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Journal articles on the topic 'Stratified flow – Mathematical models'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Ilyasov, A. M., V. N. Kireev, S. F. Urmancheev, and I. Sh Akhatov. "Mathematical modeling of steady stratified flows." Proceedings of the Mavlyutov Institute of Mechanics 3 (2003): 195–207. http://dx.doi.org/10.21662/uim2003.1.014.

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The work is devoted to the analysis of the flow of immiscible liquid in a flat channel and the creation of calculation schemes for determining the flow parameters. A critical analysis of the well-known Two Fluids Model was carried out and a new scheme for the determination of wall and interfacial friction, called the hydraulic approximation in the theory of stratified flows, was proposed. Verification of the proposed approximate model was carried out on the basis of a direct numerical solution of the Navier–Stokes equations for each fluid by a finite-difference method with phase-boundary tracking by the VOF (Volume of Fluid) method. The graphical dependencies illustrating the change in the interfase boundaries of liquids and the averaged over the occupied area of the phase velocities along the flat channel are presented. The results of comparative calculations for two-fluid models are also given, according to the developed model in the hydraulic approximation and direct modeling. It is shown that the calculations in accordance with the hydraulic approximation are more consistent with the simulation results. Thus, the model of hydraulic approximation is the most preferred method for calculating stratified flows, especially in cases of variable volumetric content of liquids.

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2

Deleersnijder, Eric, Emmanuel Hanert, Hans Burchard, and Henk A. Dijkstra. "On the mathematical stability of stratified flow models with local turbulence closure schemes." Ocean Dynamics 58, no. 3-4 (September 19, 2008): 237–46. http://dx.doi.org/10.1007/s10236-008-0145-6.

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3

Kang, Qi, Jiapeng Gu, Xueyu Qi, Ting Wu, Shengjie Wang, Sihang Chen, Wei Wang, and Jing Gong. "Hydrodynamic Modeling of Oil–Water Stratified Smooth Two-Phase Turbulent Flow in Horizontal Circular Pipes." Energies 14, no. 16 (August 23, 2021): 5201. http://dx.doi.org/10.3390/en14165201.

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In the petrochemical industry, multiphase flow, including oil–water two-phase stratified laminar flow, is more common and can be easily obtained through mathematical analysis. However, there is limited mathematical analytical model for the simulation of oil–water flow under turbulent flow. This paper introduces a two-dimensional (2D) numerical simulation method to investigate the pressure gradient, flow field, and oil–water interface height of a pipeline cross-section of horizontal tube in an oil–water stratified smooth flow. Three Reynolds average N–S equation models (k−ε, k−ω, SST k−ω) are involved to simulate oil–water stratified smooth flow according to the finite volume method. The pressure gradient and oil–water interface height can be computed according to the given volume flow rate using the iteration method. The predicted result of oil–water interface height and velocity profile by the model fit well with several published experimental data, except that there is a large error in pressure gradient. The SST k−ω turbulence model appears higher accuracy for simulating oil–water two-phase stratified flow in a horizontal pipe.

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4

Iornumbe, SI, T. Tivde, and RA Chia. "A Mathematical Model of Stratified Geophysical Fluid Flows Over Variable Bottom Topography." NIGERIAN ANNALS OF PURE AND APPLIED SCIENCES 3, no. 3b (November 15, 2020): 112–37. http://dx.doi.org/10.46912/napas.202.

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In this paper, a mathematical model of stratified geophysical fluid flow over variable bottom topography was derived for shallow water. The equations are derived from the principles of conservation of mass and conservation of momentum. The force acting on the fluid is gravity, represented by the gravitational constant. A system of six nonlinear partial differential equations was obtained as the model equations. The solutions of these models were obtained using perturbation method. The presence of the coriolis force in the shallow water equations were shown as the causes of the deflection of fluid parcels in the direction of wave motion and causes gravity waves to disperse. As water depth decreases due to varied bottom topography, the wave amplitude were shown to increase while the wavelength and wave speed decreases resulting in overturning of the wave. The results are presented graphically.

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5

Senapati, Santosh Kumar, and Satish Kumar Dewangan. "COMPARISON OF PERFORMANCE OF DIFFERENT MULTIPHASE MODELS IN PREDICTING STRATIFIED FLOW." Computational Thermal Sciences: An International Journal 9, no. 6 (2017): 529–39. http://dx.doi.org/10.1615/computthermalscien.2017017248.

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6

Regnier, P., P. Jourabchi, and C. P. Slomp. "Reactive-Transport modeling as a technique for understanding coupled biogeochemical processes in surface and subsurface environments." Netherlands Journal of Geosciences - Geologie en Mijnbouw 82, no. 1 (April 2003): 5–18. http://dx.doi.org/10.1017/s0016774600022757.

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AbstractReactive-transport models contribute significantly to the field of modern geosciences. A general mathematical approach to solving models of complex biogeochemical systems is introduced. It is argued that even though mathematical models for reactive-transport simulations can be developed at various levels of approximation, the approach for their construction and application to the various compartments of the hydrosphere is fundamentally the same. The workings of coupled transport-reaction systems are described in more detail by means of examples, which demonstrate the similarities in the approach. Three models of the carbon dynamics in redox-stratified environments are compared: porous media flow problems in a coastal sediment and in a contaminated groundwater system; and a surface flow problem in a eutrophic estuary. Considering the interdisciplinary nature of such models, a Knowledge Base System for biogeochemical processes is proposed. Incorporation of the proposed knowledge base in an appropriate modeling framework, such as the Biogeochemical Reaction Network Simulator, proves an effective approach to the modeling of complex natural systems. This methodology allows for construction of multi-component reactive-transport models applicable to a wide range of problems of interest to the geoscientist.

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7

Kwon, Young-Sam. "Singular Limit of the Rotational Compressible Magnetohydrodynamic Flows." Advances in Mathematical Physics 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/9493186.

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We consider the compressible models of magnetohydrodynamic flows giving rise to a variety of mathematical problems in many areas. We derive a rigorous quasi-geostrophic equation governed by magnetic field from the stratified flows of the rotational compressible magnetohydrodynamic flows with the well-prepared initial data and the tool of proof is based on the relative entropy. Furthermore, the convergence rates are obtained.

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8

SEZAI, I., and A. A. MOHAMAD. "Three-dimensional double-diffusive convection in a porous cubic enclosure due to opposing gradients of temperature and concentration." Journal of Fluid Mechanics 400 (December 10, 1999): 333–53. http://dx.doi.org/10.1017/s0022112099006540.

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A three-dimensional mathematical model based on the Brinkman extended Darcy equation has been used to study double-diffusive natural convection in a fluid-saturated porous cubic enclosure subject to opposing and horizontal gradients of temperature and concentration. The flow is driven by conditions of constant temperature and concentration imposed along the two vertical sidewalls of the cubic enclosure, while the remaining walls are impermeable and adiabatic. The numerical simulations presented here span a wide range of porous thermal Rayleigh number, buoyancy ratio and Lewis number to identify the different steady-state flow patterns and bifurcations. The effect of the governing parameters on the domain of existence of the three-dimensional flow patterns is studied for opposing flows (N < 0). Comprehensive Nusselt and Sherwood number data are presented as functions of the governing parameters. The present results indicate that the double-diffusive flow in enclosures with opposing buoyancy forces is strictly three-dimensional for a certain range of parameters. At high Lewis numbers multiple dipole vortices form in the transverse planes near the horizontal top and bottom surfaces, which the two-dimensional models fail to detect. The dipolar vortex structures obtained are similar to those created in laboratory experiments by the injection of fluid into a stratified medium.

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9

Strickland, Christopher, Nadiah P. Kristensen, and Laura Miller. "Inferring stratified parasitoid dispersal mechanisms and parameters from coarse data using mathematical and Bayesian methods." Journal of The Royal Society Interface 14, no. 130 (May 2017): 20170005. http://dx.doi.org/10.1098/rsif.2017.0005.

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Biological invasions have movement at the core of their success. However, due to difficulties in collecting data, medium- and long-distance dispersal of small insects has long been poorly understood and likely to be underestimated. The agricultural release of parasitic hymenoptera, a group of wasps that are critical for biological pest control, represents a rare opportunity to study the spread of insects on multiple spatial scales. As these insects are typically less than 1 mm in size and are challenging to track individually, a first-time biocontrol release will provide a known spatial position and time of initial release for all individuals that are subsequently collected. In this paper, we develop and validate a new mathematical model for parasitoid wasp dispersal from point release, as in the case of biocontrol. The model is derived from underlying stochastic processes but is fully deterministic and admits an analytical solution. Using a Bayesian framework, we then fit the model to an Australian dataset describing the multi-scale wind-borne dispersal pattern of Eretmocerus hayati Zolnerowich & Rose (Hymenoptera: Aphelinidae). Our results confirm that both local movements and long-distance wind dispersal are significant to the movement of parasitoids. The model results also suggest that low velocity winds are the primary indicator of dispersal direction on the field scale shortly after release, and that average wind data may be insufficient to resolve long-distance movement given inherent nonlinearities and heterogeneities in atmospheric flows. The results highlight the importance of collecting wind data when developing models to predict the spread of parasitoids and other tiny organisms.

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10

Koohbor, B., M. Fahs, B. Belfort, B. Ataie-Ashtiani, and C. T. Simmons. "Fourier series solution for an anisotropic and layered configuration of the dispersive Henry Problem." E3S Web of Conferences 54 (2018): 00014. http://dx.doi.org/10.1051/e3sconf/20185400014.

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Henry Problem (HP) still plays an important role in benchmarking numerical models of seawater intrusion (SWI) as well as being applied to practical and managerial purposes. The popularity of this problem is due to having a closed-form semi-analytical (SA) solution. The early SA solutions obtained for HP were limited to extensive assumptions that restrict its application in practical works. Several further studies expended the generality of the solution by assuming lower diffusion coefficients or including velocity-dependent dispersion in the results. However, all these studies are limited to homogeneous and isotropic domains. The present work made an attempt to improve the reality of the SA solution obtained for dispersive HP by considering anisotropic and stratified heterogeneous coastal aquifers. The solution is obtained by defining Fourier series for both stream function and salt concentration, applying a Galerkin treatment using the Fourier modes as trial functions and solving the flow and the salt transport equations simultaneously in the spectral space. In order to include stratified heterogeneity, a special depth-hydraulic conductivity model is applied that can be solved analytically without significant mathematical complexity. Several examples are proposed and studied. The results show excellent agreement between the SA and numerical solutions obtained with an in-house advanced finite element code.

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11

Kharchenko, Serhii, Yurii Borshch, Stepan Kovalyshyn, Mykhailo Piven, Magomed Abduev, Anna Miernik, Ernest Popardowski, and Paweł Kiełbasa. "Modeling of Aerodynamic Separation of Preliminarily Stratified Grain Mixture in Vertical Pneumatic Separation Duct." Applied Sciences 11, no. 10 (May 12, 2021): 4383. http://dx.doi.org/10.3390/app11104383.

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The productivity of most grain cleaning machines seems to be directly related to the efficiency of vertical pneumatic separation ducts. Nevertheless, improvement is accompanied by an increase in the load of the vertical duct, the design of which is limited by the width of the grain cleaning machines. This requires an increase in the thickness of the layer of grain mixture that enters the working area of the duct, which significantly worsens the conditions of separation of its components under the action of airflow. Particles of light impurities are unable to separate due to their retention by the grain medium. This reduces the quality of cleaning and requires appropriate scientific and technical solutions. The application of preliminary stratification of the granular mixture while increasing the concentration of light impurities in the top layer of the mixture seems to be a prospective method. The positive effect of the previous stratification on the intensity of redistribution of light impurity particles in the working zone has been theoretically considered and experimentally confirmed. Mathematical models were obtained to determine the trajectory of discussed particles, taking into account the previous stratification of mixtures, and the corresponding dependences were established. The influence of the initial coordination of the introduction of the particles of lightweight impurities, their sizes and densities, and technological and structural parameters of operation of the pneumatic separation duct were taken into account in the studies. The intensification of the process of cleaning grain from lightweight impurities in the working zones of pneumatic separation ducts of grain cleaning machines is theoretically substantiated.

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12

Corvaro, Sara, and Maurizio Brocchini. "A Novel Two-fluid Model for the Identification of Possible Multiple Solutions in Slightly Inclined Pipelines." International Journal of Nonlinear Sciences and Numerical Simulation 14, no. 1 (February 21, 2013): 45–59. http://dx.doi.org/10.1515/ijnsns-2012-0127.

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Abstract A novel mechanistic two-fluid model (CB model) similar, in spirit, to the Taitel and Dukler [1, 2] (TD model), for the identification of possible multiple solutions of a multi-phase (gas-liquid) stratified flow in slightly inclined pipelines, is proposed. While Blasius-type closures are used in the TD model to represent the wall friction coefficients, the newly-implemented CB model makes use of Colebrook-White-type closures. Moreover, different closures for the interfacial shear are also employed in the CB models. The predictive capabilities of the CB model have been tested by using several experimental data, finding a better agreement between measured and calculated data than that existing when the TD model is used. The region of multiple solutions is influenced by the closures in use, such a dependence is more evident when different interfacial friction factors are used. Moreover, for the CB model also the fluid mixture in use influences the boundaries of the non-uniqueness region, while by using the TD model the multiple-solution region is unchanged. The choice of closures for the interfacial friction strongly influences the holdups, the Andritsos and Hanratty [10] correlation significantly shifting the non-uniqueness region to small values of the inclination parameter. Such a behaviour is more and more significant with the increase of the superficial gas velocity, even if for values of the inclination parameter within the range of inclinations for stratified flows (i.e. less than about 30° from the horizontal [11]), multiple solutions were not found. Finally, for the fluid mixture and flow conditions analyzed, multivalued solutions are obtained only for upward flows. Moreover, the portion of multiple-solution region interested by co-current flow (that occurs for slightly upward and downward pipes) is rather small, so that the operational point unlikely falls within such a region in the case of the studied hydrocarbon gas-liquid mixture.

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13

Makinde, O. D., N. Sandeep, T. M. Ajayi, and I. L. Animasaun. "Numerical Exploration of Heat Transfer and Lorentz Force Effects on the Flow of MHD Casson Fluid over an Upper Horizontal Surface of a Thermally Stratified Melting Surface of a Paraboloid of Revolution." International Journal of Nonlinear Sciences and Numerical Simulation 19, no. 2 (April 25, 2018): 93–106. http://dx.doi.org/10.1515/ijnsns-2016-0087.

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AbstractConsidering the recent aspiration of experts dealing with the painting of aircraft and bonnet of cars to further understand the relevance of skin friction and heat transfer while painting all these objects that are neither horizontal nor vertical, neither a cone/wedge or cylinder but upper horizontal surface of a paraboloid of revolution; a two-dimensional electrically conducting Casson fluid flow on an upper horizontal thermally stratified surface of a paraboloid of revolution is analyzed. The influence of melting heat transfer and thermal stratification are properly accounted for by modifying classical boundary condition of temperature. Plastic dynamic viscosity and thermal conductivity of the fluid are assumed to vary linearly with temperature. In view of this, all necessary models were modified to suit the case$T_m<T_\infty$. It is assumed that natural convection is driven by buoyancy; hence the suitable model of Boussinesq approximation is adopted. A suitable similarity transformation is applied to reduce the governing equations to coupled ordinary differential equations. These equations along with the boundary conditions are solved numerically by using Runge–Kutta technique along with shooting method. Effects of the magnetic field, temperature-dependent plastic dynamic viscosity and buoyancy parameters on the velocity and temperature are showed graphically and discussed. Normal influence of Lorentz force exists on Casson fluid flow when the thickness of the surface is small. Scientists and experts are urge to note an adverse effect of this force occurs on the fluid flow when the thickness of the surface is large.

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14

Moiseev, K. V. "Stratified flow with natural convection weakly stratified fluid." Proceedings of the Mavlyutov Institute of Mechanics 11, no. 1 (2016): 88–93. http://dx.doi.org/10.21662/uim2016.1.013.

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In work on the basis of a mathematical model based on a linear approximation, we study the formation of the layered flows with natural convection, poorly stratified inhomogeneous liquid. The regions of the parameters under which a layered structure of the flow-cell in a side heating.

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15

Allen, J. S., and P. A. Newberger. "On Intermediate Models for Stratified Flow." Journal of Physical Oceanography 23, no. 11 (November 1993): 2462–86. http://dx.doi.org/10.1175/1520-0485(1993)023<2462:oimfsf>2.0.co;2.

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16

Kazemi, Ehsan, and Stefan Heinz. "Dynamic Large Eddy Simulations of the Ekman Layer Based on Stochastic Analysis." International Journal of Nonlinear Sciences and Numerical Simulation 17, no. 2 (April 1, 2016): 77–98. http://dx.doi.org/10.1515/ijnsns-2015-0049.

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AbstractLarge eddy simulation (LES) of the neutrally stratified turbulent Ekman layer is performed. In particular, we compare three LES models with direct numerical simulation (DNS), which was validated against existing DNS. The models considered are a standard nondynamic LES model, the Smagorinsky model (SM), a standard dynamic LES model, the stabilized dynamic Smagorinsky model (DSM), and a new linear dynamic model (LDM), which was derived from a realizable stochastic turbulence model. The following conclusions are obtained. The SM does not represent an appropriate model for the flow considered. Mean velocity and turbulence intensities are poorly predicted. With respect to instantaneous fields, the SM provides a tilting of turbulence structures in the opposite direction as seen in DNS. The stabilized DSM also suffers from significant shortcomings. First, its behavior depends on the wall distance. Close to the wall, it produces acceptable turbulence structures. Away from the wall, it suffers from the same shortcomings as the SM. Second, it incorrectly describes the effect of grid coarsening. The new LDM is free from the disadvantages of the SM and stabilized DSM. Its predictions of both mean and instantaneous velocity fields agree very well with DNS. The relevant conclusion is the following. The use of a dynamic LES method represents a mean for correctly simulating large-scale structures (means and stresses), but it does not ensure a correct simultaneous simulation of small-scale structures. Our results indicate that a dynamic method designed in consistency with a realizable stress model can correctly simulate both large-scale and small-scale structures.

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17

Farmer, David M., and Laurence Armi. "Stratified flow over topography: models versus observations." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 457, no. 2016 (December 8, 2001): 2827–30. http://dx.doi.org/10.1098/rspa.2001.0802.

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18

McCartney, M. "Comparing mathematical models of traffic flow." Teaching Mathematics and its Applications 19, no. 4 (December 1, 2000): 183–87. http://dx.doi.org/10.1093/teamat/19.4.183.

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19

Liu, W. C., W. B. Chen, and M. H. Hsu. "Different turbulence models for stratified flow and salinity." Proceedings of the Institution of Civil Engineers - Maritime Engineering 163, no. 3 (September 2010): 117–33. http://dx.doi.org/10.1680/maen.2010.163.3.117.

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20

Biberg, D. "A MATHEMATICAL MODEL FOR TWO-PHASE STRATIFIED TURBULENT DUCT FLOW." Multiphase Science and Technology 19, no. 1 (2007): 1–48. http://dx.doi.org/10.1615/multscientechn.v19.i1.10.

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21

Blackmore, Denis, Roman Samulyak, and Anthony Rosato. "New Mathematical Models for Particle Flow Dynamics." Journal of Nonlinear Mathematical Physics 6, no. 2 (January 1999): 198–221. http://dx.doi.org/10.2991/jnmp.1999.6.2.6.

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22

Takači, Arpad. "Mathematical and simulation models of traffic flow." PAMM 5, no. 1 (December 2005): 633–34. http://dx.doi.org/10.1002/pamm.200510293.

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23

Dai, Albert, and Ching-Sen Wu. "High-resolution simulations of cylindrical gravity currents in a rotating system." Journal of Fluid Mechanics 806 (September 29, 2016): 71–101. http://dx.doi.org/10.1017/jfm.2016.598.

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Cylindrical gravity currents, produced by a full-depth lock release, in a rotating system are investigated by means of three-dimensional high-resolution simulations of the incompressible variable-density Navier–Stokes equations with the Coriolis term and using the Boussinesq approximation for a small density difference. Here, the depth of the fluid is chosen to be the same as the radius of the cylindrical lock and the ambient fluid is non-stratified. Our attention is focused on the situation when the ratio of Coriolis to inertia forces is not large, namely $0.1\leqslant {\mathcal{C}}\leqslant 0.3$, and the non-rotating case, namely ${\mathcal{C}}=0$, is also briefly considered. The simulations reproduce the major features observed in the laboratory and provide more detailed flow information. After the heavy fluid contained in a cylindrical lock is released in a rotating system, the influence of the Coriolis effects is not significant during the initial one-tenth of a revolution of the system. During the initial one-tenth of a revolution of the system, Kelvin–Helmholtz vortices form and the rotating cylindrical gravity currents maintain nearly perfect axisymmetry. Afterwards, three-dimensionality of the flow quickly develops and the outer rim of the spreading heavy fluid breaks away from the body of the current, which gives rise to the maximum dissipation rate in the system during the entire adjustment process. The detached outer rim of heavy fluid then continues to propagate outward until a maximum radius of propagation is attained. The body of the current exhibits a complex contraction–relaxation motion and new outwardly propagating pulses form regularly in a period slightly less than half-revolution of the system. Depending on the ratio of Coriolis to inertia forces, such a contraction–relaxation motion may be initiated after or before the attainment of a maximum radius of propagation. In the contraction–relaxation motion of the heavy fluid, energy is transformed between potential energy and kinetic energy, while it is mainly the kinetic energy that is consumed by the dissipation. As a new pulse initially propagates outward, the potential energy in the system increases at the expense of decreasing kinetic energy, until a local maximum of potential energy is reached. During the latter part of the new pulse propagation, the kinetic energy in the system increases at the expense of decreasing potential energy, until a local minimum of potential energy is reached and another new pulse takes form. With the use of three-dimensional high-resolution simulations, the lobe-and-cleft structure at the advancing front can be clearly observed. The number of lobes is maintained only for a limited period of time before merger between existing lobes occurs when a maximum radius of propagation is approached. The high-resolution simulations complement the existing shallow-water formulation, which accurately predicts many important features and provides insights for rotating cylindrical gravity currents with good physical assumptions and simple mathematical models.

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24

MERRYFIELD, WILLIAM J., and GREG HOLLOWAY. "Eddy fluxes and topography in stratified quasi-geostrophic models." Journal of Fluid Mechanics 380 (February 10, 1999): 59–80. http://dx.doi.org/10.1017/s0022112098003656.

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Turbulent stratified flow over topography is studied using layered quasi-geostrophic models. Mean flows develop under random forcing, with lower-layer mean stream-function positively correlated with topography. When friction is sufficiently small, upper-layer mean flow is weaker than, but otherwise resembles, lower-layer mean flow. When lower-layer friction is larger, upper-layer mean flow reverses and can exceed lower-layer mean flow in strength. The mean interface between layers is domed over topographic elevations. Eddy fluxes of potential vorticity and layer thickness act in the sense of driving the flow toward higher entropy. Such behaviour contradicts usual eddy parameterizations, to which modifications are suggested.

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25

Beatty, P. A., and W. F. Hughes. "Stratified Two-Phase Flow in Annular Seals." Journal of Tribology 112, no. 2 (April 1, 1990): 372–81. http://dx.doi.org/10.1115/1.2920267.

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A new mathematical theory for the analysis of leakage rate behavior of annular shaft seals operating in the two-phase regime is presented which is based on the stratified flow of the boiling liquid and vapor phases. The flow is presumed to be axisymmetric, steady, and so rapid as to be turbulent. A set of governing equations for film-averaged liquid and vapor properties is developed. The streams are assumed to be adiabatic and moving at different average velocities. Effects of heat generation due to viscous dissipation and of interfacial mass transfer are accounted for fully. The methods of calculation for leakage under choked and unchoked conditions are explained. Many numerical results of leakage rate calculations for cryogenic oxygen are presented and are compared to corresponding results from a homogeneous-equilibrium flow model. Parametric studies show that leakage is fairly insensitive to the arrangement of the liquid and vapor phases within the seal.

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26

Vasiliev, O. F., T. E. Ovchinnikova, and G. G. Chernykh. "Numerical Models of the Vertical Turbulent Exchange in Stably Stratified Water Body: I. Mathematical Models." Journal of Engineering Thermophysics 27, no. 4 (October 2018): 522–30. http://dx.doi.org/10.1134/s1810232818040148.

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27

Kranenburg, C. "On gradient transport turbulence models for stably stratified shear flow." Dynamics of Atmospheres and Oceans 23, no. 1-4 (January 1996): 205–15. http://dx.doi.org/10.1016/0377-0265(95)00412-2.

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28

Fedler, C. B. "Mathematical models describing the flow of granular material." Mathematical and Computer Modelling 11 (1988): 510–13. http://dx.doi.org/10.1016/0895-7177(88)90545-6.

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29

Maskal, Alan B., and Fatih Aydogan. "Mathematical spacer grid models for single phase flow." Annals of Nuclear Energy 103 (May 2017): 130–46. http://dx.doi.org/10.1016/j.anucene.2017.01.019.

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30

Maskal, Alan B., and Fatih Aydogan. "Mathematical spacer grid models for two phase flow." Annals of Nuclear Energy 103 (May 2017): 173–93. http://dx.doi.org/10.1016/j.anucene.2017.01.024.

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31

Bonilla, J., L. J. Yebra, and S. Dormido. "Chattering in dynamic mathematical two-phase flow models." Applied Mathematical Modelling 36, no. 5 (May 2012): 2067–81. http://dx.doi.org/10.1016/j.apm.2011.08.013.

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32

Bachurina, Maria, Alexey Kazakov, and Natalia Trufanova. "Mathematical modelling of stratified flow of polymer melts in an axisymmetric formulation." PNRPU Mechanics Bulletin 2 (June 30, 2014): 102–24. http://dx.doi.org/10.15593/perm.mech/2014.2.05.

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33

Rao, K. J., and S. M. de Bruyn Kops. "A mathematical framework for forcing turbulence applied to horizontally homogeneous stratified flow." Physics of Fluids 23, no. 6 (June 2011): 065110. http://dx.doi.org/10.1063/1.3599704.

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34

Hayat, Tasawar, Ikram Ullah, Muhammad Waqas, and Ahmed Alsaedi. "MHD stratified nanofluid flow by slandering surface." Physica Scripta 93, no. 11 (October 5, 2018): 115701. http://dx.doi.org/10.1088/1402-4896/aae1a2.

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35

Shahzadi, Iqra, and Nabeela Kausar. "Doubly stratified non-Newtonian nanofluid flow featuring nonlinear convection." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 10 (August 6, 2020): 4389–401. http://dx.doi.org/10.1108/hff-04-2019-0351.

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Purpose The formulation of nonlinear convective non-Newtonian material is reported in this communication. Aspects of thermal radiation and heat source are taken into account for heat transport analysis. The novel stratifications (thermal and solutal) and convective conditions are considered simultaneously. The boundary-layer concept is implemented to simplify the complex mathematical expressions. Design/methodology/approach The well-known optimal homotopy scheme develops the computations. Optimal values regarding nonzero auxiliary variables are calculated and examined. Findings Nonlinear convective flow; Thixotropic non-Newtonian material; Thermal radiation; Heat source; Stratifications and convective conditions; Buongiorno model. Originality/value To the best of authors’ knowledge, no such analysis has yet been reported.

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36

Junevičius, Raimundas, and Marijonas Bogdevičius. "MATHEMATICAL MODELLING OF NETWORK TRAFFIC FLOW." TRANSPORT 24, no. 4 (December 31, 2009): 333–38. http://dx.doi.org/10.3846/1648-4142.2009.24.333-338.

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The article describes mathematical models of traffic flows to initiate different traffic flow processes. Separate elements of traffic flow models are made in a way to be connected together to get a single complex model. A model of straight road with different boundary conditions is presented as a separate part of the network traffic flow model. First testing is conducted in case the final point of the whole modelled traffic line is closed and no output from that point is possible. The second test is performed when a constant value of traffic flow speed and traffic flow rate is entered. Mathematical simulation is carried out and the obtained results are listed.

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37

Vaidheeswaran, Avinash, Alejandro Clausse, William D. Fullmer, Raul Marino, and Martin Lopez de Bertodano. "Chaos in wavy-stratified fluid-fluid flow." Chaos: An Interdisciplinary Journal of Nonlinear Science 29, no. 3 (March 2019): 033121. http://dx.doi.org/10.1063/1.5055782.

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ADACHI, Takahiro. "PERFORMANCE OF SECOND CLOSURE TURBULENCE MODELS FOR STRATIFIED OPEN CHANNEL FLOW." Doboku Gakkai Ronbunshuu B 66, no. 1 (2010): 76–86. http://dx.doi.org/10.2208/jscejb.66.76.

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39

Fowler, A. C., and C. G. Noon. "Mathematical models of compaction, consolidation and regional groundwater flow." Geophysical Journal International 136, no. 1 (January 1, 1999): 251–60. http://dx.doi.org/10.1046/j.1365-246x.1999.00717.x.

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Roy, Ranadhir, Fabiola Rios, and Daniel N. Riahi. "Mathematical Models for Flow of Chyme during Gastrointestinal Endoscopy." Applied Mathematics 02, no. 05 (2011): 600–607. http://dx.doi.org/10.4236/am.2011.25080.

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41

Emikh, V. N. "Mathematical models of groundwater flow with a horizontal drain." Water Resources 35, no. 2 (March 2008): 205–11. http://dx.doi.org/10.1134/s0097807808020097.

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Nicosia, Sebastiano, and Giuseppe Pezzinga. "Mathematical models of blood flow in the arterial network." Journal of Hydraulic Research 45, no. 2 (March 2007): 188–201. http://dx.doi.org/10.1080/00221686.2007.9521759.

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43

Krijger, Johan K. B., Berend Hillen, and Hendrik W. Hoogstraten. "Mathematical models of the flow in the basilar artery." Journal of Biomechanics 22, no. 11-12 (January 1989): 1193–202. http://dx.doi.org/10.1016/0021-9290(89)90221-2.

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44

Tyagi, V., S. Darbha, and K. R. Rajagopal. "A review of the mathematical models for traffic flow." International Journal of Advances in Engineering Sciences and Applied Mathematics 1, no. 1 (July 2009): 53–68. http://dx.doi.org/10.1007/s12572-009-0005-8.

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45

El Khatib, N., O. Kafi, A. Sequeira, S. Simakov, Yu Vassilevski, and V. Volpert. "Mathematical modelling of atherosclerosis." Mathematical Modelling of Natural Phenomena 14, no. 6 (2019): 603. http://dx.doi.org/10.1051/mmnp/2019050.

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The review presents the state of the art in the atherosclerosis modelling. It begins with the biological introduction describing the mechanisms of chronic inflammation of artery walls characterizing the development of atherosclerosis. In particular, we present in more detail models describing this chronic inflammation as a reaction-diffusion wave with regimes of propagation depending on the level of cholesterol (LDL) and models of rolling monocytes initializing the inflammation. Further development of this disease results in the formation of atherosclerotic plaque, vessel remodelling and possible plaque rupture due its interaction with blood flow. We review plaque-flow interaction models as well as reduced models (0D and 1D) of blood flow in atherosclerotic vasculature.

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Pukhnachev, V. V., A. G. Petrova, and O. A. Frolovskaya. "Polymer Solutions and Their Mathematical Models." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 2 (206) (June 18, 2020): 84–93. http://dx.doi.org/10.18522/1026-2237-2020-2-84-93.

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Mathematical models for the motion of weak solutions of polymers have been studied over the past 50 years. The initial model (Voitkunskii, Amfilokhiev, and Pavlovskii, 1970) contains two key parameters - relaxation viscosity and shear stress relaxation time. In the limiting case, when the last parameter is small, the Pavlovskii model (1971) arises. Its equations are close to second-grade fluid equations (Rivlin and Eriksen, 1955). The paper contains an overview of the works on all three models and new results related to the Pavlovskii model. The solution to the problem of the un-steady layered flow of an aqueous polymer solution in a layer with a free boundary, the boundary condition on which includes the time derivative of the desired function is constructed. We derive the equations that describe the motion of a polymer solution in a laminar boundary layer near a rectilinear plate. The parameter included in equations characterizes the ratio of the thickness of the Prandtl boundary layer to the thickness of the relaxation boundary layer. We study the influence of this parameter on the motion picture by the example of a stationary flow near a critical point.

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Rotunno, Richard, and Manuela Lehner. "Two-Layer Stratified Flow past a Valley." Journal of the Atmospheric Sciences 73, no. 10 (September 27, 2016): 4065–76. http://dx.doi.org/10.1175/jas-d-16-0132.1.

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Abstract Observations and models of nocturnal katabatic winds indicate strong low-level stability with much weaker stability aloft. When such winds encounter an embedded depression in an otherwise smooth sloping plane, the flow responds in a manner that is largely describable by the inviscid fluid dynamics of stratified flow. Building on earlier work, the present study presents a series of numerical simulations based on the simplest nontrivial idealization relevant to the observations: the height-independent flow of a two-layer stratified fluid past a two-dimensional valley. Stratified flow past a valley has received much less attention than the related problem of stratified flow past a hill. Hence, the present paper gives a detailed review of existing theory and fills a few gaps along the way. The theory is used as an interpretive guide to an extensive set of numerical simulations. The solutions exhibit a variety of behaviors that depend on the nondimensional input parameters. These behaviors range from complete flow through the valley to valley-flow stagnation to situations involving internal wave breaking, lee waves, and quasi-stationary waves in the valley. A diagram is presented that organizes the solutions into flow regimes as a function of the nondimensional input parameters.

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Yang, Jincheng, and Zhiwu Lin. "Linear Inviscid Damping for Couette Flow in Stratified Fluid." Journal of Mathematical Fluid Mechanics 20, no. 2 (May 29, 2017): 445–72. http://dx.doi.org/10.1007/s00021-017-0328-3.

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Friedlander, S. "On Nonlinear Instability and Stability for Stratified Shear Flow." Journal of Mathematical Fluid Mechanics 3, no. 1 (March 2001): 82–97. http://dx.doi.org/10.1007/pl00000965.

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Ngan, K., P. Bartello, and D. N. Straub. "Predictability of Rotating Stratified Turbulence." Journal of the Atmospheric Sciences 66, no. 5 (May 1, 2009): 1384–400. http://dx.doi.org/10.1175/2008jas2799.1.

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Abstract Although predictability represents one of the fundamental problems in atmospheric science, gaps in our knowledge remain. Theoretical understanding of the inverse error cascade is limited mostly to homogeneous, isotropic turbulence, whereas numerical simulations have focused on highly complex numerical weather prediction models. These results cannot be easily reconciled. This paper describes selected aspects of the predictability behavior of rotating stratified turbulence. The objective is to determine how the predictability varies with scale when the dynamics are more realistic than the idealized models that underlie the classical picture of predictability and yet are free of the parameterizations that complicate interpretation of NWP models. Using a numerical model of the nonhydrostatic Boussinesq equations, it is shown that the predictability decay, as diagnosed by the relative error, is slower for subsynoptic flow. The dependence on the deformation radius, differences between balanced and unbalanced modes, and implications for NWP models are discussed.

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