摘要:

This is the first of two companion papers dealing with the evaluation and enhancements of some control volume finite-element methods (CVFEMs) for fluid flow and heat transfer. This paper examines three CVFEMs for two-dimensional convection-diffusion problems. In the first CVFEM, the scalar dependent variable is interpolated by a flow-oriented upwind type function which does not explicitly account for the influence of source terms. In the second CVFEM, the interpolation function employs flow-oriented upwinding and, in addition, includes a flow-oriented term which explicitly accounts for the influence of sources. The third CVFEM represents an attempt to enhance the performance of the first and second CVFEMs. The interpolation function used in the third CVFEM employs flow-oriented upwinding and includes terms which explicitly account for the influence of sources in directions both parallel and normal to the flow. It was found that significant improvements in the accuracy of the solutions can often be obtained when a source-related term is included in the interpolation function. The proper choice of this source-related term, however, depends on the nature of the problem being solved.

ISSN:0149-5720    

DOI:10.1080/10407788808913643

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

This is the second of two companion papers dealing with the evaluation and enhancements of some control volume finite-element methods (CVFEMs) for fluid flow and heat transfer. One unequal-order CVFEM and two versions of an equal-order CVFEM, for the prediction of two-dimensional incompressible fluid flow are examined in this paper. In the unequal-order CVFEM, six-node macroelements and three-node subelements are used to discretize the calculation domain, and the velocity components are interpolated by flow-oriented upwind-type functions. In the equal-order CVFEM, the calculation domain is discretized by three-node triangular elements, the dependent variables are colocated, and the velocity components are interpolated by flow-oriented upwind-type functions which explicitly account for the influence of the pressure gradient on the velocity distribution in each element. The SIMPLEC procedure is used to solve the discretized equations in all three CVFEMs. The proposed equal-order CVFEM is more accurate than the unequal-order CVFEM, however, it requires much more CPU time to achieve converged solutions, due to the type of equations which arise in the proposed solution algorithm. This difficulty may be alleviated by implementing the equal-order method in conjunction with solution algorithms other than SIMPLEC.

ISSN:0149-5720    

DOI:10.1080/10407788808913644

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

A general calculation procedure for computing fluid flow and related phenomena in arbitrary-shaped domains is presented. The scheme has been developed for a generalized nonorthogonal coordinate system and is based on a control-volume approach with a staggered grid arrangement. The physical covariant velocity components are selected as the dependent variables in the momentum equations. The discretization equations for these velocity components are obtained by an algebraic manipulation of the discretization equations for the Cartesian velocity components. Such a practice avoids any reference to the differential form of the governing equations for the covariant velocity components. The coupling between the continuity and momentum equations is effected using the SIMPLER algorithm.

ISSN:0149-5720    

DOI:10.1080/10407788808913645

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

The capabilities of a new curvilinear coordinate-based calculation procedure for incompressible flows are demonstrated by its application to a variety of test problems. The results are compared with the results of independent numerical and experimental studies available in the literature. These comparisons indicate that the proposed scheme can be successfully used to predict fluid flow and heat transfer phenomena in complex configurations.

ISSN:0149-5720    

DOI:10.1080/10407788808913646

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

A series of computations have been conducted to study the performance of a newly developed numerical algorithm for highly compressible flows. The algorithm is based on a generalization of a low-speed algorithm developed earlier and utilizes many features different from the conventionally adopted approach for solving compressible flows. By combining it with an adaptive grid procedure, both laminar and turbulent (closed by the k-ε model) flows can be satisfactorily computed and compared with the inviscid-flow solutions. The issue related to the adaptive gridding technique, the finite-difference operator, as well as the fluid dynamical aspects of inviscid, laminar, and turbulent flows are studied here. By assessing the results against generally established knowledge in terms of the flow separation, and shock wave and boundary-layer interaction, physically sensible solutions with a wide range of Mach numbers and Reynolds numbers can be observed from the present numerical algorithm.

ISSN:0149-5720    

DOI:10.1080/10407788808913647

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

A new method involving the combined use of the Laplace transform and the finite-difference method is applicable to two- and three-dimensional linear transient heat conduction problems. The method removes the time dependences from the governing differential equations and boundary conditions by using the Laplace transform and then solves the transformed equations with the finite-difference method. The transformed temperature is inverted by the method of Honig and Hirdes to obtain the result in the physical quantity. The results are compared in tables with exact solutions and other numerical data, and the agreement is found to be good. The method can also be used to calculate the specific nodal temperature at a specific time.

ISSN:0149-5720    

DOI:10.1080/10407788808913648

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

The existing single-step finite-difference schemes for solving time-dependent parabolic partial differential equations become, due to the inadequate approximation of the time derivative, either inaccurate or unstable, or introduce spurious oscillations in the solution when the time step is relatively large. An optimal single-step exponential scheme is developed herein based on a study of the analytic behavior of time variation of the time derivative. Its excellent performance is demonstrated by its application to the one-dimensional transient diffusion equation. The comparison among a class of commonly used existing single-step schemes shows that it is by far the most accurate for a wide range of time steps. Its performance, the author believes, could be even more optimized if it is utilized in the context of an algorithm that automatically varies the time step based on the local truncation error. Generalizations to multidimensional problems are also discussed.

ISSN:0149-5720    

DOI:10.1080/10407788808913649

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

This paper presents an analysis of the flow and heat transfer between two parallel infinite disks that are separated by a distance L. One of the disks is solid, heated, and rotated; the other disk is porous, unheated, and stationary. Fluid is injected through the porous disk normal to its surface and toward the rotating disk. The three-dimensional Navier-Stokes and energy equations have been reduced to a system of ordinary differential equations by means of a similarity transformation and have been solved over a range of values of the two Reynolds numbers Reωequals; L2ω/νLand Reν = LU/νL, for two values of the temperature ratio Tr = (Ts- TL)/TL, of 0.001 (constant property flow) and 2.33. For Tr = 0.001 the velocity profiles are independent of the temperature profile which is determined for Pr = 0.67; for Tr = 2.33, the velocity and temperature profiles are determined for helium. The assumptions made in the analysis are shown to be valid provided that the mixed convection parameter, is small. Velocity and temperature profiles and the shear stress and the heat flux at the surface of the rotating disk are persented for a range of the above parameters.

ISSN:0149-5720    

DOI:10.1080/10407788808913650

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

ISSN:0149-5720    

DOI:10.1080/10407788808913651

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor