A new benchmark quality solution for the buoyancy-driven cavity by discrete singular convolution
01 Sep 2001-Numerical Heat Transfer Part B-fundamentals (Informa UK Ltd)-Vol. 40, Iss: 3, pp 199-228
TL;DR: In this article, a high-accuracy discrete singular convolution (DSC) approach is proposed for the numerical simulation of coupled convective heat transfer problems, where the problem of a buoyancy-driven cavity is solved by two completely independent numerical procedures.
Abstract: This article introduces a high-accuracy discrete singular convolution (DSC) for the numerical simulation of coupled convective heat transfer problems. The problem of a buoyancy-driven cavity is solved by two completely independent numerical procedures. One is a quasi-wavelet-based DSC approach, which uses the regularized Shannon's kernel, while the other is a standard form of the Galerkin finite-element method. The integration of the Navier-Stokes and energy equations is performed by employing velocity correction-based schemes. The entire laminar natural convection range of 10 3 h Ra h 10 8 is numerically simulated by both schemes. The reliability and robustness of the present DSC approach is extensively tested and validated by means of grid sensitivity and convergence studies. As a result, a set of new benchmark quality data is presented. The study emphasizes quantitative, rather than qualitative comparisons.
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TL;DR: In this article, a numerical study is conducted to investigate the transport mechanism of mixed convection in a lid-driven enclosure filled with nanofluids, where two vertical walls of the enclosure are insulated while the horizontal walls are kept at constant temperatures with the top surface moving at a constant speed.
Abstract: A numerical study is conducted to investigate the transport mechanism of mixed convection in a lid-driven enclosure filled with nanofluids. The two vertical walls of the enclosure are insulated while the horizontal walls are kept at constant temperatures with the top surface moving at a constant speed. The numerical approach is based on the finite volume technique with a staggered grid arrangement. The SIMPLE algorithm is used for handling the pressure velocity coupling. Numerical solutions are obtained for a wide range of parameters and copper-water nanofluid is used with Pr = 6.2 . The streamlines, isotherm plots and the variation of the average Nusselt number at the hot wall are presented and discussed. It is found that both the aspect ratio and solid volume fraction affect the fluid flow and heat transfer in the enclosure. Also, the variation of the average Nusselt number is linear with solid volume fraction.
236 citations
04 Jan 2010
TL;DR: This study pursues mixed MPI-CUDA implementations and investigates three strategies to probe the efficiency and scalability of incompressible flow computations on the Lincoln Tesla cluster at the National Center for Supercomputing Applications (NCSA).
Abstract: Modern graphics processing units (GPUs) with many-core architectures have emerged as general-purpose parallel computing platforms that can accelerate simulation science applications tremendously. While multiGPU workstations with several TeraFLOPS of peak computing power are available to accelerate computational problems, larger problems require even more resources. Conventional clusters of central processing units (CPU) are now being augmented with multiple GPUs in each compute-node to tackle large problems. The heterogeneous architecture of a multi-GPU cluster with a deep memory hierarchy creates unique challenges in developing scalable and efficient simulation codes. In this study, we pursue mixed MPI-CUDA implementations and investigate three strategies to probe the efficiency and scalability of incompressible flow computations on the Lincoln Tesla cluster at the National Center for Supercomputing Applications (NCSA). We exploit some of the advanced features of MPI and CUDA programming to overlap both GPU data transfer and MPI communications with computations on the GPU. We sustain approximately 2.4 TeraFLOPS on the 64 nodes of the NCSA Lincoln Tesla cluster using 128 GPUs with a total of 30,720 processing elements. Our results demonstrate that multi-GPU clusters can substantially accelerate computational fluid dynamics (CFD) simulations.
182 citations
TL;DR: In this article, a set of complete two-and three-dimensional direct numerical simulations (DNS) in a differentially heated air-filled cavity of aspect ratio 4 with adiabatic horizontal walls is presented.
Abstract: A set of complete two- and three-dimensional direct numerical simulations (DNS) in a differentially heated air-filled cavity of aspect ratio 4 with adiabatic horizontal walls is presented in this paper. Although the physical phenomenon is three-dimensional, owing to its prohibitive computational costs the majority of the previous DNS of turbulent and transition natural convection flows in enclosed cavities assumed a two-dimensional behaviour. The configurations selected here (Rayleigh number based on the cavity height 6.4 ×10 8 , 2×10 9 and 10 10 , Pr=0.71) are an extension to three dimensions of previous two-dimensional problems. An overview of the numerical algorithm and the methodology used to verify the code and the simulations is presented. The main features of the flow, including the time-averaged flow structure, the power spectra and probability density distributions of a set of selected monitoring points, the turbulent statistics, the global kinetic energy balances and the internal waves motion phenomenon are described and discussed. As expected, significant differences are observed between two- and three-dimensional results. For two-dimensional simulations the oscillations at the downstream part of the vertical boundary layer are clearly stronger, ejecting large eddies to the cavity core. In the three-dimensional simulations these large eddies do not persist and their energy is rapidly passed down to smaller scales of motion. It yields on a reduction of the large-scale mixing effect at the hot upper and cold lower regions and consequently the cavity core still remains almost motionless even for the highest Rayleigh number. The boundary layers remain laminar in their upstream parts up to the point where these eddies are ejected. The point where this phenomenon occurs clearly moves upstream for the three-dimensional simulations. It is also shown that, even for the three-dimensional simulations, these eddies are large enough to permanently excite an internal wave motion in the stratified core region. All these differences become more marked for the highest Rayleigh number.
157 citations
TL;DR: In this paper, a two-dimensional double Multiple Relaxation Time-Thermal Lattice Boltzmann Equation (2-MRT-TLBE) method is developed for predicting convective flows in a square differentially heated cavity filled with air.
Abstract: A two-dimensional double Multiple Relaxation Time-Thermal Lattice Boltzmann Equation (2-MRT-TLBE) method is developed for predicting convective flows in a square differentially heated cavity filled with air (Pr=071) In this Letter, we propose a numerical scheme to solve the flow and the temperature fields using the MRT-D2Q9 model and the MRT-D2Q5 model, respectively Thus, the main objective of this study is to show the effectiveness of such model to predict thermodynamics for heat transfer This model is validated by the numerical simulations of the 2-D convective square cavity flow Excellent agreements are obtained between numerical predictions These results demonstrate the accuracy and the effectiveness of the proposed methodology
142 citations
References
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11 Sep 1985
TL;DR: This paper introduced the physical effects underlying heat and mass transfer phenomena and developed methodologies for solving a variety of real-world problems, such as energy minimization, mass transfer, and energy maximization.
Abstract: This undergraduate-level engineering text introduces the physical effects underlying heat and mass transfer phenomena and develops methodologies for solving a variety of real-world problems.
13,209 citations
"A new benchmark quality solution fo..." refers background in this paper
...According to Incropera and Dewitt [ 11 ], the laminar natural convection at a local Rayleigh number larger than 109 may be pro-...
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TL;DR: In this paper, a finite-difference method for solving the time-dependent Navier-Stokes equations for an incompressible fluid is introduced, which is equally applicable to problems in two and three space dimensions.
Abstract: A finite-difference method for solving the time-dependent Navier- Stokes equations for an incompressible fluid is introduced. This method uses the primitive variables, i.e. the velocities and the pressure, and is equally applicable to problems in two and three space dimensions. Test problems are solved, and an ap- plication to a three-dimensional convection problem is presented.
4,991 citations
TL;DR: This work extends earlier work on the efficient implementation of ENO (essentially non-oscillatory) shock-capturing schemes by providing a new simplified expression for the ENO constructio...
Abstract: In this paper we extend our earlier work on the efficient implementation of ENO (essentially non-oscillatory) shock-capturing schemes. We provide a new simplified expression for the ENO constructio...
3,688 citations
TL;DR: In this paper, the authors used mesh refnement and extrapolation to obtain an accurate solution of the equations describing two-dimensional natural convection in a square cavity with differentially heated side walls.
Abstract: Details are given of the computational method used to obtain an accurate solution of the equations describing two-dimensional natural convection in a square cavity with differentially heated side walls. Second-order, central difference approximations were used. Mesh refnement and extrapolation led to solutions for 103⩽Ra⩽10 6 which are believed to be accurate to better than 1 per cent at the highest Rayleigh number and down to one-tenth of that at the lowest value.
2,529 citations
"A new benchmark quality solution fo..." refers background or methods in this paper
...Table 2 also summarizes the maximum values obtained by de Vahl Davis [3], Ramaswamy et al....
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...° Numerical simulation of a buoyancy-driven cavity is extended to the entire laminar natural-convection range 103 μ Ra μ 108, while the earlier benchmark data of de Vahl Davis [3] was con® ned to the range 103 μ Ra μ 106....
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...Also illustrated are the values given in [3], [6], and [10]....
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...It is pertinent to quote Professor de Vahl Davis from his seminal article [3]:...
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...De Vahl Davis [3] used forward di erence for the temporal discretization and second-order central di erence for the spatial discretization, to solve the stream function-vorticity form of the equations....
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01 Jan 1976
TL;DR: In this article, the authors present a computer program for two-dimensional field problems for structural and solid mechanics, including axisymmetric elasticity and Torsion of noncircular sections.
Abstract: BASIC CONCEPTS. One-Dimensional Linear Element. A Finite Element Example. Element Matrices: Galerkin Formulation. Two-Dimensional Elements. Coordinate Systems. FIELD PROBLEMS. Two-Dimensional Field Equation. Torsion of Noncircular Sections. Derivative Boundary Conditions: Point Sources and Sinks. Irrotational Flow. Heat Transfer by Conduction and Convection. Acoustical Vibrations. Axisymmetric Field Problems. Time-Dependent Field Problems: Theoretical Considerations. Time-Dependent Field Problems: Practical Considerations. Computer Program for Two-Dimensional Field Problems. STRUCTURAL AND SOLID MECHANICS. The Axial Force Member. Element Matrices: Potential Energy Formulations. The Truss Element. A Beam Element. A Plane Frame Element. Theory of Elasticity. Two-Dimensional Elasticity. Axisymmetric Elasticity. Computer Programs for Structural and Solid Mechanics. LINEAR AND QUADRATIC ELEMENTS. Element Shape Functions. Element Matrices. Isoparametric Computer Programs. References. Appendices.
1,027 citations
"A new benchmark quality solution fo..." refers methods in this paper
...The details of the ® nite-element shape functions are available in Segarlind [ 31 ]....
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