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Polygonal Finite Element for Two-Dimensional lid-driven cavity Flow

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Computers, Materials & Continua 2022年第3期70卷 4217-4239页

作者： T.Vu-Huu C.Le-Thanh H.Nguyen-Xuan M.Abdel-Wahab Faculty of Civil Engineering Vietnam Maritime University484 Lach Tray Str.Hai PhongVietnam Faculty of Civil Engineering and Electricity Ho Chi Minh City Open UniversityVietnam CIRTech Institute Ho ChiMinh City University of Technology(HUTECH)Ho Chi Minh CityVietnam Department of Architectural Engineering Sejong University209 NeungdongroGwangjinguSeoul05006Republic of Korea Soete Laboratory Faculty of Engineering and ArchitectureGhent UniversityTechnologiepark Zwijnaarde903B-9052ZwijnaardeBelgium

This paper investigates a polygonal finite element(PFE)to solve a two-dimensional(2D)incompressible steady fluid problem in a cavity square.It is a well-known standard benchmark(i.e.,lid-driven cavity flow)-to evaluate the numerical methods in solving fluid problems controlled by the Navier-Stokes(N-S)equation system.The approximation solutions provided in this research are based on our developed equal-order mixed PFE,called Pe1Pe1.It is an exciting development based on constructing the mixed scheme method of two equal-order discretisation spaces for both fluid pressure and velocity fields of flows and our proposed stabilisation technique.In this research,to handle the nonlinear problem of N-S,the Picard iteration scheme is applied.Our proposed method’s performance and convergence are validated by several simulations coded by commercial software,i.e.,MATLAB.For this research,the benchmark is executed with variousReynolds numbers up to the maximum Re=1000.All results then numerously compared to available sources in the literature.

关键词： lid-driven cavity incompressible steady Navier-Stokes equations polygonal finite element method

Mixed convection in a lid-driven cavity filled with single and multiple-walled carbon nanotubes nanofluid having an inner elliptic obstacle

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Propulsion and Power Research 2019年第2期8卷 128-137页

作者： Fatih Selimefendigil Mechanical Engineering Department Celal Bayar UniversityManisa 45140Turkey

In this study,numerical analysis and optimization in a single and multiple walled carbon nanotube-water nanofluid filled lid driven cavity having an inner elliptic obstacle were performed by using finite element method and COBYLA optimization solver.The top wall is moving with constant speed and vertical walls are kept at constant temperatures.An optimal size of the inner elliptic obstacle was determined by using an optimization study to maximize the average heat transfer along the hot wall of the cavity.Numerical simulation was performed by for various values of Richardson numbers(between 0.05 and 50)and various solid particle volume fraction(between 0 and 0.06)for single and multiple-walled carbon nanotubes water nanofluid.A larger obstacle(higher values of radii in the major and minor axis)with lower values of Richardson number results in higher heat transfer rates.The average Nusselt number versus solid particle volume fraction shows a linear trend and the discrepancy between the average Nusselt number for the cavity with the optimized obstacle and other obstacles becomes higher with higher particle volume fraction.The average heat transfer enhances significantly which is about 120.20%for single wall carbon nanotube-water nanofluid at solid volume fraction of 0.06 when compared to pure water.The discrepancy between the average Nusselt number for single and multiple walled carbon nanotubes becomes higher for higher values of Richardson number and solid particle volume fraction.A polynomial type correlation was proposed for the average Nusselt number along the hot wall which is fifth order for Richardson number an first order for nanoparticle volume fraction.

关键词： lid-driven cavity Carbon nanotubes Optimization Finite element method

Mixed Convection Heat Transfer for Nanofluids in a lid-driven Shallow Rectangular cavity Uniformly Heated and Cooled from the Vertical Sides:The Opposing Case

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Journal of Electronics Cooling and Thermal Control 2013年第3期3卷 111-130页

作者： Hassan El Harfi Mohamed Naimi Mohamed Lamsaadi Abdelghani Raji Mohammed Hasnaoui Physics Department Faculty of Sciences and TechnologiesSultan Moulay Slimane UniversityLaboratory of Flows and Transfers Modelling(LAMET)Beni-MellalMorocco Polydisciplinary Faculty Sultan Moulay Slimane UniversityInterdisciplinary Laboratory of Research in Sciences and Technologies(LIRST)Beni-MellalMorocco Physics Department Faculty of Sciences SemlaliaCadi Ayyad UniversityLaboratory of Fluid Mechanics and Energetics(LMFE)MarrakechMorocco

An investigation on flow and heat transfer due to mixed convection, in a lid-driven rectangular cavity filled with Cu- water nanofluids and submitted to uniform heat flux along with its vertical short sides, has been conducted numerically by solving the full governing equations with the finite volume method and the SIMPLER algorithm. In the case of a slender enclosure, these equations are considerably reduced by using the parallel flow concept. Solutions, for the flow and temperature fields, and the heat transfer rate, have been obtained depending on the governing parameters, which are the Reynolds, the Richardson numbers and the solid volume fraction of nanoparticles. A perfect agreement has been found between the results of the two approaches for a wide range of the abovementioned parameters. It has been shown that at low and high Richardson numbers, the convection is ensured by lid and buoyancy-driven effects, respectively, whereas between these extremes, both mechanisms compete. Moreover, the addition of Cu-nanoparticles, into the pure water, has been seen enhancing and degrading heat transfer by lid and buoyancy-driven effects, respectively.

关键词： Component Nanofluids Mixed Convection Heat Transfer lid-driven cavity Parallel Flow Assumption Finite Volume Method

l_(1)-based calibration of POD-Galerkin models of two-dimensional unsteady flows

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Chinese Journal of Aeronautics 2021年第1期34卷 226-236页

作者： Riccardo RUBINI Davide LASAGNA Andrea DA RONCH Faculty of Engineering and Physical Sciences University of SouthamptonSouthampton SO171BJUnited Kingdom

This paper discusses a physics-informed methodology aimed at reconstructing efficiently the fluid state of a system.Herein,the generation of an accurate reduced order model of twodimensional unsteady flows from data leverages on sparsity-promoting statistical learning techniques.The cornerstone of the approach is l_(1) regularised regression,resulting in sparselyconnected models where only the important quadratic interactions between modes are retained.The original dynamical behaviour is reproduced at low computational costs,as few quadratic interactions need to be evaluated.The approach has two key features.First,interactions are selected systematically as a solution of a convex optimisation problem and no a priori assumptions on the physics of the flow are required.Second,the presence of a regularisation term improves the predictive performance of the original model,generally affected by noise and poor data quality.Test cases are for two-dimensional lid-driven cavity flows,at three values of the Reynolds number for which the motion is chaotic and energy interactions are scattered across the spectrum.It is found that:(A)the sparsification generates models maintaining the original accuracy level but with a lower number of active coefficients;this becomes more pronounced for increasing Reynolds numbers suggesting that extension of these techniques to real-life flow configurations is possible;(B)sparse models maintain a good temporal stability for predictions.The methodology is ready for more complex applications without modifications of the underlying theory,and the integration into a cyberphysical model is feasible.

关键词： Computational methods Dynamical systems lid-driven cavity L_(1)-based regression Reduced order models Sparsification Stabilization of ROMs

A Consistent Fourth-Order Compact Finite Difference Scheme for Solving Vorticity-Stream Function Form of Incompressible Navier-Stokes Equations

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Numerical Mathematics(Theory,Methods and Applications) 2019年第1期12卷 312-330页

作者： Tao Wang Tiegang Liu School of Mathematicsand SystemsScience Beihang UniversityBeijing 100191China School of Mathematics and Information Science North Minzu UniversityYinchuan 750021China

The inconsistent accuracy and truncation error in the treatment of boundary usually leads to performance defects,such as decreased accuracy and even numerical instability,of the entire computational method,especially for higher order methods.In this work,we construct a consistent fourth-order compact finite difference scheme for solving two-dimensional incompressible Navier-Stokes(N-S)equations.In the pro-posed method,the main truncation error term of the boundary scheme is kept the same as that of the interior compact finite difference scheme.With such a feature,the nu-merical stability and accuracy of the entire computation can be maintained the same as the interior compact finite difference scheme.Numerical examples show the effec-tiveness and accuracy of the present consistent compact high order scheme in L^(∞).Its application to two dimensional lid-driven cavity flow problem further exhibits that un-der the same condition,the computed solution with the present scheme is much close to the benchmark in comparison to those from the 4^(th)order explicit scheme.The compact finite difference method equipped with the present consistent boundary technique im-proves much the stability of the whole computation and shows its potential application to incompressible flow of high Reynolds number.

关键词： Navier-Stokes equations compact finite difference scheme consistent boundary scheme lid-driven cavity

Coupling of discrete-element method and smoothed particle hydrodynamics for liquid-solid flows

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Theoretical & Applied Mechanics Letters 2012年第1期2卷 55-58页

作者： Yrj Jun Huang Ole Jφrgen Nydal Department of Energy and Process Engineering Norwegian University of Science and Technology(NTNU)

Particle based methods can be used for both the simulations of solid and fluid phases in multiphase medium, such as the discrete-element method for solid phase and the smoothed particle hydrodynamics for fluid phase. This paper presents a computational method combining these two methods for solid-liquid medium. The two phases are coupled by using an improved model from a reported Lagrangian-Eulerian method. The technique is verified by simulating liquid-solid flows in a two-dimensional lid-driven cavity.

关键词： discrete-element method smoothed particle hydrodynamics liquid-solid flows lid-driven cavity