACI over China during January 2015 and July 2016. Our sensitivity simulations show that including ARI and ACI improves the model's performance in simulating regional meteorology and air quality. WRF-GC generally reproduces the magnitudes and spatial variability of observed aerosol and cloud properties and surface meteorological variables over East Asia during January 2015 and July 2016, although WRF-GC consistently shows a low bias against observed aerosol optical depths over China. WRF-GC simulations including both ARI and ACI reproduce the observed surface concentrations of PM2.5 in January 2015 (normalized mean bias of −9.3 %, spatial correlation r of 0.77) and afternoon ozone in July 2016 (normalized mean bias of 25.6 %, spatial correlation r of 0.56) over eastern China. WRF-GC v2.0 is open source and freely available from http://wrf.geos-chem.org (last access: 20 June 2021).

It is still a challenging task to get a satisfying numerical solution to the time-dependent Nernst-Planck (NP) equation, which satisfies the following three physical properties: solution nonnegativity, total mass conservation, and energy dissipation. In this work, we propose a structure-preserving finite element discretization for the time-dependent NP equation combining a reformulated Jordan-Kinderlehrer-Otto (JKO) scheme and Scharfetter-Gummel (SG) approximation. The JKO scheme transforms a partial differential equation solution problem into an optimization problem. Our finite element discretization strategy with the SG stabilization technique and the Fisher information regularization term in the reformulated JKO scheme can guarantee the convexity of the discrete objective function in the optimization problem. In this paper, we prove that our scheme can preserve discrete solution nonnegativity, maintain total mass conservation, and preserve the decay property of energy. These properties are all validated with our numerical experiments. Moreover, the later numerical results show that our scheme performs better than the traditional Galerkin method with linear Lagrangian basis functions in keeping the above physical properties even when the convection term is dominant and the grid is coarse.

In this work we propose a method for mini-frac analysis via the direct numerical modeling for permeability and closure stress determination. The idea is to adjust the model parameters to match the simulated and field pressure curves by the virtue of the optimization algorithm to automatize the routine. To this end, the Planar 3D hydraulic fracturing model is improved to take into account the wellbore storage, fracture initiation and pumping through a finite perforation interval. The reservoir mechanical behavior is based on Biot’s equations naturally coupled with the mass conservation law and force balance in the fracture and wellbore. This model is capable to describe all the pressure curve features from the fracture initiation up to the after closure filtration. The optimization workflow is based on Levenberg–Marquardt algorithm with Jacobi matrix calculated via a direct differentiation method. The numerical stability and performance of the inverse problem solution is verified. The pressure curve sensitivity analysis is conducted and the impact of the parameters’ uncertainties on the pressure change is calculated. The proposed method is applied to a field case and compared with classical mini-frac methods. We demonstrate that the wellbore storage impact governs the pressure increase during the fracture initiation and prevents the steep pressure decline after closure. We also show that the shortening of the perforation length generates additional pressure support at the end of and after the fracture closure. The recovered permeability and closure stress appears to be stable in presence of uncertainties in Young’s modulus and Biot’s coefficient.

Submarine landslides are a major geohazard among worldwide continental slopes, posing significant threats to offshore infrastructure, marine animal habitats and coastal urban centres. This study establishes an original numerical package for time-efficient modelling of the entire submarine landslide evolution covering the pre-failure shear band propagation, slab failure and post-failure dynamics. The numerical scheme is based on the conservation of mass and the conservation of momentum and combines the shear band propagation theory and the depth-integrated method, with the consideration of the drag force from the ambient water. Shear band propagation in the weak layer and slab failure in the sliding layer are controlled by the strain softening and rate dependency of the corresponding undrained strength parameters. The post-failure behaviour in the sliding layer, such as retrogression upslope and frontally confined and frontally emergent mechanisms downslope, is also simulated. The numerical results from the proposed method are comparable to the analytical solutions and the large deformation finite element analysis. Application of this method to a back analysis of the St. Niklausen slide in Lake Lucerne reproduced the observed shape of the mass transport deposits, the position of the main scar and the travel distance. Because of its easy implementation and efficiency, the proposed numerical method for modelling of submarine landslides seems promising for practical applications., Landslides, 18 (9), ISSN:1612-510X

In this study, a linearized locally conservative scheme, based on using a weak Galerkin (WG)-mixed finite element method (MFEM), is developed for the Poisson–Nernst–Planck (PNP) system. In the dual-mixed formulation of the PNP equation, in addition to the three unknowns of concentrations p , n and the potential ψ , their fluxes, namely, σ p = ∇ p + p σ ψ and σ n = ∇ n − n σ ψ and σ ψ = ∇ ψ are introduced. These fluxes have an essential role in specifying the Debye layer and computing the electric current. The WG-MFEM considered here uses discontinuous functions to construct the approximation space. Also, a linearization scheme is employed to treat nonlinear terms. In the proposed method, the important physical laws of mass conservation and free energy dissipation are preserved without any restriction on the time step. Error estimates are developed and analyzed for both semi- and fully discrete WG-MFEM schemes. Furthermore, optimal error estimates (under adequate regularity assumptions on the solution) are derived. Several numerical results are provided and they demonstrate the efficiency of the proposed method and validate the convergence theorems.

In this study, based on different numberical simulation methods, the gas-liquid two-phase flow is taken as the research object. By coupling the continuity equation of incompressible fluid, Navier-Stokes equation, electric field equation and other control equations, a multi-field coupling model for rising bubbles in viscous fluids is established, and numerical simulations are carried out. The two-phase popularity of coupled electric field is studied, and the effect of electric field on bubble motion is analyzed.The Level-set and phase field method are used to track the changes of deformation and rupture during the rising of the bubble. The accuracy and validity of the two methods are verified by mass conservation. At the same time, the calculation area is determined for the accuracy of calculation, and the optimal mesh size is calculated by using mesh independence test. Compared with the level set method, the phase field method has a certain improvement in the calculation efficiency and accuracy. Among them, the calculation efficiency of the phase field calculation method in the same grid is increased by 5 times, and by 3 times in the vertical electric field environment. Moreover, using the phase field method is easier to capture the bubbles slight changes while they are rising, and the quality of the simulation results is better.The simulation analysis of bubble rising process under coupled electric field by two methods shows that under the interaction of electrostatic force, buoyancy and surface tension, the bubble is stretched into an ellipsoid along the direction of the electric field line, and the ratio of the length to the short axis is proportional to the applied electric field strength. In addition, the bubble rising velocity is affected by the electric field, and the vertical electric field accelerates the rising of the bubble.

The coupled Darcy–Stokes problem is widely used for modeling fluid transport in physical systems consisting of a porous part and a free part. In this work we consider preconditioners for monolithic solution algorithms of the coupled Darcy–Stokes problem, where the Darcy problem is in primal form. We employ the operator preconditioning framework and utilize a fractional solver at the interface between the problems to obtain order optimal schemes that are robust with respect to the material parameters, i.e. the permeability, viscosity and Beavers–Joseph–Saffman condition. Our approach is similar to that of Holter et al. (2020), but since the Darcy problem is in primal form, expressing mass conservation at the interface involves the normal derivative, which introduces some mathematical challenges. These challenges will be specifically addressed in this paper, in particular we will employ fractional Laplacians at the interface. Numerical experiments illustrating the performance are provided. The preconditioner is posed in non-standard Sobolev spaces which may be perceived as an obstacle for its use in applications. However, we detail the implementational aspects and show that the preconditioner is quite feasible to realize in practice.

The paper analyzes a model of optical transmittance of ultra-diluted gas, considering gas particles' non-locality and the quantum effect of their wave function spreading derived from solving the Schr\"odinger equation for a free particle. The analysis does not depend on a particular form of the wave function, but it assumes the reality of wave function. Among others, we show conserved mass gas clouds may become significantly more transparent than predicted by classic transmittance laws. This unexpected phenomenon is possible because mass conservation is governed by the sum of probabilities, while the Markov chain's product of probabilities controls the transmittance. Furthermore, we analytically derive the upper limit the closed system transmittance may grow and demonstrate a boundless, open gas cloud transmittance may grow up to 100%. Finally, we show the impact on interpretations of quantum mechanics. The model is naturally applicable in deep space conditions, where the environment is sparse. Furthermore, the model responds to dark matter requirements., Comment: Rev. September 2022, 12 pages, 6 figures

Chemistry transport models (CTMs) play an important role in understanding fluxes and atmospheric distribution of carbon dioxide (CO2). They have been widely used for modeling CO2 transport through forward simulations and inferring fluxes through inversion systems. With the increasing availability of high-resolution observations, it has been become possible to estimate CO2 fluxes at higher spatial resolution. In this work, we implemented CO2 transport in the Model for Prediction Across Scales – Atmosphere (MPAS-A). The objective is to use the variable-resolution capability of MPAS-A to enable a high-resolution CO2 simulation in a limited region with a global model. Treating CO2 as an inert tracer, we implemented in MPAS-A (v6.3) the CO2 transport processes, including advection, vertical mixing by boundary layer scheme, and convective transport. We first evaluated the newly implemented model's tracer mass conservation and then its CO2 simulation accuracy. A 1-year (2014) MPAS-A simulation is evaluated at the global scale using CO2 measurements from 50 near-surface stations and 18 Total Carbon Column Observing Network (TCCON) stations. The simulation is also compared with two global models: National Oceanic and Atmospheric Administration (NOAA) CarbonTracker v2019 (CT2019) and European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecasting System (IFS). A second set of simulation (2016–2018) is used to evaluate MPAS-A at regional scale using Atmospheric Carbon and Transport – America (ACT-America) aircraft CO2 measurements over the eastern United States. This simulation is also compared with CT2019 and a 27 km WRF-Chem simulation. The global-scale evaluations show that MPAS-A is capable of representing the spatial and temporal CO2 variation with a comparable level of accuracy as IFS of similar horizontal resolution. The regional-scale evaluations show that MPAS-A is capable of representing the observed atmospheric CO2 spatial structures related to the midlatitude synoptic weather system, including the warm versus cold sector distinction, boundary layer to free troposphere difference, and frontal boundary CO2 enhancement. MPAS-A's performance in representing these CO2 spatial structures is comparable to the global model CT2019 and regional model WRF-Chem.

A two-phase depth-averaged debris flow model simplified by momentum equations is presented to solve the tracking of density evolution and simulate high-velocity impact problems. In the model, the Herschel-Bulkley rheology is used to describe the internal and basal frictions in the debris flow, and the treatments of complex terrains and entrainments are also included. To solve the debris flow model numerically, a relevant finite volume formulation including the Harten-Lax-van Leer-Contact (HLLC) scheme is introduced to solve the conservation equation with a debris interface. A circular dam-break, a dam-break of non-Newtonian fluid, and multiple debris flow cases are carried out based on the proposed model to validate the shock-capturing capability, the numerical isotropy, the model accuracy, and the mass conservation. These results indicate that the implemented schemes can produce sufficient numerical stability and accuracy for the debris flow problem. Finally, the debris flow of various rheological properties is systematically simulated, and how the debris rheology affects debris flow behavior is discussed.

The differential continuity equation is elegantly derived in advanced fluid mechanics textbooks using the divergence theorem of Gauss, where the surface integral of the mass flux flowing out of a finite control volume is replaced by the volume integral of the divergence of the mass flux within the control volume. To avoid the need for introducing the Gauss divergence theorem in an introductory fluid mechanics course, introductory textbooks in fluid mechanics have opted to use a more simple approach, which depends on the consideration of an infinitesimal control volume and the use of Taylor series expansion. This approach, however, involves a first order truncation of the Taylor series expansion and the use of approximate equality signs which may imply to undergraduate students that the derived continuity equation is an approximate equation. The present study proposes an alternative derivation of the differential continuity equation using a finite control volume and is based on the simple concept of the antiderivative function and the fundamental theorem of calculus. The proposed derivation eliminates the need to formally introduce the Gauss divergence theorem in an introductory engineering fluid mechanics course while avoiding the use of truncated Taylor series expansion and approximate equality signs, hence providing a more simple and sound understanding of the derivation of the differential continuity equation to undergraduate engineering students.

We investigate limit models resulting from a dimensional analysis of quite general heterogeneous catalysis models with fast sorption (i.e.\ exchange of mass between the bulk phase and the catalytic surface of a reactor) and fast surface chemistry for a prototypical chemical reactor. For the resulting reaction-diffusion systems with linear boundary conditions on the normal mass fluxes, but at the same time nonlinear boundary conditions on the concentrations itself, we provide analytic properties such as local-in time well-posedness, positivity and global existence of strong solutions in the class $\mathrm{W}^{(1,2)}_p(J \times \Omega; \mathbb{R}^N)$, and of classical H\"older solutions in the class $\mathrm{C}^{(1+\alpha, 2 + 2\alpha)}(\overline J \times \overline{\Omega})$. Exploiting that the model is based on thermodynamic principles, we further show a priori bounds related to mass conservation and the entropy principle., Comment: 29 pages, published in Journal of Evolution Equations (2021)

High energy consumption and increasing energy cost have encouraged investment in energy efficiency. In hot areas, like the Middle East, the share of space cooling accounts for most of the total energy use in buildings. Earth-to-air heat exchangers represent an energy-efficient and environmentally friendly cooling technique. An earth-to-air heat exchanger buried near the ground surface with short-grass cover, which lowers the soil temperature by evapotranspiration, is an alternative to conventional deep buried types. In this study, a steady three-dimensional numerical model of this earth-to-air heat exchanger was developed by considering the conservation of mass, momentum, energy, and species. Soil temperature and moisture content measurements were used as boundary conditions for the model. In addition, the variations of soil temperature and thermal conductivity with depth were considered in the model. Numerical predictions of temperature matched experimental measurements within ±0.5 °C. Using the validated numerical model, the effect of inlet air temperature, airflow rate, tube length, material, wall thickness, and soil thermal conductivity on the earth-to-air heat exchanger thermal performance was investigated. Increasing the airflow rate and tube length resulted in an asymptotic increase and decrease in the earth-to-air heat exchanger outlet temperature, respectively. By increasing the tube wall thickness from 1 to 10 mm, the outlet temperature for an aluminum tube remained unchanged, while for PE and PVC tubes, the outlet temperature increased by about 1.1 and 2.2 °C, respectively. By increasing the soil thermal conductivity from 1 to 5 W m−1 K−1 the outlet temperature decreased by about 4.4 °C.

Closed-form expressions for poroelastic coefficients are derived for anisotropic materials exhibiting single and double porosity. A novel feature of the formulation is the use of the principle of superposition to derive the governing mass conservation equations from which analytical expressions for the Biot tensor and Biot moduli, among others, are derived. For single-porosity media, the mass conservation equation derived from the principle of superposition is shown to be identical to the one derived from continuum principle of thermodynamics, thus confirming the veracity of both formulations and suggesting that this conservation equation can be derived in more than one way. To provide further insight into the theory, numerical values of the poroelastic coefficients are calculated for granite and sandstone that are consistent with the material parameters reported by prominent authors. In this way, modelers are guided on how to determine these coefficients in the event that they use the theory for full-scale modeling and simulations.

This scientific article is devoted to the problems associated with the flow of suspensions and emulsions and some simplifications of the real picture of the flow of a polydisperse medium are made. It is also stipulated that differential equations characterizing the motion of suspensions and emulsions should take into account the fundamental discontinuity of the medium and the physicochemical processes of heat and mass transfer occurring in it. Taking into account all these factors, a general equation for multiphase systems is proposed with certain simplifications that do not change. The behavior of particles in two-phase systems, their concentration, collision and coagulation are considered. As a result, it was concluded that there is a multifactorial interaction and mutual influence of both phases in a dispersed flow. A differential equation of motion of a single i-th spherical particle in suspension was proposed, and an equation describing the drag force of a solid spherical particles. Equations of conservation of mass and momentum are presented for one-dimensional laminar motion of two incompressible phases in a gravity field with the same pressure in the phases. Having studied the parameters of the flow of fine particles in a turbulent gas flow, some assumptions were made. It was found that the pulsating motion of particles, performed by them during one period of gas pulsations, can be represented as a change in the pulsating gas velocity in time. The parameter of entrainment of particles by a pulsating medium is an important characteristic in determining the transport coefficients in a turbulent flow. It is concluded that the presence of various kinds of particles in the liquid complicates the problem of solving hydromechanical problems in turbulent and laminar flow, and the assumptions given in the work facilitate the study of this problem.

Cauchy problem for the Caputo-type time fractional Cahn–Hilliard equation in $${\mathbb {R}}^3$$ is examined. The local existence and uniqueness of mild solutions and strong solutions are obtained for the initial data $$u_0$$ satisfying $$u_0-{\bar{u}}\in L^\infty ({\mathbb {R}}^3)\cap L^1({\mathbb {R}}^3)$$ , where $${\bar{u}}$$ is an equilibrium constant. The local solutions are extended globally if $$u_0-{\bar{u}}$$ is small in $$L^1({\mathbb {R}}^3)$$ . These results are consistent with those of the traditional Cahn–Hilliard equation such as the property of mass conservation. However, extra difficulties arise in dealing with the singularity of Mittag-Leffler operators and non-Markovian property in the Caputo-type time fractional problem.

In this paper, the nonlinear dispersion wave model in both 1D and 2D is studied by the compact finite difference method, which is called the generalized Rosenau–RLW equation. A fourth-order compact three-level and linearized difference scheme that maintains the original conservative properties of equation is proposed. The discrete mass conservation and discrete energy conservation of compact difference scheme are obtained. The solvability of numerical scheme is obtained. By using the discrete energy method, convergence and unconditional stability can also be obtained without relying on the grid ratio, and the optimal error estimates in the L ∞ norm are fourth-order and second-order accuracy for the spatial and temporal step sizes, respectively. The scheme is conservative so can be used for long time computation. Numerical experiment results show that the theory is accurate and the method is efficient and reliable. Finally, the new numerical scheme is used to study the nonlinear dynamic of 1D generalized Rosenau–RLW equation and the wave interference of 2D generalized Rosenau–RLW equation, focusing on the influence of nonlinear convection term on the wave and the conservation of wave propagation.

A two-dimensional analytical model based on the Reynolds equation considering mass conservation cavitation is proposed to investigate the performance of partially textured thrust bearings with circular grooves. The geometrical and distribution parameters of the circular grooves are numerically optimized to obtain the maximum load-carrying capacity. The samples of partially textured thrust bearings are machined by the picosecond laser, and tribological experiments are carried out on an MMW-1 tribological rig. The average friction coefficient and the friction reduction ratio are applied to analyze the tribological performance of partially textured thrust bearings. Through a comparative analysis, the optimal geometrical values obtained from the experimental results are in good agreement with the theoretical analysis, especially at high rotation speeds and a low load condition.

The phenomena of mean pressure distribution around two square cylinders in tandem has been carried out. Also the mean velocity distribution in the wake of the two cylinder are studies. The Navier-Stokes equation for conservation of momentum and the continuity equation for conservation of mass are used to study the pressure and velocity distribution for various longitudinal spacing of the cylinder. The turbulent k-ω stationary flow at a high Reynolds number of Re= 6.5e4 is used to simulate single-phase flow. A critical longitudinal spacing equal to four times the side dimension of the square cylinder (L/D= 4) is investigated. Beyond that critical spacing both the cylinders are subjected to drag force. When L/D < 4 only the downstream cylinder is subjected to negative drag. Also, the form of the streamline profile behind upstream cylinder is different from that of single cylinder. However, beyond L/D= 4 the nature of the pressure behind both of the cylinder becomes kind of like that of the single cylinder.

We introduce a method for generating a continuous, mass-conserving and high-order differentiable density field from a discrete point distribution such as particles or halos from an N-body simulation or galaxies from a spectroscopic survey. The method consists on generating an ensemble of point realizations by perturbing the original point set following the geometric constraints imposed by the Delaunay tessellation in the vicinity of each point in the set. By computing the mean field of the ensemble we are able to significantly reduce artifacts arising from the Delaunay tessellation in poorly sampled regions while conserving the features in the point distribution. Our implementation is based on the Delaunay Tessellation Field Estimation (DTFE) method, however other tessellation techniques are possible. The method presented here shares the same advantages of the DTFE method such as self-adaptive scale, mass conservation and continuity, while being able to reconstruct even the faintest structures of the point distribution usually dominated by artifacts in Delaunay-based methods. Additionally, we also present preliminary results of an application of this method to image denoising and artifact removal, highlighting the broad applicability of the technique introduced here., Submitted to MNRAS

A number of important questions concern processes at the margins of ice sheets where multiple components of the Earth system, most crucially ice sheets and oceans, interact. Such processes include thermodynamic interaction at the ice–ocean interface, the impact of meltwater on ice shelf cavity circulation, the impact of basal melting of ice shelves on grounded ice dynamics and ocean controls on iceberg calving. These include fundamentally coupled processes in which feedback mechanisms between ice and ocean play an important role. Some of these mechanisms have major implications for humanity, most notably the impact of retreating marine ice sheets on the global sea level. In order to better quantify these mechanisms using computer models, feedbacks need to be incorporated into the modelling system. To achieve this, ocean and ice dynamic models must be coupled, allowing runtime information sharing between components. We have developed a flexible coupling framework based on existing Earth system coupling technologies. The open-source Framework for Ice Sheet–Ocean Coupling (FISOC) provides a modular approach to coupling, facilitating switching between different ice dynamic and ocean components. FISOC allows fully synchronous coupling, in which both ice and ocean run on the same time step, or semi-synchronous coupling in which the ice dynamic model uses a longer time step. Multiple regridding options are available, and there are multiple methods for coupling the sub-ice-shelf cavity geometry. Thermodynamic coupling may also be activated. We present idealized simulations using FISOC with a Stokes flow ice dynamic model coupled to a regional ocean model. We demonstrate the modularity of FISOC by switching between two different regional ocean models and presenting outputs for both. We demonstrate conservation of mass and other verification steps during evolution of an idealized coupled ice–ocean system, both with and without grounding line movement.

Interface partial differential equations (PDEs) are very important in science and engineering. A new mass preserving solution-flux scheme is proposed in this paper for solving parabolic multi-layer interface problems. In the scheme, the domain is divided into staggered meshes for layers. At grid points in each subdomain, the solution-flux scheme is proposed to approximate the equation. However, due to the interface jump conditions, it is difficult to define the approximate fluxes at the irregular points next to interfaces for satisfying mass conservation for the scheme across the interfaces. The important feature of our work is that at the irregular grid points, the novel corrected approximate fluxes from two sides of the interface are proposed by combining with the interface jump conditions at interfaces, which ensure the developed solution-flux scheme mass conservative while keeping the same accuracy. We prove theoretically that our scheme satisfies mass conservation in the discrete form over the whole domain for the parabolic interface equations with multi-layers. Numerical experiments show mass conservation and convergence orders of our scheme and numerical results in multi-layer media show its excellent performance.

This study presents a robust, sharp interface immersed boundary (IBM) framework for moving body problems. The in-house solver makes use of a density-based finite volume framework for solving unsteady, 3D Favre averaged Navier Stokes equation in a generalized curvilinear coordinate system. The immersed boundary formulation is capable of handling arbitrarily complex three-dimensional bodies. The sharp interface approach allows for the exact imposition of boundary conditions at the immersed surface by reconstructing the flow field along its local normal. The implemented reconstruction schemes maintain second-order accuracy. The study focuses on issues of mass conservation and spurious temporal oscillations (pressure as well as force) that the sharp interface IBM approach typically faces when encountering moving body problems. A ghost node-based field extension technique provides an efficient way to improve mass conservation and as a result, reduces not only spurious oscillations but also increases temporal accuracy. Flow past both bluff body (triangular, circular and spherical), as well as streamlined body (airfoil), is presented here as validation studies. The ability of the present formulation to deal with moving body problems in the laminar incompressible flow regime is demonstrated by presenting cases that involve motions such as pitching and in-line oscillation. The predictions are found to be in good agreement with the published results and measurements as well.