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1

The analytical expressions to describe wave propagation and heat release during microwave treatment of porous inhomogeneous plate based on the W.K.B. solution model

Holubets Taras, Terletskiy Rostyslav, Yuzevych Vlodymyr

Advances in Materials Science

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2023

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Vol. 23, nr 1(75)

69--81

EN

In this paper study for wave propagation in non-homogeneous porous plate sample with slowly varyingrefractive indexis presented. It is based on simple symmetricsolution of the wave equation for linearlypolarized electromagnetic wave aligned into the porous plate perpendicularlyto the external surface. Using correct boundary conditions both the transverseelectric (T.E) and transversemagnetic (T.M) modes, named shortly by (T.E.M) mode for electromagnetic wave, are considered. The Wentzel-Kramers-Brillouin (W.K.B.) solutions for symmetric incident irradiation of fixed power generated at the plate surfaceswas obtained. It isdonethe analysis of the reflection and transmission coefficients on the surfaces of plate.

2

Alternative relationships to enhance the applicability of nonlinear filtration models in porous media

Banerjee Ashes, Jagupilla Sarath Chandra K., Pasupuleti Srinivas, Annavarapu Chandra Sekhara Rao

Acta Geophysica

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2023

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Vol. 71, no. 4

1787--1799

EN

Nonlinear filtration in porous packing has remained a research challenge till this day. There have been numerous attempts to model the flow characteristics under such conditions. However, as demonstrated in the present study, these models are applicable for only some specific conditions. The present study attempts to develop an empirical model which can be widely applicable. The Forchheimer-type models have been the most widely used in the literature for prediction of flow in porous media. The study identifies that the Ergun equation (the most popular form of the Forchheimer equation) with its original coefficients is unable to predict the flow properties over a wide range of data. Similar observation can be made for all other identical models. However, by optimising the coefficient values (A = 3705.79 and B = 6.17), the equation's performance can be significantly improved. The current study aims to create a working model that can be used to predict flow in porous media under a variety of packing, fluid, and flow conditions using multivariate polynomial regression and machine learning tools. It was observed that media size has far greater influence on the coefficients than any other parameter. Empirical models were created to predict Forchheimer coefficients, which represent R2 values greater than 0.9 for training, validation, and test data. These models were further tested on a separate dataset with velocity and hydraulic gradient data compiled from the literature. The models were found to have very reliable performance with R2 values above 0.90.

3

Method of Designing a Distortion Gauze for Testing a Boundary Layer Ingesting Fan

Kwiatkowski Tomasz, Sieradzki Adam, Łukasik Borys

Transactions on Aerospace Research

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2022

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Nr 1 (266)

1--17

EN

As global trends aim to reduce emissions of pollutants, boundary layer ingesting (BLI) propulsions are attracting more and more attention. As such, N+2 generation aircraft with propulsion placed in the aft of the aircraft are gaining in popularity. The boundary layer is formed on the fuselage before entering the engine located in the aft of the aircraft. Due to significant difficulties in performing experimental tests of BLI propulsors with full-size aircraft, distortion gauzes are one of the methods to provide the desired air velocity profile at the inlet. This paper describes a novel method of designing such gauzes, a topic which is not well covered in the existing literature. In the first stage of the presented method, single orifices of different sizes were calculated using CFD tools. The relationship between their size and the gauze resistance coefficient was identified, making it possible to model the distortion gauze using porous media. An iterative approach was used to design a gauze that meets the requirements. This is, to our knowledge, the first distortion gauze design description where a porous media model has been used. Experimental tests demonstrated that the produced distortion gauze yields a velocity profile comparable to the desired one. This indicates the great potential of using the presented approach in further research on boundary layer ingesting propulsions. It offers an opportunity to reduce substantially both the costs of experimental research and the time required to design a distortion-tolerant fan.

4

Influence of structural characteristics of porous materials on the coefficient of thermal conductivity

Cheilytko Andrii

Journal of New Technologies in Environmental Science

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2022

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Vol. 6, nr 3

104--112

EN

The existing dependences of the effective coefficient of thermal conductivity of the material depending on the size and location of pores in it are analyzed and compared with each other and with previously obtained experimental data. It is shown that the resulting thermophysical properties of the material are affected not only by the porosity, but also by the location of the pores in the volume of the material. The disadvantages of the existing dependences of determining the effective thermal conductivity of the material on the type of porosity (both for porous material and for dispersed systems) are shown. Also, the most reliable dependences of the thermal conductivity coefficients on the porosity of dispersed systems for backfill materials and the need for their correction by empirical coefficients are determined. Complex indicators that fully describe the porous structure and on which the mathematical model of heat exchange processes in a porous medium should be based are proposed.

5

A Novel Approach to Quantifying the Effect of the Density of Sand Cores on Their Gas Permeability

Sundaram Dinesh, Svidró József Tamás, Svidró Judit, Diószegi Attila

Journal of Casting & Materials Engineering

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2022

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Vol. 6, no. 2

33--38

EN

The density of moulding mixtures used in the foundry industry plays a significant role since it influences the strength, porosity, and permeability of moulds and cores. The latter is routinely tested in foundries using different solutions to control the properties of the moulding materials that are used to make moulds and cores. In this paper, the gas permeability of sand samples was measured using a custom-made setup to obtain the gas permeability in standard units instead of the usual permeability numbers (PN) with calibrated units. The aim of the work was to explore the effect of density variations in moulding materials on their gas permeabilities. Permeability in this work is quantified in SI units, square metres [m2]. The setup works based on Darcy’s law and the numbers obtained from the measurements can be used to deduce the gas permeability, k, of a sample. Two furan resin bonded mixtures with the same grain size distribution were hand-rammed with varying compaction forces to obtain a variation in density. Cylindrical samples (50 × 50 mm) were prepared using a silica sand aggregate sourced from a Swedish lake. The results of the measurement provided the difference in gas permeability between the samples that have varying densities. The results of permeability were then extrapolated by modifying the viscosity value of the air passed through the sample. In order to find the effect of apparent density variation on the pore characteristics of the samples, mercury intrusion porosimetry (MIP) was also performed. The results were in line with the gas permeability measurements.

6

Effect of MHD on unsteady oscillatory Couette flow through porous media

Sharma Bhupendra K., Sharma Pawan Kumar, Cauhan Sudhir Kumar

International Journal of Applied Mechanics and Engineering

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2022

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Vol. 27, no. 1

188--202

EN

This paper describes the effects of a magnetic field on unsteady free convection oscillatory systems. When temperature and species concentration fluctuate with time around a non-zero constant, "Couette flow" across a porous medium occurs. The system of non-linear ODEs that governs the flow is solved analytically using the perturbation approach because the amplitude of fluctuations is very tiny. Mean flow and transient velocity, transient concentration, transient temperature, heat transfer, mean skin friction and phase and amplitude of skin friction. All have approximate solutions. The influence of different parameters on flow characteristics has been specified and discussed.

7

An efficient method of tortuosity estimation

Sobieski W.

Archives of Mechanics

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2022

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Vol. 74, nr 1

39--64

EN

The paper presents a comparative analysis of tortuosity calculations in two types of 2D random geometries: with non-overlapping circles and with overlapping squares. Both geometries were converted to binary geometries with different resolution. Next, simulations involving the Lattice Boltzmann Method were performed to obtain velocity fields in a pore space. Based on the obtained velocity fields, Hydraulic tortuosity and streamline tortuosity were calculated, based on the obtained velocity fields, for all considered cases. Hydraulic tortuosity was calculated with the methodology proposed by Koponen et al., whereas streamline tortuosity was determined with the use of a new iterative algorithm. Two variants of the algorithm were proposed. Additionally, the obtained results were compared with selected formulas from the literature. The study demonstrated that calculations of streamlines exiting local inlet velocity maxima are a good alternative to calculations where all possible streamlines are taken into account. Computation time was significantly shorter and estimation quality was comparable.

8

On convergence of explicit finite volume scheme for one-dimensional three-component two-phase flow model in porous media

Mostefai Mohamed Lamine, Choucha Abdelbaki, Cherif Bahri

Demonstratio Mathematica

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2021

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Vol. 54, nr 1

510--526

EN

In this work, we develop and analyze an explicit finite volume scheme for a one-dimensional nonlinear, degenerate, convection–diffusion equation having application in petroleum reservoir. The main difficulty is that the solution typically lacks regularity due to the degenerate nonlinear diffusion term. We analyze a numerical scheme corresponding to explicit discretization of the diffusion term and a Godunov scheme for the advection term. L∞ stability under appropriate CFL conditions and BV estimates are obtained. It is shown that the scheme satisfies a discrete maximum principle. Then we prove convergence of the approximate solution to the weak solution of the problem, and we mount convergence results to a weak solution of the problem in L1 . Results of numerical experiments are presented to validate the theoretical analysis.

9

Phenomenological and numerical issues concerning dynamics of nonisobaric multicomponent diffusion of gases in macroporous media

Bizon Katarzyna, Tabiś Bolesław

Chemical and Process Engineering

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2021

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Vol. 42, nr 3

223-–234

EN

The homogeneity of an immiscible liquid–liquid system was investigated in a baffled vessel agitated by a Rushton turbine. The dispersion homogeneity was analyzed by comparing Sauter mean diameters and drop size distribution (DSD) determined in different measured regions for various impeller speeds. The sizes of droplets were obtained by the in-situ measurement technique and by the Image Analysis (IA) method. Dispersion kinetics was successfully fitted with Hong and Lee (1983) model. The effect of intermittency turbulence on drop size reported by Bałdyga and Podgórska (1998) was analyzed and the multifractal exponent 𝛼𝐹𝑇 was evaluated.

10

The stability of poro elastic wave equations in saturated porous media

Xiong Fansheng, Sun Weitao, Liu Jiawei

Acta Geophysica

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2021

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Vol. 69, no. 1

65--75

EN

Poro-elastic wave equations are one of the fundamental problems in seismic wave exploration and applied mathematics. In the past few decades, elastic wave theory and numerical method of porous media have developed rapidly. However, the math ematical stability of such wave equations have not been fully studied, which may lead to numerical divergence in the wave propagation simulation in complex porous media. In this paper, we focus on the stability of the wave equation derived from Tuncay’s model and volume averaging method. By analyzing the stability of the frst-order hyperbolic relaxation system, the mathematical stability of the wave equation is proved for the frst time. Compared with existing poro-elastic wave equations (such as Biot’s theory), the advantage of newly derived equations is that it is not necessary to assume uniform distribution of pores. Such wave equations can spontaneously incorporate complex microscale pore/fracture structures into large-scale media, which is critical for unconventional oil and gas exploration. The process of proof and numerical examples shows that the wave equations are mathematically stable. These results can be applied to numerical simulation of wave feld in reservoirs with pore/fracture networks, which is of great signifcance for unconventional oil and gas exploration.

11

Numerical studies of internal flow in different types of filters

Stanik Magdalena, Caban Szymon, Klonecka Marlena, Buczak Mateusz, Wiśniewski Piotr

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2020

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Vol. 24, No 4

335--344

EN

The quality of ambient air attracts considerable, widespread interest. Over the last decades, air purification has become an integral part of HVAC systems, process engineering, automotive and respiratory protection. Efficient separation of micro- and nano- particles is solidly linked with the development of new, sophisticated filtrating materials, as well as generating and validating mathematical models of such porous structures. The paper regards the numerical modeling of various filters. The presented work aims to validate four virtual filtrating materials – the fiberglass HEPA filter, the paper filter used in the automotive industry, knitted wire mesh and polyurethane foam. The pressure drop obtained for the filters under investigation was examined. The CFD results were validated against the data available in the literature. The agreement of the results of numerical and experimental studies proves the suitability of the proposed methods. At the same time, the simplifications employed in the simulations leave room for further improvement in future works.

12

Natural and mixed convection of a nanofluid in porous cavities: critical analysis using buongiorno’s model

Zahmatkesh Iman, Habibi Mohammad Reza

Journal of Theoretical and Applied Mechanics

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2019

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Vol. 57 nr 1

221--233

EN

In this paper, Buongiorno’s mathematical model is adopted to simulate both natural convection and mixed convection of a nanofluid in square porous cavities. The model takes into account the Brownian diffusion and thermophoresis effects. Both constant and variable temperatures are prescribed at the side walls while the remaining walls are maintained adiabatic. Moreover, all boundaries are assumed to be impermeable to the base fluid and the nanoparticles. The governing equations are transformed to a form of dimensionless equations and then solved numerically using the finite-volume method. Thereafter, effects of the Brownian diffusion parameter, the thermophoresis number, and the buoyancy ratio on the flow strength and the average Nusselt number as well as distributions of isocontours of the stream function, temperature, and nanoparticles fraction are presented and discussed.

13

Fuzzy logic approach in the analysis of heat transfer in a porous sorbent bed of the adsorption chiller

Grabowska K., Krzywański J., Sztekler K., Kalawa W., Nowak W.

Technical Sciences / University of Warmia and Mazury in Olsztyn

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2018

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nr 21(4)

281--290

EN

Thermal conductivity in the boundary layer of heat exchange surface is the crucial parameter of adsorption process efficiency which occurs in the adsorption bed. In order to improve heat transfer conditions in the adsorption chiller, novel constructions of adsorption beds are currently investigated. The porous structure of the sorbent layer causes low thermal conductivity in the adsorption bed. One of the methods to improve heat transfer conditions is a modification of porous media bed structure with glue which is characterized with higher thermal conductivity. The optimum parameters of sorbents and glues to build the novel coated construction, in terms of improving the chiller Coefficient of Performance (COP) were defined in (Grabowska et al. 2018a). The paper implements fuzzy logic approach for predicting thermal conductivity of modified porous media layers. The developed model allows determination of the sorbent layer thermal conductivity based on various input parameters: arithmetic average of particle distribution d, density ρ and thermal diffusivity k. The data from empirical research was used to build up the model by fuzzy logic methods.

14

The effect of the magnetic field on the Rayleigh-Taylor instability in a couple-stress fluid

Chavaraddi K. B., Awati V. B., Nandeppanavar M. M., Gouder P. M.

International Journal of Applied Mechanics and Engineering

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2018

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Vol. 23, no. 3

611--622

EN

In this study we examine the effect of the magnetic field parameter on the growth rate of the Rayleigh-Taylor instability (RTI) in a couple stress fluids. A simple theory based on fully developed flow approximations is used to derive the dispersion relation for the growth rate of the RTI. The general dispersion relation obtained using perturbation equations with appropriate boundary conditions will be reduced for the special cases of propagation and the condition of instability and stability will be obtained. In solving the problem of the R-T instability the appropriate boundary conditions will be applied. The couple-stress parameter is found to be stabilizing and the influence of the various parameters involved in the problem on the interface stability is thoroughly analyzed. The new results will be obtained by plotting the curves between the dimensionless growth rate and the dimensionless wave number for various physical parameters involved in the problem (viz. the magnetic field, couple-stress, porosity, etc.) in the problem. It is found that the magnetic field and couple-stress have a stabilization effect whereas the buoyancy force (surface tension) has a destabilization effect on the RT instability in the presence of porous media.

15

The effect of rheology with gas bubbles on linear elastic waves in fluid-saturated granular media

ALI A. A., Strunin D. V.

International Journal of Applied Mechanics and Engineering

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2018

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Vol. 23, no. 3

575--594

EN

Elastic waves in fluid-saturated granular media depend on the grain rheology, which can be complicated by the presence of gas bubbles. We investigated the effect of the bubble dynamics and their role in rheological scheme, on the linear Frenkel-Biot waves of P1 type. For the wave with the bubbles the scheme consists of three segments representing the solid continuum, fluid continuum and bubbles surrounded by the fluid. We derived the Nikolaevskiy-type equation describing the velocity of the solid matrix in the moving reference system. The equation is linearized to yield the decay rate λ as a function of the wave number k. We compared the λ (k) -dependence for the cases with and without the bubbles, using typical values of the input mechanical parameters. For both the cases, the λ(k) curve lies entirely below zero, which implies a global decay of the wave. We found that the increase of the radius of the bubbles leads to a faster decay, while the increase in the number of the bubbles leads to slower decay of the wave.

16

A Study on the Wilkins and Forchheimer Equations used in Coarse Granular Media Flow

Banerjee A., Pasupuleti S., Singh M. K., Kumar G. N. P.

Acta Geophysica

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2018

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Vol. 66, no. 1

81--91

EN

Complexity of the pore geometry and the random nature of flow velocity make it difficult to predict and represent post laminar flow through porous media. Present study experimentally investigates the applicability of Forchheimer and Wilkins equations for post laminar flow where Darcy’s law is invalid due to predominant inertial effect. It is observed that both porosity and media size have significant influence over the coefficients of the Forchheimer coefficients. To incorporate the effect of porosity and media size, behaviour of Forchheimer coefficients are investigated with hydraulic radius as characteristic length. An inversely proportional variation trend is found for all the present and earlier reported data. A new empirical relation between Forchheimer coefficients and hydraulic radius is obtained which can be universally applicable for all media size and porosity. Coefficients of the Wilkins equation are found to be non-deviating for different hydraulic radius in the present study and in the reported literature validating its applicability in predicting the non laminar flow through porous media. Further the Wilkins equation is modified after incorporating the correction factors for better applicability on the field.

17

The analysis of the relations between porosity and tortuosity in granular beds

Sobieski W., Lipiński S.

Technical Sciences / University of Warmia and Mazury in Olsztyn

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2017

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nr 20(1)

75--85

EN

In the paper, functions describing different porosity-tortuosity relations were collected, and then the tortuosity values were calculated for a one granular bed consisting of spherical particles with normal distribution of diameters. Information about the bed porosity and particle sizes was obtained from measurements conducted for an artificial granular bed, consisting of glass marbles. The results of calculations were compared with the results of two other methods of tortuosity determination, performed for the same case (details are not described in this paper): the first of them uses the Path Tracking Method, the second one - information about the velocity components in a creeping flow (the Lattice-Boltzmann Method was applied to obtain the velocity field in the flow). The main aim of our article was to test whether the functions linking tortuosity with porosity, which are available in the literature, give similar results as the methods described above. To achieve this aim, the relative errors between results of calculations for the collected formulas and values from the both previous mentioned methods were calculated.

18

Non-isothermal constitutive relations and heat transfer equations of a two-phase medium

Uciechowska-Grakowicz A., Strzelecki T.

Studia Geotechnica et Mechanica

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2017

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Vol. 39, nr 3

67--78

EN

In the case of a two-phase medium – such as the soil, which consists of an elastic skeleton and is filled with pore fluids – stress and strain within the medium are dependent on both phases. Similarly, in the case of heat transfer, heat is conducted through the two phases at different rates, with an additional heat transfer between the phases. In the classical approach to modelling a porous medium, it is assumed that the fluid filling the pore space is water, which is incompressible. In the case of gas, the volume of which is strongly dependent on temperature and pressure, one should take this behavior into account in the constitutive relations for the medium. This work defines the physical relations of a two-phase medium and provides heat transfer equations, constructed for a porous, elastic skeleton with fluid-filled pores, which may be: liquid, gas, or mixture of liquid and a gas in non-isothermal conditions. The paper will present constitutive relations derived from the laws of irreversible thermodynamics, assuming that pores are filled with either a liquid or a gas. These relations, in the opinion of the authors, may be used as the basis for the construction of a model of the medium filled partly with a liquid and partly with a gas. It includes the possibility of independent heat transfer through any given two-phase medium phase, with the transfer of heat between the phases.

19

Fenomenologiczne ujęcie hydrodynamiki przepływu gazu przez struktury porowate

Wałowski G.

Przemysł Chemiczny

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2017

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T. 96, nr 5

1171--1178

PL

Opisano zagadnienia hydrodynamiki przepływu gazu przez struktury porowate oraz dokonano przeglądu wybranych modeli hydrodynamicznych. Przeanalizowano podane w literaturze warunki wykonanych badań dotyczących opisu hydrodynamiki przepływu gazu przez struktury porowate. Zagadnienie procesowe rozpatrzono w kategorii "przegląd badań w zakresie wybranych sposobów opisu hydrodynamiki przepływu gazu przez złoża porowate". Ma ono istotne znaczenie dla poszerzenia wiedzy na temat oceny hydrodynamiki przepływu gazu w mediach porowatych dotąd nierozpoznanych dla rozwoju nowej generacji czystych źródeł energii, zwłaszcza w kontekście produkcji biogazu lub syngazu.

EN

A review, with 57 refs., of selected hydrodynamic models with their characteristics and applicability areas.

20

The interaction between PDE and graphs in multiscale modeling

Morales F. A., Alvares S.N.

Opuscula Mathematica

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2017

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Vol. 37, no. 2

327--345

EN

In this article an upscaling model is presented for complex networks with highly clustered regions exchanging/trading quantities of interest at both, microscale and macroscale level. Such an intricate system is approximated by a partitioned open map in R2 or R3. The behavior of the quantities is modeled as flowing in the map constructed and thus it is subject to be described using partial differential equations. We follow this approach using the Darcy Porous Media, saturated fluid flow model in mixed variational formulation.