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Comparison of simple- and PISO-type algorithms for transient flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 1998年第4期26卷 459-483页

作者： Barton, IE Univ Cambridge Dept Engn Div A CFD Lab Cambridge CB2 1PZ England

Various pressure-based schemes are proposed for transient flows based on well-established simple and PISO algorithms. The schemes are applied to the solution of unsteady laminar how around a square cylinder and steady laminar flow over a backward-facing step. The implicit treatment and the performance of the various schemes are evaluated by using benchmark solutions with a small time step. Three different second-order-accurate time derivatives based on different time levels are presented. The different time derivatives are applied to the various schemes under consideration. Overall the PISO scheme was found to predict accurate results and was robust. However, for small time step values, alternative schemes can predict accurate results for approximately half the computational cost. The choice of time derivative proved to be very significant in terms of the accuracy and robustness of a scheme. Significantly, the one-sided forward differencing scheme was the most successful used in conjunction with a strongly implicit-based algorithm. However, a greater degree of accuracy was achieved using the standard PISO algorithm with the Crank-Nicolson time derivative. Recommendations for future work are discussed. (C) 1998 John Wiley & Sons, Ltd.

关键词： simple algorithm PISO algorithm unsteady incompressible flow

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Algebraic multigrid methods for the solution of the Navier-Stokes equations in complicated geometries

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 1998年第3期26卷 281-301页

作者： Griebel, M Neunhoeffer, T Regler, H Univ Bonn Inst Angew Math Abt Wissensch Rechnen & Numer Simulat D-53115 Bonn Germany Tech Univ Munich Inst Informat D-80290 Munich Germany

The application of standard multigrid methods for the solution of the Navier-Stokes equations in complicated domains causes problems in two ways. First, coarsening is not possible to full extent since the geometry must be resolved by the coarsest grid used. Second, for semi-implicit time-stepping schemes, robustness of the convergence rates is usually not obtained for convection-diffusion problems, especially for higher Reynolds numbers. We shaw that both problems can be overcome by the use of algebraic multigrid (AMG), which we apply for the solution of the pressure and momentum equations in explicit and semi-implicit time-stepping schemes. We consider the convergence rates of AMG for several model problems and demonstrate the robustiness of the proposed scheme. (C) 1998 John Wiley & Sons, Ltd.

关键词： Navier-Stokes equations simple algorithm algebraic multigrid methods

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Shock-Tunnel investigation of hypervelocity free shear layers in a planar duct

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JOURNAL OF PROPULSION AND POWER 1996年第5期12卷 998-1001页

作者： Buttsworth, DR Morgan, RG UNIV QUEENSLAND DEPT MECH ENGNST LUCIAQLD 4072AUSTRALIA

Pitot pressure measurements obtained in four different developing hypervelocity free shear layers are reported. There exists a high degree of similarity across the present four mixing cases, including the case where the primary and secondary stream flow velocities were approximately matched. It is inferred that it is probable that the relatively large primary stream boundary layers had a strong influence on these developing shear layers. There was reasonable agreement between the experimental results and predictions made using a parabolized Navier-Stokes code with a k-epsilon turbulence model. (AIAA)

关键词： Boundary Layer Thickness Shock Tunnels Stagnation Pressure Contoured Nozzles Compressibility Turbulence Models Static Pressure Scramjet simple algorithm Combustion Process

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SOLUTAL CONVECTION AND MASS-TRANSFER IN INCLINED ENCLOSURES

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 1995年第2期9卷 262-269页

作者： GAU, C JENG, DZ National Cheng Kung Univ. Tainan Taiwan

Both experimental and numerical work are performed to study the solutal convection now and transport process in the enclosures that can be inclined at different angles, The enclosure is filled with an aqueous solution containing CuSO4 + H2SO4, where the flow structure is visualized by both a particle tracer and shadowgraph, With a nonintrusive optical method the concentration fluctuations at desired locations are measured, The mass transfer Sherwood numbers across the enclosure at various inclinations are also measured and the results are correlated in terms of relevant nondimensional parameters, In the experiments, the Rayleigh number ranges from 1.126 x 10(8) to 1.157 x 10(11), the Schmidt numbers from 2500 to 3989, the angles of inclination from 30 to 150 deg, and the aspect ratios of the enclosure from 0.25 to 1, The simple algorithm developed by Patankar is employed to calculate the solutal convection, and the results are compared with the data. It was found that both the inclination and the aspect ratio of the enclosure have a significant effect on the now structure and mass transfer, For a large angle of inclination, the accumulation of solutal boundary-layer flow leads to stratification of the core and reduction of the mass transfer, For a small inclination, generation and protrusion of solutal plumes leads to oscillation of concentration and enhancement of mass transfer.

关键词： Natural Convection Mass Transfer Coefficient High Aspect Ratio Boundary Layer Thickness Schmidt Numbers simple algorithm Heat Transfer Correlations Buoyancy Force Flow Patterns Boussinesq Approximation

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EFFECT OF TORSION ON HEAT-TRANSFER IN THE CURVED ANNULAR SECTOR DUCT

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 1994年第3期8卷 580-586页

作者： YANG, G EBADIAN, MA Florida International University Miami Florida 33199

The effect of torsion on convective heat transfer in a curved annular sector duct with a finite pitch is numerically studied. Seven parameters are identified as major variables describing the flow pattern. The results indicate that torsion will rotate the temperature contours to one side and distort their symmetry. Increasing the Prandtl number will significantly enhance the effect of torsion on the temperature distribution. The torsion effect may also be considerably enhanced by increasing the curvature, the axial pressure gradient, and decreasing the radius ratio. Furthermore, the predicted results are compared with the experimental data and excellent agreement is achieved.

关键词： Heat Transfer Coefficients Temperature Distribution Prandtl Number Flow Patterns Dean Numbers Vortices Kinematic Viscosity simple algorithm Wall Temperature Friction Coefficient

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GENERAL STRONG CONSERVATION FORMULATION OF NAVIER-STOKES EQUATIONS IN NONORTHOGONAL CURVILINEAR COORDINATES

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AIAA JOURNAL 1994年第5期32卷 936-941页

作者： YANG, HQ HABCHI, SD PRZEKWAS, AJ CFD Research Corporation Huntsville Alabama 35805

The selection of primary dependent variables for the solution of Navier-Stokes equations in the curvilinear body-fitted coordinates is still an unsettled issue. Reported formulations with primitive variables involve contra-variant velocity components, Cartesian components, and velocity projections, also known as resolutes. Most of the formulations result in a weak conservation form of the momentum equations which contain grid line curvature and divergence-related Coriolis and centrifugal terms. This paper presents a general strong conservation formulation of the momentum equations allowing the flexibility in choosing the various forms of the velocity components as the dependent variables. Ambiguous issues relating geometrical topology and forms of governing equations are discussed and clarified. Computational results obtained with both strong and weak forms are presented and compared to known analytical/experimental data. The results confirm the soundness of the formulation.

关键词： Navier Stokes Equations Curvilinear Coordinates Rankine Hugoniot Conditions Incompressible Viscous Flow Drag Coefficient simple algorithm Flow Distribution Coriolis Force Oblique Shock Energy Law

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NUMERICAL STUDY OF TURBULENT OFFSET JETS WITH ENTRAINMENT BOUNDARY

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 1994年第1期8卷 182-184页

作者： YANG, YT YEH, YY National Cheng-Kung University Tainan Taiwan Republic of China

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DIFFERENCING OF DENSITY IN COMPRESSIBLE FLOW FOR A PRESSURE-BASED APPROACH

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AIAA JOURNAL 1994年第3期32卷 659-661页

作者： GREYVENSTEIN, GP MEYER, JP Potchefstroom University for CHE Potchefstroom 2520 South Africa

Because of the difference in nature between compressible and incompressible flows, different computational schemes have been developed through the years to deal with these two types of flows. In the case of compressible flows, methods have been developed that use density as a primary variable, Such methods are known as density-based methods. Examples of density-based methods are the well-known emthods of MacCormack and Beam and Warming. Unlike density-based methods, pressure-based methods use pressure as a primary variable. Examples of pressure-based methods are the well-known simple and PISO method. The purpose of this paper is to investigae the differencing scheme of density used for the convection terms in the momentum transport equations. To provide a clear understanding, we will discuss these concepts in the framework of a one-dimensional scheme. Fortunately, all of these concepts as developed within this one-dimensional framework are readily extended to two or three dimensions.

关键词： One Dimensional Flow Continuity Equation Convection Heat and Mass Transfer simple algorithm Inlet Pressure Mass Flux Numerical Heat Transfer Explicit Methods Rockets

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A simple algorithm giving an interesting Mandelbrot set

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The Visual Computer 1992年第3期8卷 200-201页

作者： Tippetts, John R. Department of Mechanical and Process Engineering University of Sheffield Sheffield S1 3JD Mappin Street United Kingdom

The Mandelbrot set derived from a particular a cubic function has a fractal boundary. The function is produced implicitly by removing a statement from the algorithm needed to calculate Mandelbrot's well-known quad... 详细信息

关键词： Colour-plots Cubic Mandelbrot simple algorithm

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A COMPARISON OF COARSE AND FINE-GRAIN PARALLELIZATION STRATEGIES FOR THE simple PRESSURE CORRECTION algorithm

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 1993年第10期16卷 891-914页

作者： LEWIS, AJ BRENT, AD BHP Research Newcastle Laboratories P.O. Box 188 Wallsend NSW 2287 Australia

The primary aim of this work was to determine the simplest and most effective parallelization strategy for control-volume-based codes solving industrial problems. It has been found that for certain classes of problems, the coarse-grain functional decomposition strategy, largely ignored due to its limited scaling capability, offers the potential for significant execution speed-ups while maintaining the inherent structure of traditional serial algorithms. Functional decomposition requires only minor modification of the existing serial code to implement and, hence, code portability across both concurrent and serial computers is maintained, Fine-grain parallelization strategies at the 'DO loop' level are also easy to implement and largely preserve code portability. Both coarse-grain functional decomposition and fine-grain loop-level parallelization strategies for the simple pressure correction algorithm are demonstrated on a Silicon Graphics 4D280S eight CPU shared memory computer system for a highly coupled, transient two-dimensional simulation involving melting of a metal in the presence of thermal-buoyancy-driven laminar convection. Problems requiring the solution of a larger number of transport equations were simulated by including further scalar variables in the calculation. While resulting in slight degradation of the convergence rate, the functional decomposition strategy exhibited higher parallel efficiencies and yielded greater speed-ups relative to the original serial code. Initially, this strategy showed a significant degradation in convergence rate due to an inconsistency in the parallel solution of the pressure correction equation. After correcting for this inconsistency, the maximum speed-up for 16 dependent variables was a factor of 5.28 with eight processors, representing a parallel efficiency of 67%. Peak efficiency of 76% was achieved using five processors to solve for 10 dependent variables.

关键词： COMPUTATIONAL FLUID DYNAMICS PARALLEL COMPUTING PARALLEL PROCESSING FUNCTIONAL DECOMPOSITION simple algorithm PRESSURE CORRECTION SCHEMES

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