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Comparative study of flux-limiters based on MUST differencing scheme

INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS 2004年第7期18卷 569-576页

作者： Juntasaro, V Marquis, AJ Kasetsart Univ CML Fac Engn Dept Mech Engn Bangkok 10900 Thailand Univ London Imperial Coll Sci Technol & Med Dept Mech Engn London England

A comparative study of a number of flux-limiters based on MUST methodology is presented in this paper to find the most suitable flux-limiter to be used in unsteady and steady convective flow calculations. The accuracy and convergence behaviour of these flux-limiters are assessed in five pure convection problems: (1) rotation of a cone-shaped scalar field, (2) advection of a square-shaped scalar field, (3) mixing of a hot with a cold front, (4) deformation of cone-shaped scalar field and (5) IAHR. The superbee flux-limiter results in the most accurate solutions in unsteady flow problems, and the Koren flux-limiter is the more appropriate in steady flow problems because of its good convergence behaviour.

关键词： differencing scheme flux-limiter convective flow steady flow unsteady flow unstructured mesh

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A VECTOR UPSTREAM differencing scheme FOR PROBLEMS IN FLUID-FLOW INVOLVING SIGNIFICANT SOURCE TERMS IN STEADY-STATE LINEAR-SYSTEMS

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 1981年第1期1卷 3-16页

作者： LILLINGTON, JN U.K.A.E.A. A.E.E. Winfrith Dorchester Dorset England

AbstractThis paper considers a finite difference scheme for modelling the convection/diffusion equation in strongly convective flow regimes including circumstances in which significant source terms are *** main objective is to provide an alternative approach to central and/or upwind difference methods which for various reasons are unsatisfactory. To illustrate the main features of the scheme, an assessment of its accuracy is made by means of a Taylor expansion analysis and a study of its performance in two model problems. As a demonstration of its generality for use in large‐scale practical problems, some numerical results are presented for the prediction of the temperature distribution in a flow through a partially blocked heated rod *** main conclusions are that in almost all practical circumstances results obtained using the scheme are not susceptible to false diffusion or spatial oscillations, which are, respectively, the inherent weaknesses in many upwind and central difference scheme formulations, and in general its use results in improved overall accurac

关键词： Vector Upstream differencing scheme Significant Sources False Diffusion Spatial Oscillation Steady‐state Linear Systems Convective Flow Rod Bundle Geometry Temperature Prediction

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AN IMPROVEMENT OF THE EXPONENTIAL differencing scheme FOR SOLVING THE CONVECTION-DIFFUSION EQUATION

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ADVANCES IN ENGINEERING SOFTWARE 1994年第1期19卷 1-19页

作者： VIRAG, Z TRINCAS, G UNIV ZAGREB FAC MECH ENGN & NAVAL ARCHITECTUREZAGREB 41000CROATIA UNIV TRIESTE DEPT NAVAL ARCHITECTURE OCEAN & ENVIRONM ENGNI-34127 TRIESTEITALY

In order to reduce false diffusion in numerical solutions of the convection-diffusion equation both in orthogonal and body-fitted coordinates, a simple differencing scheme suitable to the control-volume method is proposed. The scheme is based on the one-dimensional exact solution of the convection-diffusion equation with constant coefficients and constant source term. Accuracy of the proposed scheme is assessed through a number of test situations of pure convective and convective-diffusive transport with known exact solutions. Results show relevant accuracy improvements with respect to the popular exponential differencing scheme (EDS). The proposed scheme is simple, accurate and easy to implement in existing codes based on the EDS. The extension to three-dimensional situations is straightforward.

关键词： CONVECTION DIFFUSION EQUATIONS CONTROL-VOLUME METHOD BODY-FITTED COORDINATES differencing scheme FALSE DIFFUSION

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Applications of high-resolution schemes based on normalized variable formulation for 3D indoor airflow simulations

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2008年第7期73卷 948-981页

作者： Ng, K. C. Ng, E. Y. K. Yusoff, M. Z. Lim, T. K. OYL R&D Ctr Dept Res & Applicat Sungai Buloh 47000 Selangor Darul Malaysia Nanyang Technol Univ Sch Mech & Aerosp Engn Singapore 639798 Singapore Univ Tenaga Nas Dept Mech Engn Kajang 43009 Selangor Darul Malaysia

Computational fluid dynamics (CFD) has been used in a routine manner for the design of indoor environments. The quality of these CFD studies varies from poor to excellent, and only in year 2003 Sorensen and Nielsen recommend a detailed guideline on imposing quality control in the CFD-related works for indoor airflow simulations. One of these recommendations is to use monotone high-resolution (HR) schemes that apply flux limiters to ensure solution boundedness while preserving the high-order accuracy of the differencing schemes. In this paper, based on the gamma-formulations derived from the normalized variable formulation, four recently developed HR schemes, GAMMA, CUBISTA, AVLSMART and HOAB, are applied to several indoor airflow problems such as (1) Smith-Hutton problem (dead-end channel);(2) forced convection problem (horizontal/oblique inflow) in a parallelepiped room;(3) mixing ventilation problem focusing on the prediction of local mean age of air;(4) flow in a two-room chamber with internal partition and (5) displacement ventilation in a mockup office. Based on the flow results, the aspects of accuracy and robustness of these HR schemes are addressed for appropriate selection of an 'ideal' differencing scheme to improve the quality of 3D indoor CFD calculations. Copyright (c) 2007 John Wiley & Sons, Ltd.

关键词： cFD differencing scheme indoor airflow normalized variable formulation (NVF) turbulence model

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Numerical simulation of cavity flows based on transformed equations

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APPLIED MATHEMATICS AND COMPUTATION 2006年第2期176卷 506-515页

作者： Xu, H. Zhang, C. Barron, R. Univ Western Ontario Dept Mech & Mat Engn London ON N6A 5B9 Canada Univ Windsor Dept Mech Automot & Mat Engn Windsor ON N9B 3P4 Canada Univ Windsor Dept Math & Stat Windsor ON N9B 3P4 Canada

A new numerical algorithm is applied to simulate two-dimensional lid-driven cavity flows. In this new algorithm, the momentum equations are first transformed using an exponential function to eliminate the convection terms in the equations. Then a central differencing scheme is employed to discretize the transformed equations. The cavity flows studied in this work include those with non-zero velocity component in the y-direction on the upper and lower boundaries. The results for the velocity components along the geometric centerline, stream function patterns, and vorticity contours are presented and discussed. The predicted results are in excellent agreement with benchmark solutions. (c) 2005 Elsevier Inc. All rights reserved.

关键词： partial differential equation differencing scheme fluid flow cavity flow numerical approach

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A new numerical algorithm based on transformed equations and its applications to very low Re fluid flows

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APPLIED MATHEMATICS AND COMPUTATION 2006年第1期181卷 619-633页

作者： Xu, H. Barron, R. Zhang, C. Univ Western Ontario Dept Mech & Mat Engn London ON N6A 5B9 Canada Univ Windsor Fluid Dynam Res Inst Windsor ON N9B 3P4 Canada Univ Windsor Dept Mech Automot & Mat Engn Windsor ON N9B 394 Canada

A new numerical algorithm is presented in this study to solve the partial differential equations that govern fluid flows. This new algorithm is based on first transforming the partial differential equations by introducing an exponential function to eliminate the convection terms. A fourth-order central differencing scheme and a second-order central differencing scheme are used to discretize the transformed equations. The algorithm is then applied to simulate fluid flows with exact solutions to validate this new algorithm. The fluid flows used in this study are a self-designed quasi-fluid flow problem, stagnation in plane flow (Hiemenz flow), and flow between two concentric cylinders. Comparisons against the exact solution are made for the results obtained using the new numerical algorithm as well as the power-law scheme. The comparisons indicate that the present fourth-order scheme performs the best and the present second-order scheme is the next most accurate. (c) 2006 Elsevier Inc. All rights reserved.

关键词： partial differential equation differencing scheme fluid flow numerical algorithm

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A new numerical approach to solve an elliptic equation

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APPLIED MATHEMATICS AND COMPUTATION 2005年第1期171卷 1-24页

作者： Xu, H Zhang, C Barron, R Univ Western Ontario Dept Mech & Mat Engn London ON N6A 5B9 Canada Univ Windsor Dept Mech Automot & Mat Engn Windsor ON N9B 3P4 Canada Univ Windsor Dept Math & Stat Windsor ON N9B 3P4 Canada

A new numerical approach to solve an elliptic partial differential equation that originates from the governing equations of steady state fluid flow and heat transfer is presented. The elliptic partial differential equation is transformed by introducing all exponential function to eliminate the convection terms in the equation. A fourth-order central differencing scheme and a second-order central differencing scheme are used to numerically solve the transformed elliptic partial differential equation. Analytical solutions of this equation are also given. Comparisons are made between the analytical solutions, the numerical results using the present schemes, and those using the four classical differencing schemes, namely, the first-order upwind scheme, hybrid scheme,. power-law scheme, and exponential scheme. The comparisons illustrate that the proposed algorithm performs better than the four classical differencing schemes. (c) 2005 Elsevier Inc. All rights reserved.

关键词： elliptic partial differential differencing scheme fluid flow heat transfer numerical approach differencing scheme

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Model analysis of the transportation of chloride into concrete under dry-wet cyclic conditions

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INTERNATIONAL JOURNAL OF MODELLING IDENTIFICATION AND CONTROL 2009年第2期7卷 185-189页

作者： Dong Rongzhen Wei Jun Yu Jing Cent S Univ Sch Civil Engn & Architecture Changsha 410075 Hunan Peoples R China Huazhong Univ Sci & Technol Sch Civil Engn & Mech Wuhan 430074 Peoples R China

The dry-wet cyclic experimental method is designed to imitate the reinforced concrete corrosion in the natural environment. The polynomial model of chloride ions transporting inside the concrete is discussed and its numerical calculation is analysed through the reasonable differencing scheme, and the stability of the differencing scheme is discussed accordingly. The chloride concentration distribution in concrete can be obtained respectively by the chemistry titration method and calculated using the above model by selecting the parameters according to the concrete material property and the stability of differencing scheme. The statistical characteristic analysis and the relativity of the calculated value and the tested value both verify the accuracy of the model.

关键词： concrete Cl- transportation model differencing scheme

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