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Mixed convection in thermally anisotropic non-Darcy porous medium in double lid-driven cavity using Bejan's heatlines

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ALEXANDRIA ENGINEERING JOURNAL 2016年第1期55卷 299-309页

作者： Ahmed, Sameh E. South Valley Univ Dept Math Fac Sci Qena 83523 Egypt

This paper discusses the problem of mixed convection in two-sided lid-driven enclosures saturated non-Darcy porous medium. The vertical walls of the cavity were kept thermally insulated. The bottom wall is cooled while the top wall is uniformly heated. The bottom and the top walls are moving in opposite direction. The governing equations were solved using finite volume method with simple algorithm. A new form for the heat function was derived. The obtained results were presented in contours maps for the streamlines, the isotherms and the heat function. The profiles of the horizontal velocity component and the maximum values of vertical velocity components as well as the mean Nusselt number were presented graphically. It is found that, for the low values of the Richardson number, the forced convection plays a dominant role in the flow region. The increase in inverse Darcy number leads to decrease the mean Nusselt number. (C) 2015 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons. org/licenses/by-nc-nd/4.0/).

关键词： Heatlines Lid-driven Non-Darcy Heat generation simple algorithm

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Spatiotemporal distribution of rainfall erosivity in the Yanhe River watershed of hilly and gully region, Chinese Loess Plateau

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ENVIRONMENTAL EARTH SCIENCES 2016年第4期75卷 1-13页

作者： Wu, Lei Liu, Xia Ma, Xiao-yi Northwest A&F Univ State Key Lab Soil Eros & Dryland Farming Loess P Xianyang 712100 Shaanxi Peoples R China Northwest A&F Univ Coll Water Resources & Architectural Engn 23 Weihui Rd Xianyang 712100 Shaanxi Peoples R China Northwest A&F Univ Key Lab Agr Soil & Water Engn Arid Reg Minist Educ Xianyang 712100 Shaanxi Peoples R China Northwest A&F Univ Construct Dept Xianyang 712100 Shaanxi Peoples R China

Rainfall erosivity is considered as one of the most important factors in the universal soil loss equation (USLE) or its revised form (RUSLE);it can directly reflect the potential of soil erosion caused by rainfall. In this study, the simple algorithms of rainfall erosivity including the Wischmeier model and the half-month model are selected and used to estimate rainfall erosivity values from 1971 to 2013 in the Yanhe River watershed of the hilly and gully region, Chinese Loess Plateau. Results demonstrate that: (1) the applicability of the simple algorithms of rainfall erosivity in loess hilly and gully region is good and the half-month model is more suitable for the Yanhe River watershed;(2) the overall variations of annual rainfall erosivity values estimated by the two models are similar and show a decreased trend during the relatively steady rainfall period from 1971 to 2012;but they will have a certain degree of deviation for the extreme rainfall with high intensity and short duration in 2013;the monthly variations of rainfall erosivity within a year are highly concentrated in 5-10 months, the rainfall erosivity in other months are almost zero;(3) the spatial distributions of the rainfall erosivity have strong correlation with the erosive rainfall, precipitation and rainfall erosivity which both present an increasing trend from northwest to southeast in the Yanhe River watershed;the central and southern regions both have the highest rainfall and the most serious erosivity;and both rainfall and erosivity in southeast are more serious than that in northwest of the watershed. Results may provide scientific theoretical guidance and data support for soil loss management of the hilly and gully region, Chinese Loess Plateau.

关键词： Rainfall erosivity simple algorithm Spatiotemporal distribution Yanhe River watershed Loess Plateau

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A high-order discontinuous Galerkin solver for low Mach number flows

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 2016年第8期81卷 489-520页

作者： Klein, B. Mueller, B. Kummer, F. Oberlack, M. Tech Univ Darmstadt Chair Fluid Dynam Petersenstr 30 D-64287 Darmstadt Germany Tech Univ Darmstadt Grad Sch Computat Engn D-64293 Darmstadt Germany Tech Univ Darmstadt Ctr Smart Interfaces Petersenstr 30 D-64287 Darmstadt Germany

In this work, we present a high-order discontinuous Galerkin method (DGM) for simulating variable density flows at low Mach numbers. The corresponding low Mach number equations are an approximation of the compressible Navier-Stokes equations in the limit of zero Mach number. To the best of the authors'y knowledge, it is the first time that the DGM is applied to the low Mach number equations. The mixed-order formulation is applied for spatial discretization. For steady cases, we apply the semi-implicit method for pressure-linked equation (simple) algorithm to solve the non-linear system in a segregated manner. For unsteady cases, the solver is implicit in time using backward differentiation formulae, and the simple algorithm is applied to solve the non-linear system in each time step. Numerical results for the following three test cases are shown: Couette flow with a vertical temperature gradient, natural convection in a square cavity, and unsteady natural convection in a tall cavity. Considering a fixed number of degrees of freedom, the results demonstrate the benefits of using higher approximation orders. Copyright (c) 2015 John Wiley & Sons, Ltd.

关键词： finite element discontinuous Galerkin Navier-Stokes low Mach variable density flows simple algorithm

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A comparative study of mixed convection and its effect on partially active thermal zones in a two sided lid-driven cavity filled with nanofluid

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ENGINEERING SCIENCE AND TECHNOLOGY-AN INTERNATIONAL JOURNAL-JESTECH 2016年第3期19卷 1283-1298页

作者： Malik, Sumit Nayak, A. K. Indian Inst Technol Roorkee Dept Math Roorkee 247667 Uttar Pradesh India

In the present study, a two sided lid-driven mixed convection nanofluid flow with discrete heat sources have been numerically investigated. A two dimensional computational visualization technique is used to study the flow behavior using four different cases;depending on the direction of moving vertical walls with fixed upper and lower walls. Two discrete heat sources of equal lengths are taken on the lower wall and the rest of it is kept insulated. The other walls are kept at constant low temperature. The effect of flow governing parameters such as Reynolds number 1 <= Re <= 100, Richardson number 0.1 <= Ri <= 10 and solid volume fraction 0.0 <= phi <= 0.2 with Prandtl number Pr = 6.2 is studied to understand the fluid flow pattern and the heat transfer effect using isotherms and average Nusselt number. (C) 2016 Karabuk University. Publishing services by Elsevier B.V.

关键词： Mixed convection Nanofluid Lid-driven cavity Flow and heat transfer Finite volume method simple algorithm

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Application of simple algorithm on Non-Staggered Grids to Numerical Simulation of the Yellow River Flow and Sediment Transport in Shapotou Reach

Application of SIMPLE Algorithm on Non-Staggered Grids to Nu...

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2011 International Symposium on Water Resource and Environmental Protection(ISWREP 2011)

作者： Cheng Yang Chunguang Li School of Civil and Hydraulic Engineering Ningxia University Research Institute of Numerical Computation and Engineering Applications North University for Nationalities

ISBN: (纸本)9781612843377

In this paper,the Yellow River flow and sediment transport in Shapotou Reach was studied using a two- dimensional flow and sediment mathematical *** control equations were discretized using finite volume method and were solved using simple algorithm on non-staggered ***- dimensional numerical simulation was conducted for the flow and sediment transport in the studied reach and the good consistence between calculated and measured results indicates that the model can be used to simulate the flow and sediment transport in natural rivers.

关键词： non-staggered grids simple algorithm numerical simulation Yellow River

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Parallel domain decomposition method with non-blocking communication for flow through porous media

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JOURNAL OF COMPUTATIONAL PHYSICS 2015年 281卷 970-981页

作者： Lemmer, Andreas Hilfer, Rudolf Univ Stuttgart Inst Computat Phys D-70569 Stuttgart Germany

This paper introduces a domain decomposition method for numerically solving the Stokes equation for very large, complex geometries. Examples arise from realistic porous media. The computational method is based on the simple (Semi-Implicit Method for Pressure Linked Equations) algorithm which uses a finite-differences approach for discretizing the underlying equations. It achieves comparable speed and efficiency as lattice Boltzmann methods. The domain decomposition method splits a large three-dimensional region into slices that can be processed in parallel on multi-processor computation environments with only minimal communication between the computation nodes. With this method, the flow through a porous medium with grid sizes up to 2048(3) voxel has been calculated. (C) 2014 Published by Elsevier Inc.

关键词： Domain decomposition method Parallel computing Porous media Stokes equation simple algorithm

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An extension of the simple based discontinuous Galerkin solver to unsteady incompressible flows

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 2015年第10期77卷 571-589页

作者： Klein, B. Kummer, F. Keil, M. Oberlack, M. Tech Univ Darmstadt Chair Fluid Dynam D-64287 Darmstadt Germany Tech Univ Darmstadt Grad Sch Computat Engn D-64293 Darmstadt Germany Stanford Univ Ctr Turbulence Res Stanford CA 94305 USA Tech Univ Darmstadt Ctr Smart Interfaces D-64287 Darmstadt Germany

In this paper, we present a simple based algorithm in the context of the discontinuous Galerkin method for unsteady incompressible flows. Time discretization is done fully implicit using backward differentiation formulae (BDF) of varying order from 1 to 4. We show that the original equation for the pressure correction can be modified by using an equivalent operator stemming from the symmetric interior penalty (SIP) method leading to a reduced stencil *** assess the accuracy as well as the stability and the performance of the scheme, three different test cases are carried out: the Taylor vortex flow, the Orr-Sommerfeld stability problem for plane Poiseuille flow and the flow past a square cylinder. (1) Simulating the Taylor vortex flow, we verify the temporal accuracy for the different BDF schemes. Using the mixed-order formulation, a spatial convergence study yields convergence rates of k + 1 and k in the L-2-norm for velocity and pressure, respectively. For the equal-order formulation, we obtain approximately the same convergence rates, while the absolute error is smaller. (2) The stability of our method is examined by simulating the Orr-Sommerfeld stability problem. Using the mixed-order formulation and adjusting the penalty parameter of the symmetric interior penalty method for the discretization of the viscous part, we can demonstrate the long-term stability of the algorithm. Using pressure stabilization the equal-order formulation is stable without changing the penalty parameter. (3) Finally, the results for the flow past a square cylinder show excellent agreement with numerical reference solutions as well as experiments. Copyright (c) 2015 John Wiley & Sons, Ltd.

关键词： finite element discontinuous Galerkin Navier-Stokes incompressible flow segregated solution algorithms simple algorithm

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On the stabilization of finite volume methods with co-located variables for incompressible flow

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JOURNAL OF COMPUTATIONAL PHYSICS 2015年 297卷 84-89页

作者： Klaij, C. M. Maritime Res Inst Netherlands NL-6700 AA Wageningen Netherlands

Finite volume methods with co-located variables for incompressible flow suffer from spurious pressure oscillations unless a stabilization method is applied. Variations of the pressure-weighed interpolation (PWI) method are typically used for this purpose. But the PWI method does not only prevent spurious oscillations. Counter-intuitively, it also simplifies the approximation of the Schur complement (pressure matrix) which appears in iterative solution methods such as simple. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Finite volume method Incompressible flow Co-located variables Velocity-pressure decoupling Pressure-weighted interpolation simple algorithm

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Mathematical modelling and numerical simulation of CO₂/CH₄ separation in a polymeric membrane

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APPLIED MATHEMATICAL MODELLING 2015年第21期39卷 6599-6611页

作者： Gilassi, Sina Rahmanian, Nejat Univ Teknol PETRONAS Dept Chem Engn Bandar Seri Iskandar 31750 Perak Malaysia Univ Bradford Fac Engn & Informat Sch Engn Chem Engn Programme Bradford BD7 1DP W Yorkshire England

CO2 capture from natural gas was experimentally and theoretically studied using a dead-end polymeric permeation cell. A numerical model was proposed for the separation of CO2/CH4 using Polytetrafluoroethylene (PTFE) in a flat sheet membrane module and developed based upon the continuity, momentum and mass transfer equations. The slip velocity condition was considered to show the reflection of gas flow in contact with the membrane surface. The solution method was based on the well-known simple algorithm and implemented using MATLAB to determine the velocity and concentration profiles. Due to change in velocity direction in the membrane module, the hybrid differencing scheme was used to solve the diffusion-convection equation. The results of the model were compared with the experimental data obtained as part of this work and good agreement was observed. The distribution of CO2 concentration inside the feed and permeate chambers was shown and the velocity profile at the membrane surface was also determined using reflection factor for polymeric membrane. The modelling result revealed that increasing the amount of CO2 in gas feed resulted in an increase in the CO2 in the permeate stream while the gas feed pressure increased. By changing the permeability, the model developed by use of the solution-diffusion concept could be used for all polymeric membranes with flat sheet modules. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Mathematical modelling Solution-diffusion model PTFE membrane simple algorithm CO2/CH4 separation Cross flow membrane cell

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A simple algorithm for the Multi-objective Transportation Model

A simple Algorithm for the Multi-objective Transportation Mo...

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2011 International Conference on Business Management and Electronic Information(BMEI 2011)

作者： Guozhong Bai Department of Mathematics Guangdong University of Business Studies Guangzhou, 510320, P.R. China Lina Yao Capital Construction Division Guangdong University of Business Studies Guangzhou, 510320, P.R. China

On the basis of the especial demands of sustainable development, and the need of protecting natural resources and environment, this paper provides a mathematical model for the multi-objective transportation problem, introduces the efficient solution, optimal solution and the check vector, and gives a simple algorithm for the multi-objective transportation model.

关键词： sustainable development multi-objective transportation model efficient solution simple algorithm

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