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In this article, we are concerned with the tempered fractional parabolic problem $$ \begin{align*}\frac{\partial u}{\partial t}(x, t)-\left(\Delta+\lambda\right)^{\frac{\alpha}{2}} u(x, t)=f(u(x, t)), \end{align*} $$ where $-\left (\Delta +\lambda \right)^{\frac {\alpha }{2}}$ is a tempered fractional operator with $\alpha \in (0,2)$ and $\lambda $ is a sufficiently small positive constant. We first establish maximum principle principles for problems involving tempered fractional parabolic operators. And then, we develop the direct sliding methods for the tempered fractional parabolic problem, and discuss how they can be used to establish monotonicity results of solutions to the tempered fractional parabolic problem in various domains. We believe that our theory and methods can be conveniently applied to study parabolic problems involving other nonlocal operators. [ABSTRACT FROM AUTHOR]

A microscale multi-relaxation-time lattice Boltzmann model with the regularization procedure is adopted to simulate gas flow in different porous media. The diffuse reflection boundary condition is used to deal with the random solid boundaries. Because of the complex geometry of the pores, the characteristic length is no longer a constant but a function of the pore locations for the porous media. A rational method is proposed to obtain the local characteristic lengths of the porous media for the microscale gas flow simulations. The simulation results show that gas flow characteristics in different flow regions are notably different. In the continuum flow region and slip flow region, the gas flow abilities in different pores are quite different. The effect of heterogeneity of the porous media on gas velocity distribution is very obvious. As the Knudsen number increases, the differences of gas flow abilities in different pores decrease. For gas flow in the strong transition flow region and free molecular flow region, the gas flow abilities in small pores are similar to those in large pores and the effect of heterogeneity becomes small. Such phenomena are mainly caused by the different gas flow mechanisms in different flow regions. In addition, two commonly used apparent permeability calculation models are evaluated by the simulation results and a better coefficient for the Klinkenberg model is proposed according to the simulation results. [ABSTRACT FROM AUTHOR]

In the present investigation, the roughness characteristics of the gravel bed is tested and modelled for the no-load condition. A straight trapezoidal channel having gravel bed surface of grain size D50 as 13.5 mm for no-load condition is used to carry out the investigation. Depth averaged velocity (DAV) and boundary shear stress (BSS) have been measured for five different depths. An improved model for prediction of friction factor is derived as the function of corresponding hydraulic radius and average diameter of the gravel. This improved model is validated with the models of past investigators. Furthermore, BSS is then calculated using Shiono and Knight Method (SKM), which is dependent on the following hydraulic parameters, such as friction factor f, coefficient of eddy viscosity λ and secondary flow term Г. Since friction factor is modelled for the given channel, same model is used to calculate the value of f over the bed, which tests the reliability of the model while using numerical method. The lateral distribution of DAV and BSS is shown for five different flow depths, which elaborate the bed friction due to the no-load condition. Finally, friction factor model is corroborated on two reaches of the natural river. [ABSTRACT FROM AUTHOR]

The aim of this study is to assess how much the results of nucleation experiments in a laminar flow diffusion chamber (LFDC) are influenced by the complexity of the model of the transport properties. The effects of the type of fluid dynamic model (the steady state compressible Navier-Stokes system for an ideal gas/parabolic profile approximation) and the contributions of the coupled terms describing the Dufour effects and thermodiffusion on the predicted magnitude of the nucleation maxima and its location were investigated. This study was performed on the model of the homogeneous nucleation of an n-butanol-He vapor mixture in a LFDC. The isothermal dependencies of the nucleation rate on supersaturation were determined at three nucleation temperatures: 265 K, 270 K, and 280 K. For this purpose, the experimental LFDC data measured by A. P. Hyvärinen et al. [J. Chem. Phys. 124, 224304 (2006)] were reevaluated using transport models at different levels of complexity. Our results indicate that the type of fluid dynamical model affects both the position of the nucleation maxima in the LFDC and the maximum value of the nucleation rate. On the other hand, the Dufour effects and thermodiffusion perceptibly influence only the value of the maximal nucleation rate. Its position changes only marginally. The dependence of the maximum experimental nucleation rate on the saturation ratio and nucleation temperature was acquired for each case. Based on this dependence, we presented a method for the comparison and evaluation of the uncertainties of simpler models' solutions for the results, where we assumed that the model with Navier-Stokes equations and both coupled effects taken into account was the basis. From this comparison, it follows that an inappropriate choice of mathematical models could lead to relative errors of the order of several hundred percent in the maximum experimental nucleation rate. In the conclusion of this study, we also provide some general recommendations concerning the proper choice and setting of the mathematical model of transport processes in the LFDC. [ABSTRACT FROM AUTHOR]

We study the transient behavior of a model fluid composed by soft repulsive spheres subjected to a planar uniform shear. To this aim, we use a dynamical non-equilibrium molecular dynamics method originally developed by Ciccotti and Jacucci [Phys. Rev. Lett. 35, 789 (1975)] and recently applied to the study of the transient regimes in various fluid systems. We show that the dynamical method allows one to study the transient behavior of the viscous time-dependent response over a wide range of applied shear rates, provided that a temperature control is enforced on the system. In this study, we adopt in particular the configurational thermostat of Braga and Travis [J. Chem. Phys. 123, 134101 (2005)]. The initial behavior of the dynamical response to a θ-like perturbation is characterized by a rapid increase, culminating in a pronounced peak, later relaxing to a plateau value. The latter positively reproduces the values of the viscosity observed in standard steady-state non-equilibrium molecular dynamics. [ABSTRACT FROM AUTHOR]

A comprehensive investigation is conducted to study the thermodynamics, structure, and mean free volume of rigid two-center Lennard-Jones fluids through Monte Carlo simulations. For a large number of states, the self-diffusion coefficient is computed using the following two different approaches: the equilibrium molecular dynamics simulation method and the modified Cohen–Turnbull theory. The effects of the bond elongation on different thermophysical properties are studied. The generic van der Waals theory, which has recently been extended to rigid polyatomic fluids [A. Eskandari Nasrabad and R. Laghaei, J. Chem. Phys. 125, 154505 (2006)], is used to compute the mean free volume needed in the modified Cohen–Turnbull theory. The effective site diameter is computed using the virial minimization method and the results are applied within the generic van der Waals theory. The Gibbs ensemble Monte Carlo simulation technique is applied to determine the location of the fluid phase envelope. The NVT Monte Carlo simulation method is then utilized to compute the equation of state and the correlation functions appearing in the generic van der Waals theory. It appears that the logarithm of the mean free volume versus density is almost linear at ρ>ρc independent of the bond length, which suggests a universal behavior. The self diffusion coefficient results of the modified Cohen–Turnbull theory are analyzed in detail. [ABSTRACT FROM AUTHOR]

In this paper several fractional calculus operators have been introduced and investigated. The aim is to establish the Marichev-Saigo-Maeda (MSM) fractional calculus operators and Caputo-type MSM fractional differential operators involving the product of extended Mittag-Leffler function (EMLF) and generalized Galue Struve Type Function. Some of the particular cases of the main results are also derived. The results given in this paper are general in character and likely to find some applications in the theory of special functions. [ABSTRACT FROM AUTHOR]

Abstract The particle formation by supercritical technology is an active research field. Rapid expansion of supercritical fluid (RESS) is a promising new technology for particle formation using supercritical fluids. In this study, numerical modeling of particle formation of TBTPP (5, 10, 15, 20-tetrakis (3, 5-bis (trifluoromethyl) phenyl) porphyrin) through RESS process is investigated. The RESS process contains two pre-expansion (nozzle part) and expansion vessel (supersonic free jet) parts. In the first section, mass, momentum and energy balances in addition to extended generalized Bender equation of state (egB-EoS) as accurate equation of state is used to calculate temperature, pressure, density and velocity of supercritical carbon dioxide (SC-CO 2) based on mathematical modeling and computational fluid dynamics (CFD) simulation methods. Both models include friction in the nozzle and heat exchange in the expansion vessel and in the nozzle region. Using calculated pressure and temperature, the solubility of TBTPP in the supercritical CO 2 is predicted by Peng-Robinson EoS with Kwak-Mansoori mixing rule and the results are compared with experimental data and a semi-empirical correlation. Supersaturation, homogenous nucleation and critical radius of TBTPP based on classical nucleation theory are calculated. The effect of pre-expansion temperature on supersaturation, nucleation and critical radius parameters is also studied. The results of hydrodynamic and particle formation modeling present the same trend as reported in the literature. Highlights • Proving accuracy of simple mathematical model in comparison to CFD in RESS process • Modeling of TBTPP-CO 2 solubility (required for particle formation) by PR/KM EoS • Study on TBTPP supersaturation and nucleation by classical nucleation theory • Investigation of pre-expansion temperature on TBTPP particle formation parameters • Calculation of TBTPP particle size using simple model [ABSTRACT FROM AUTHOR]

Due to its capability of duplicating the deformation scenario of erythrocytes (red blood cells), in in vivo time scales, passing through interendothelial slits in the spleen, the understanding of the dynamic response of erythrocytes in oscillatory shear flows is of critical importance to the development of an effective in vitro methodology to study the mechanics, metabolism, and aging procedure in vivo [R. Asaro et al., "Erythrocyte aging, protection via vesiculation: An analysis methodology via oscillatory flow," Front. Physiol. 9, 1607 (2018)]. Accordingly, we conducted a systematic computational investigation of the dynamics of erythrocytes in high-frequency oscillatory shear flows by using a fluid-cell interaction model based on the Stokes-flow framework and a multiscale structural depiction of the cell. Within the range of parameters we consider, we identify five different response modes (wheeling, tilted wheeling, tank treading mode 1, tank treading mode 2, and irregular). The occurrence and stability of these response modes depend on the frequency of the flow, the peak capillary number, the viscosity ratio, the initial orientation of the cell, and the stress-free state of the protein skeleton. Through long-term simulations [ O (1 0 2 ) periods], mode switching events have been discovered, during which the cell transfers from one mode to another, often via an intermediate transient mode. The deformation of the skeleton and the contact stress between the skeleton and the lipid bilayer are computed since these are of direct importance to describing vital cell phenomena such as vesiculation by which the cell protects itself from premature elimination. [ABSTRACT FROM AUTHOR]

The proper design, development, and appropriate tuning of the Hybrid Neural Network architecture, mainly for its parsimoniousity and optimal training can help practitioners to generate a robust predictive tool for modeling several important hydrological processes within the water resources sector. In this paper, the Feedforward Artificial Neural Network (FFANN) and the hybrid WANN model have been developed, and later, coupled with the Gamma and M-tests (GT) approach for forecasting spatio-temporal groundwater fluctuations in a complex alluvial aquifer system. The performance of these hybrid models were evaluated using goodness-of-fit criteria. An analysis of the modeling results indicates that the GT coupled with the WANN model was able to provide significantly improved results, with lower values of the root mean square error (RMSE) and higher values of the NSE metric for the 1-week and 3-week lead times. Hence, utilizing this hybrid model, the groundwater level prediction tests were extended for 6-week and 12-week lead times with the GT approach, coupled with the WANN hybrid model only. The results showed that the accuracy of the GT-WANN hybrid model was better for the unconfined aquifer system compared to the leaky confined aquifer system. Furthermore, the present study also examined the interdependence between different model inputs and output variables for the selected study sites by means of the Wavelet Coherent Analysis (WCA). These results indicated that all the model's input variables have a significant effect on the groundwater level of unconfined aquifers, and confirmed the nature of the aquifers tapped within the present study sites. The study finally concludes that the GT-WANN approach can be a robust predictive tool for modeling spatio-temporal fluctuations of groundwater levels. [ABSTRACT FROM AUTHOR]

In this study, mathematical models of air cooled condensers with circular and elliptic cross-sections were developed and performances were evaluated with artificial neural networks. Air velocity, orientation angle and ambient temperature were used as the input to the neural network structure while heat transfer rate to the air was used as the output. The data sets were generated from high fidelity, computationally inefficient expensive three dimensional computational fluid dynamics simulations. It was observed that artificial neural network model replaces computational fluid dynamics model and based on the mathematical model with artificial neural network, elliptic condensers perform better in terms of heat transfer compared to circular ones. [ABSTRACT FROM AUTHOR]

In this paper, the development of a solver for the Multi-Fluid and Multi-Pressure model (MFMP) is presented. MFMP is the extension of the two-fluid model. In this model, the number of fluids can be greater than or equal to two. The fluids are considered to be in mechanical nonequilibrium. The pressure across the interface is not considered to be equal. A pressure-based and semi-implicit numerical method is proposed. This is different from the method used for the two-fluid model or single-pressure model. The solver is verified by classical two-fluid benchmark problems and multifluid problems. The Multi-Fluid and Single-Pressure model (MFSP) and MFMP are used. Bestion's model is used in MFMP to consider the nonequilibrium effect of pressure. The computation shows that MFSP is unstable if the number of meshes is large enough, while MFMP is stable for the two-fluid problems and most cases of the multifluid problems. The results of MFMP are in agreement with the reference solution or analytical solution for the two-fluid problems and reasonable for most cases of the multifluid problems. [ABSTRACT FROM AUTHOR]

Abstract Ferrofluid pocket bearings are a type of bearing that are able to carry a load using an air pocket encapsulated by a ferrofluid seal. Previously designed ferrofluid bearings show the great potential of the stick-slip-free and low viscous friction bearings, however until now the load capacity is limited. In this article a method is presented to increase the load capacity in a simple and cost effective way by the addition of ferromagnetic material around the magnet. First, a mathematical model of the bearing is presented and is validated by experiments using an axially magnetized ring magnet surrounded by two steel rings. The model is used to optimize the dimensions of the added ferromagnetic material for maximum load capacity. Depending on the fly height, the load capacity has been increased by a factor three to four by the addition of steel rings to the ferrofluid pocket bearing configuration. Highlights • Predicted load capacity of ferrofluid double pocket bearings analytically. • Validated model of load capacity by experiments. • Geometrical optimization of ferromagnetic rings. • Improvement of load capacity of ferrofluid bearing by factor of 4. [ABSTRACT FROM AUTHOR]

Abstract A high resolution Computational Flow Dynamics (CFD) numerical model is built based on a laboratory experiment in this research to study impacts of tidal turbines on surface wave dynamics. A reduction of ∼ 3 % in wave height is observed under the influence of a standalone turbine located 0.4 m from the free surface. The artificial wave energy dissipation routine 'OBSTACLE' within FVCOM is shown to effectively capture the correct level of wave height reduction, reproducing the CFD results with significantly less computational effort. The turbine simulation system is then applied to a series of test cases to investigate impact of a standalone turbine on bed shear stress. Results suggest an apparent increase in bed stress (∼ 7 %) upstream of the turbine due to the inclusion of surface waves. However, in the immediate wake of the turbine, bed stress is dominated by the presence of the turbine itself, accounting for a ∼ 50 % increase, with waves having a seemingly negligible effect up to 9D (D is the turbine diameter) downstream of the turbine. Beyond this point, the effect of waves on bed shear stress become apparent again. The influence of OBSTACLE on bed stress is also noticeable in the far wake, showing a reduction of ∼ 2 % in wave height. Highlights • Impact of tidal stream energy device on surface wave dynamics are studied. • A 3D wave-current-sediment fully coupled large-scale numerical model is used. • Impact of turbines on surface waves are incorporated in the large-scale model. • Model prediction indicates a 3% turbine-caused drop in wave height. • Impact of the wave height drop on bed stress in the immediate wake is small. [ABSTRACT FROM AUTHOR]

Abstract In this article we consider weak solutions of the Euler- α equations in the full plane. We take, as initial unfiltered vorticity, an arbitrary nonnegative, compactly supported, bounded Radon measure. Global well-posedness for the corresponding initial value problem is due M. Oliver and S. Shkoller. We show that, for all time, the support of the unfiltered vorticity is contained in a disk whose radius grows no faster than O ((t log ⁡ t) 1 / 4). This result is an adaptation of the corresponding result for the incompressible 2D Euler equations with initial vorticity compactly supported, nonnegative, and p -th power integrable, p > 2 , due to D. Iftimie, T. Sideris and P. Gamblin and, independently, to Ph. Serfati. [ABSTRACT FROM AUTHOR]

A novel three dimensional (3D) simulation tool based on lattice Boltzmann method (LBM), which is more efficient than the conventional computational fluid dynamics approach, was developed to analyze the head/disk interface (HDI) dynamics. For handling general geometrical structures, Taylor series expansion and least squares based LBM was employed to simulate the flow conditions under a model slider. Truncated power-law and Bird–Carreau models were incorporated to capture the non-Newtonian fluid flow behavior of lubricant liquid film undergoing extremely high shear rates by modifying the relaxation time as a function of shear rate. After the benchmark study of two dimensional/3D Poiseuille flows, pressure and shear profiles under the model slider were calculated for different constitutive relationships. The results indicate that our LBM techniques could be an attractive computational tool for next generation HDI design. [ABSTRACT FROM AUTHOR]

Highlights • Blood flow pulsatility induces oscillatory disturbances in the transport of species. • Disturbances can cause the period-average transport to differ from its steady-state. • The OKEI and OSAFI are used to identify the spatial distribution of disturbances. • The RPA model is developed to compute the period-average of species transport. • The RPA model approximates the period-average better than the steady-state model. Abstract Time-averaging is a technique that is often applied in models of the cardiovascular system to filter out temporal variations. In the context of modelling pulsatile blood flow, it is used to derive the time-invariant state, about which the flow periodically oscillates. It is known from past studies, that blood flow oscillations can interact to produce disturbances that directly influence the period-average of their local flow field. In this study, it is shown that the transport of blood-borne species also inherits disturbances that can influence its period-average. Over the course of a period of oscillation, the influence of disturbances can aggregate and cause the period-average to substantially differ from its equivalent steady-state. This poses a problem for models of physiological processes that rely on the long-term transport of blood-borne species, such as of atherosclerosis and thrombosis growth. This is because an explicit resolution of all periods of oscillation can be computationally expensive to resolve, significantly more so than the equivalent steady-state. To overcome this problem, the Reynolds Period-Average (RPA) species transport model is developed in this study, to model the period-average of pulsatile species transport. In the present form of the RPA model, the influence of flow disturbances is integrated, whereas species transport disturbances are assumed to be relatively negligible. This simplification is observed to hold well for conditions of low to moderate flow pulsatility, such as within human coronary arteries. Under these conditions, the present form of the RPA model is shown to well approximate the period-average transport of species, such as low density lipoprotein, with relatively little computational expense. [ABSTRACT FROM AUTHOR]

Abstract This investigation aims to study experimentally and numerically the performance of a twisted modified Savonius rotor at various twisting angles. The experiments are conducted in front of a free air jet. The computations are performed using the three-dimensional incompressible unsteady Reynolds-Average Navier-Stokes (RANS) equations along with the RNG k-ε turbulence model. The comparison with the present measurements shows good prediction of the RNG k-ε turbulence model to the rotor performance. Furthermore, the power coefficient ( C P ) and the torque coefficient ( C T ) at different tip speed ratios (λ) for twist angles ranging from 0° to 180° are predicted under constant aspect ratio of 1.0 and overlap ratio of 0.15. The numerical results show that the maximum power coefficient ( C P max ) increases with the increase of twist angle up to an optimum value of 45° and then decreases except for twist angle of 135°. The twisted modified rotor with a twist angle of 45° has the highest C P and C T (0.22 and 0.41, respectively) compared to the other studied twist angles. Highlights • A twisted modified Savonius rotor is experimentally and numerically tested. • Computations based on RNG k-ε turbulence model are performed. • Measurements are carried out on four different shapes of rotors. • The helical modified rotor of 45° twist has the best performance. [ABSTRACT FROM AUTHOR]

A multilevel Monte Carlo (MLMC) method for Uncertainty Quantification (UQ) of advection-dominated contaminant transport in a coupled Darcy–Stokes flow system is described. In particular, we focus on high-dimensional epistemic uncertainty due to an unknown permeability field in the Darcy domain that is modelled as a lognormal random field. This paper explores different numerical strategies for the subproblems and suggests an optimal combination for the MLMC estimator. We propose a specific monolithic multigrid algorithm to efficiently solve the steady-state Darcy–Stokes flow with a highly heterogeneous diffusion coefficient. Furthermore, we describe an Alternating Direction Implicit (ADI) based time-stepping for the flux-limited quadratic upwinding discretization for the transport problem. Numerical experiments illustrating the multigrid convergence and cost of the MLMC estimator with respect to the smoothness of permeability field are presented. [ABSTRACT FROM AUTHOR]

Shape transformations in biological membranes are crucial in a variety of cellular processes such as transport in the Golgi apparatus and endoplasmic reticulum, shaping the cell organelles and signaling in neuronal synapses. Dynamic analysis of lipid bilayer membranes is popular among researchers as valuable information about cell functions can be retrieved. There are several limitations in experimental tests and simulations such as computational and implementation cost while in theoretical studies, different phenomena can be modeled and the effect of each parameter can be investigated. In this paper, a continuum model including elastic energies and dissipation functions is utilized with energy approach to obtain the governing equations of an enclosed lipid bilayer membrane. The governing equations are solved numerically for vesicles initially disturbed and the relaxation dynamics is studied. The stationary shape of the vesicles for different values of reduced volume and reduced area difference is obtained to explore the phase diagram and verify the governing equations. Then, the density asymmetry in bilayers caused by the change in the density or the equilibrium density of the outer monolayer is studied. This leads to the formation of buds, tubules, and pearls. This can be observed in the recruitment of proteins to the outer monolayer or pH gradients of the environment of a vesicle. The effect of density difference and curvature on creation and growth of tubules are investigated. An interesting metastable state in the adsorption of the final bud due to the increase in the density of the outer monolayer is observed in which the shape of the vesicle is almost unchanged. A prolate vesicle relaxes toward an oblate or a stomatocyte vesicle when the equilibrium density of the outer monolayer increases. [ABSTRACT FROM AUTHOR]

A filter-based Euler-Lagrange multiphase flow model is used to study the mixing behavior in a combined blowing steelmaking converter. The Euler-based volume of fluid approach is employed to simulate the top blowing, while the Lagrange-based discrete phase model that embeds the local volume change of rising bubbles for the bottom blowing. A filter-based turbulence method based on the local meshing resolution is proposed aiming to improve the modeling of turbulent eddy viscosities. The model validity is verified through comparison with physical experiments in terms of mixing curves and mixing times. The effects of the bottom gas flow rate on bath flow and mixing behavior are investigated and the inherent reasons for the mixing result are clarified in terms of the characteristics of bottom-blowing plumes, the interaction between plumes and top-blowing jets, and the change of bath flow structure. [ABSTRACT FROM AUTHOR]

In order to simulate nanofluid MHD transportation in a permeable cavity, Darcy law is utilized. Impacts of radiation parameter, buoyancy and Lorentz forces on nanofluid characteristics have been depicted via CVFEM. Al 2 O 3 -water nanofluid is selected considering shape factor and Brownian motion impacts on its properties. Results reveal that conduction mode improves with rise of magnetic forces. So, thermal boundary layer becomes thinner with increase of magnetic forces. [ABSTRACT FROM AUTHOR]

Packing configuration is widely used in chemical industries such as chemical reaction and chromatograph where the flow distribution has a significant effect on the performance of heat and mass transfer. In the present paper, numerical simulation is carried out to investigate the fluid-flow in three 2-D array configurations including in-line array, staggered array and hexagonal array. Meanwhile, a simplified equivalent circuit network model based on the Voronoi tessellation is proposed to simulate the flow models. It is found that firstly, the local Reynolds number could be used as a criterion to determine the flow regime. Flow with maximum local Reynolds number less than 40 could be regarded as Darcy flow. Secondly, the flow pattern can be well represented by the network model in the range of Darcy flow with the determination method of hydraulic resistance proposed in the present paper. [ABSTRACT FROM AUTHOR]

We prove a version of Onsager’s conjecture on the conservation of energy for the incompressible Euler equations in the context of statistical solutions, as introduced recently by Fjordholm et al. (2017). As a byproduct, we also obtain an alternative proof for the conservative direction of Onsager’s conjecture for weak solutions, under a weaker Besov-type regularity assumption than previously known. [ABSTRACT FROM AUTHOR]

We consider the chemotaxis-fluid system given by nt + u ·∇n = Δnm - ∇· (n∇c), ct + u ·∇c = Δc - c + n, ut + (u · ∇)u = Δu + ∇P + n∇φ, and ∇ · u = 0, for x ∈ Ω and t > 0, where Ω ⊂ R3 is a bounded domain with smooth boundary and m > 1. Assuming m > 4/3 and sufficiently regular nonnegative initial data, we ensure the existence of global solutions to the no-flux-Dirichlet boundary value problem for this system under a suitable notion of very weak solvability, which in different variations has been utilized in the literature before. Comparing this with known results for the fluid-free setting of the system above the condition appears to be optimal with respect to global existence. In the case of the stronger assumption m > 5/3 we moreover establish the existence of at least one global weak solution in the standard sense. In our analysis we investigate a functional of the form ∫Ωnm-1 + ∫Ωc2 to obtain a spatio-temporal L2 estimate on ∇nm-1, which will be the starting point in deriving a series of compactness properties for a suitably regularized version of the system above. As the regularity information obtainable from these compactness results vary depending on the size of m, we will find that taking m > 5/3 will yield sufficient regularity to pass to the limit in the integrals appearing in the weak formulation, while for m > 4/3 we have to rely on milder regularity requirements making only very weak solutions attainable. [ABSTRACT FROM AUTHOR]

The fluid flow conveyed by a cantilevered pipe might be a multi-phase flow, the density of which can fluctuate with time and space. In this paper, variable density fluid is simulated by a new mathematical model that satisfies the continuity of the fluid flow. The fluid forces acting on the pipe are derived from Newton’s second law. Combined with a Bernoulli–Euler beam model, a new dynamic model for a cantilevered pipe conveying a variable density fluid is established. The numerical results of the present model can be obtained by utilizing finite difference methods and agree with the classical theoretical results. The influences of the fluctuating amplitude, wave number and initial phase angle of the fluid density on the stability and dynamics of the cantilevered pipe system are analysed in detail. It can be found that when the fluid density varies with a large amplitude, the cantilevered pipe system is prone to losing its stability, which consequently leads to flutter. A small wave number of the fluid density has a notable influence on the system’s stability. Moreover, the stability of this system is seldom affected by the initial phase angle of the fluid density. Based on the current research work, an improved stability criterion is proposed with which the stability of the present system can be more precisely determined. [ABSTRACT FROM AUTHOR]

This paper develops two causal four-field theories of relativistic fluid dynamics, one for viscous fluids that are barotropic and the other for viscous heat-conductive fluids that are “thermo-barotropic,” a property that is newly defined here. While similar to the deduction of a five-field theory in the authors’ article Causal dissipation for the relativistic dynamics of ideal gases [Freistühler, H. and Temple, B., Proc. R. Soc. A 473, 20160729 (2017)], the argumentation is consistently carried out in a way that stays closer to Eckart’s flow frame (than to Landau’s), and the result is directly compared with the four-field theories resulting from early proposals made by Eckart, Lichnerowicz, and Choquet-Bruhat. The key idea is to impose second-order symmetric hyperbolicity in the sense of Hughes, Kato, and Marsden [Arch. Rational Mech. Anal. 63, 273–294 (1976)], in the natural Godunov variables that make the corresponding system of perfect-fluid conservation laws symmetric hyperbolic in the first order sense. The new theory for viscous heat-conductive thermo-barotropic fluids belongs to the Hughes-Kato-Marsden class; the new theory for viscous general barotropic fluids lies on the boundary of that class. As in the five-field theory, the coefficients of bulk viscosity ζ, shear viscosity η, and, in the case of thermo-barotropic fluids, that of heat conductivity χ are free parameters, and in terms of these, the relativistic dissipation tensor is uniquely determined under three conditions which the authors propose as definitive: symmetric hyperbolicity, sharp causality, and first-order equivalence with Eckart—the requirement that the resulting equations be equivalent to the Eckart equations to leading order in ζ, η, and χ. The new theory for general viscous barotropic fluids complements the one given in the abovementioned paper for massive ideal gases. The new theory for viscous heat-conductive thermo-barotropic fluids notably includes the case of pure radiation, providing as one application a quantitative correction to the authors’ previous proposal in Causal dissipation and shock profiles in the relativistic fluid dynamics of pure radiation [Freistühler, H. and Temple, B., Proc. R. Soc. A 470, 20140055 (2014)]. [ABSTRACT FROM AUTHOR]

A fluid-kinetic model of the collisionless plasma flow in a convergent-divergent magnetic nozzle is presented. The model combines the leading-order Vlasov equation and the fluid continuity and perpendicular momentum equation for magnetized electrons, and the fluid equations for cold ions, which must be solved iteratively to determine the self-consistent plasma response in a three-dimensional magnetic field. The kinetic electron solution identifies three electron populations and provides the plasma density and pressure tensor. The far downstream asymptotic behavior shows the anisotropic cooling of the electron populations. The fluid equations determine the electric potential and the fluid velocities. In the small ion-sound gyroradius case, the solution is constructed one magnetic line at a time. In the large ion-sound gyroradius case, ion detachment from magnetic lines makes the problem fully three-dimensional. [ABSTRACT FROM AUTHOR]

In this series of articles, the authors discuss various phenomena in fluid dynamics, which may be investigated via tabletop experiments using low-cost or home-made instruments. The thirteenth article in this series demonstrates some experiments with Hele-Shaw cells. [ABSTRACT FROM AUTHOR]

The Accelerator-Driven System (ADS) is one of the most effective tools to deal with the spent fuels by nuclear transmutation. In the ADS, the neutrons could be produced by bombarding a proper spallation target with a concentrated beam of high-energy accelerator protons. Subsequently, the produced neutrons drive the nuclear transmutation in the sub-critical reactor. Therefore, the spallation target is an essential part of the ADS. Recently researchers proposed a gravity-driven dense granular target, which has both solid and fluid target characteristics. This study developed the FOCUS code to simulate the granular flow and heat transfer behaviors involved in the gravity-driven dense granular target. A solid sedimentation experiment was performed and simulated by FOCUS code. The simulation results were consistent with the findings in the experiment, which proved FOCUS to be an appropriate code to simulate the granular flow. Then the sensitivity analyses were performed to investigate the influence of the inlet flow rate and the target area shape on the state of the granular flow in the ADS granular spallation target. The simulation results showed that the velocity of each granular spallation target was related with the height of piled-up particles in the targets area. The geometry size of the target area obviously affected the flow state of targets. Meanwhile the inlet flow rate had a slight influence on the stable flow, unless the inlet flow was so large that targets overflow the target area. Furthermore, the study also calculated the heat transfer between each target and found that heat conduction between two contacted granular spallation targets was the main process in the targets area. The present work would be instructive for the ADS system design. [ABSTRACT FROM AUTHOR]

Fluids are high mobility environments that, under the action of external forces, are continuously and irreversibly deformed. The flow of fluid through a pipe is ensured by a pressure difference between its ends. The presented paper aims to experimentally determine the velocity profile of flowing a Newtonian fluid through a circular section pipe by measuring the local speed at five points on the pipe radius. [ABSTRACT FROM AUTHOR]

We present a primal–dual interior point algorithm for the resolution of steady-state viscoplastic fluid flows formulated as a conic optimization problem. We give a complete description of the algorithm including some advanced aspects such as a predictor–corrector and scaling scheme to improve its efficiency. Our interior-point approach is shown to be largely more efficient than Augmented Lagrangian (AL) approaches which are traditionally used to solve such problems. In particular, the interior-point approach is roughly 5 times faster than the modern accelerated version of AL algorithms. The yield surfaces are shown to be accurately predicted and various examples ranging from channel flows to three-dimensional flows through a porous medium demonstrate its efficiency. [ABSTRACT FROM AUTHOR]

The nonisothermal two-phase porous media flow of oil and hot water in a horizontal oil reservoir is considered. An asymptotic method for calculating the flow and solving related optimal control problems is proposed. Namely, the problem of choosing optimal control actions to maximize the oil production for a given level of financial costs and to minimize the costs for a given level of oil production is considered. [ABSTRACT FROM AUTHOR]

Numerical evidence is given that spherically symmetric perturbations of stable spherically symmetric steady states of the gravitational Vlasov–Poisson system lead to solutions which oscillate in time. The oscillations can be periodic in time or damped. Along one-parameter families of polytropic steady states we establish an Eddington–Ritter type relation which relates the period of the oscillation to the central density of the steady state. The numerically obtained periods are used to estimate possible periods for typical elliptical galaxies. [ABSTRACT FROM AUTHOR]

We present a computationally efficient sparse grid approach to allow for multiscale simulations of non-Newtonian polymeric fluids. Multiscale approaches for polymeric fluids often involve model equations of high dimensionality. A conventional numerical treatment of such equations leads to computing times in the order of months even on massively parallel computers. For a reduction of this enormous complexity, we propose the sparse grid combination technique. Compared to classical full grid approaches, the combination technique strongly reduces the computational complexity of a numerical scheme but only slightly decreases its accuracy. Here, we use the combination technique in a general formulation that balances not only different discretization errors but also considers the accuracy of the mathematical model. For an optimal weighting of these different problem dimensions, we employ a dimension-adaptive refinement strategy. We finally verify substantial cost reductions of our approach for simulations of non-Newtonian Couette and extensional flow problems. [ABSTRACT FROM AUTHOR]

No abstract is available for this article. [ABSTRACT FROM AUTHOR]

This study is mainly to explore gas transport process in heterogeneous media, which is to lay the foundation for oil-gas exploitation and development. Anomalous transport is observed to be ubiquitous in complex geological formations and has a paramount impact on petroleum engineering. Simultaneously, the random motion of particles usually exhibits obvious path- and history- dependent behaviors. This paper investigates the time-space fractional derivative models as a potential explanation for the time memory of long waiting time and the space non-locality of large regional-scale. A one-dimensional fractional advection-dispersion equation (FADE) based on fractional Fick’s law is firstly used to accurately describe the transport of Carbon dioxide (CO2) in complex media. The new fractional Darcy-advection-dispersion equation (FDADE) model has subsequently been proposed to make a comparison with FADE model and demonstrate its physical mechanism. Finally, the priori estimation of the parameters (fractional derivative index) in fractional derivative models and corresponding physical explanation are presented. Combined with experimental data, the numerical simulations show the fractional derivative models can well characterize the heavy-tailed and early breakthrough phenomenon of CO2 transport. [ABSTRACT FROM AUTHOR]

In this paper, a CFD simulation of falling film on a horizontal rotating tube is illustrated. The objective of this simulation is to explore the influence of various parameters on this kind flow. The simulation results show that in a certain range, the offset angle of the liquid column increases with the increase of the rotational speed, which agrees well with the experimental values. Compared to a stationary tube, the liquid film thickness at the left side of the liquid column is thinner but the right gets larger when the tube is rotating counterclockwise. And the liquid film velocity at the left side of the liquid column is equivalent to the linear superposition of the velocity at the standstill and the rotational velocity denoted by ω . Rotation has a great influence on the velocity distribution at the right side of liquid column. Increasing the rotational speed and the diameter, decreasing the inlet velocity and the inlet hole diameter will make the offset angle of the liquid film larger. The high temperature reduces the offset angle of the liquid column, and the gradient of the liquid column offset angle to temperature becomes smaller. When the temperature is above 65 °C, the effect of temperature on the offset angle of liquid column is negligible. When ω  = 200 rpm, the offset angle increases first and then decreases with the increase of the inlet height, but when ω  = 300 rpm, the offset angle increases with the increase of the inlet height. [ABSTRACT FROM AUTHOR]

Experimental study of wave evolution on the surface of isothermal liquid films falling down vertical plate conducted by means of field measuring system has revealed three typical scenarios of the evolution in the range of low and moderate liquid flow rates. At low liquid flow rates transverse modulation of 2D waves develops without formation of 3D waves. Two dimensional waves break up into 3D waves only when Reynolds number Re of the film flow exceeds some threshold value which depends on physical properties of working fluid. The fully developed steady-state 3D wave regimes are observed when Re exceeds another threshold value. The obtained results allow to determine the boundaries within which the adequate comparison between modeling and experiments on 3D wave flow of liquid films is possible. [ABSTRACT FROM AUTHOR]

Unconventional fractured gas wells occasionally exhibit bilinear flow during early production. When this flow regime is observed, important fracture properties can be estimated such as conductivity and/or spacing. However, the application of present-day rate-transientanalysis (RTA) methods to bilinear flow results in up to 18% error. This error is rate-dependent, and occurs because of nonlinearities in the gas-diffusivity equation. This paper presents a new correction factor that handles the rate dependency of bilinear flow, and enables more-accurate reservoir characterization. The diffusivity equation of gas in porous media has some nonlinearities that cannot be addressed by only using the real-gas pseudopressure. Even though neglecting these nonlinearities results in a model that is sufficiently accurate for the radial-flow case, errors arise in the boundary-dominated-flow (BDF) (Fraim and Wattenbarger 1987), the linear-flow (Ibrahim and Wattenbarger 2006; Nobakht and Clarkson 2012), and, as shown in this article, the bilinear-flow cases. Currently, no research studies provide an accurate bilinear-flow analytical model for gas reservoirs. To bridge this gap and to provide rate-transient analysts with a practical tool, this work presents a correction factor that can be incorporated into the existing bilinear-flow models. The correction factor was developed following an approach similar to that of Ibrahim and Wattenbarger (2006). The first step was to simulate a number of reservoir and well conditions. Second, fracture properties were back calculated with the current bilinear-flow models. Finally, errors between the back calculated and the simulated properties were correlated to dimensionless drawdown. After these steps, a correction factor was obtained that applied to various bilinear-flow cases. The obtained numerical results indicate that errors in bilinear-flow models are correlated with rate, or more precisely, dimensionless drawdown [a similar behavior is observed in the analytical model of linear flow, as demonstrated by Ibrahim and Wattenbarger (2006)]. This correlation can be used to reduce error to less than ±3%. Because the simulated cases cover an extensive range of unconventionalreservoir conditions, the empirical correction is robust and applicable to a wide variety of reservoir conditions. Most importantly, the correction is practical and can be readily incorporated into existing bilinear-flow models. The application of the new correction is demonstrated in this article with synthetic and field examples. [ABSTRACT FROM AUTHOR]

Maximum flow problem is one of the most fundamental network optimization problems. Recently, experimental observations showed that an amoeboid organism, Physarum polycephalum, contains a tube network by means of nutrients and signals circulating through the body. The tube network can sense and adopt to local shear stress difference in its own body until the shortest tubes of connecting two food sources (placed at two exits of a maze) keep alive while longer tubes vanish eventually. Unlike to the global optimization algorithm Physarum solver, we develop a mathematical model of a dynamical system which capture the local control behavior of Physarum when searching for foods. With this new model, a novel adaptive amoeba algorithm for maximum flow problem is proposed, which can be used to solve shortest path problem as Physarum solver. Furthermore,we firsts apply this model to solve maximum flow problem, where its convergence is proved in this paper as well. Additionally, numerical results demonstrate the validity and efficiency of the proposed algorithm to solve maximum flow problem. [ABSTRACT FROM AUTHOR]

Liquid-rich gas (LRG) reservoirs can exhibit complex phase and flow behavior due to gas condensation and re-vaporization and differences in phase mobilities that results in compositional variations inside the system. To date, the analysis of composition variation in liquid-rich wells has been largely limited to numerical modeling. This work uses a similarity-based analytical approach to study the in situ and flowing fluid composition of gas condensate wells producing under infinite-acting linear and radial flow under constant bottomhole pressure (BHP) condition. We propose a semi-analytical solution to the governing partial differential equations (PDEs) written in terms a compositional fluid formulation for multiphase (gas, oil and water) flow system in liquid rich gas reservoirs. The proposed solution is developed using similarity-theory ( i.e. Boltzmann’s transformation) and is validated by both analytical development and numerical simulation data. Using proposed method, pressure and overall composition are solved simultaneously and rigorously without any kind of simplification or approximation, from which producing fluid composition can be fully predicted prior to the availability of field production data. Moreover, results corroborate that when LRG wells are producing under 1 D linear regime – a commonly-observed flow condition for hydraulically-fractured horizontal wells completed in unconventional formations – and against a constant BHP constraint, the producing wellbore fluid composition remains constant as long as the system remains infinite acting, leading to a constant producing gas-oil ratio (GOR). For radial flow, however, producing wells team composition and GOR are shown to be time-dependent before stabilization at a nearly-constant value. [ABSTRACT FROM AUTHOR]

The article focuses on the theoretical model of the spherical active particles migration among natural microswimmers through catalytic Janus particles. Topics discussed include the alignment of the particles in the propulsion axes, the presentation of the directional response which emerge from the interplay of near surface swimming activity and shear flow, and the computation of the probability distributions for the orientation of the swimmer through the effect of thermal noise.