摘要:

A three-dimensional numerical method based on the superposition principle for the solution of the heat diffusion equation is derived for Cartesian coordinates and tested for three different boundary conditions: a constant heat flux density, a convective-type surface heat flux, and a sudden cooling of the surface to a constant temperature, In addition, this three-dimensional numerical method is compared with the popular three-dimensional Brian's alternating direction implicit (ADI) method. The method based on the superposition principle has the same degree of accuracy in most cases as the method normally used for these types of calculations. In addition, its algorithm is considerably simpler to formulate and easier to program, and it requires about half the computing time needed to solve the problem when using Brian's ADI method. On the other hand, Brian's ADI method is unconditionally stable, but the method based on the superposition principle is not.

ISSN:0149-5720    

DOI:10.1080/01495728408961816

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

Variations of the SIMPLE method of Patankar and Spalding have been widely used over the past decade to obtain numerical solutions to problems involving incompressible flows. The present paper shows several modifications to the method which both simplify its implementation and reduce solution costs. The performances of SIMPLE, SIMPLER, and SIMPLEC (the present method) are compared for two recirculating flow problems.

ISSN:0149-5720    

DOI:10.1080/01495728408961817

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

The locally analytic differencing (LOAD) scheme of Wong and Raithby is applied to solve a variety of one- and two-dimensional convection-diffusion problems. The results are compared with those obtained with the exponential differencing (ED) scheme of Spalding. The LOAD scheme is significantly more accurate; at grid Peclet numbers ≥ 5 the errors in the solution obtained with the LOAD scheme can be one to two orders of magnitude less than the errors obtained with the ED scheme on the same grid. For a prescribed accuracy, the LOAD scheme requires far fewer grid points (computer memory) and much less computer time (cost). For two-dimensional problems, the cross-wind (false) diffusion in the LOAD scheme is much less than in the ED scheme. The LOAD scheme is easy to implement: the discretization coefficients remain the same as in the ED scheme and only the term corresponding to the source term receives some additional correction. This correction term is presented. Existing computer programs based on the ED scheme can be easily modified to incorporate the LOAD scheme.

ISSN:0149-5720    

DOI:10.1080/01495728408961818

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

A solution methodology has been developed for convection-diffusion problems in which one boundary of the solution domain does not lie along a coordinate line. A nonorthogonal, algebraic coordinate transformation is used which yields a rectangular solution domain. This transformation avoids the task of numerically generating boundary-fitted coordinates. The discretized conservation equations are derived on a control-volume basis. These equations contain pseudodiffusion terms that result from the nonorthogonal nature of the transformation. The entire discretization procedure is documented in detail. Although it is not an essential feature of the method, the discretized equations and their solutions are tied in with the well-documented practices of the Patankar solution scheme for orthogonal systems. Application of the methodology is illustrated by two numerical examples.

ISSN:0149-5720    

DOI:10.1080/01495728408961819

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

A detailed numerical study of the combined modes of heat transfer in a furnace is carried out. The furnace considered is a heat treatment furnace and the conjugate modes involving radiation )particularly gas radiation), conduction, and convection are considered in order to determine the transient temperature variation in the furnace and in the material undergoing heat treatment. The thermal processes are coupled through the boundary conditions and the property variations. Strong non-linearity is introduced due to the radiative heat transfer mechanisms. The nonlinear coupled system of partial differential equations is solved numerically by time marching, which allows study of the time-dependent temperature field in the system. The initial temperature of the system and the inflow temperature of the hot gases are the main inputs. Interest lies in determining the temperature decay in the gases as they flow from the inlet to the outlet and in the transient increase in temperature level in the furnace. By use of implicit techniques, numerical results are obtained and considered in terms of the underlying physical mechanisms. The numerical results are also compared with experimental data. Close agreement is observed, lending support to the numerical simulation and analysis of the complex combined heat transfer processes involved.

ISSN:0149-5720    

DOI:10.1080/01495728408961820

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

A simple and efficient numerical solution method for simultaneous nonlinear equations in many variables is presented. The number of function evaluations is shown to be linearly proportional to the number of equations. Furthermore, the method does not require evaluation of function derivatives. Three simple examples are presented. Finally, the method is applied to the solution of steady-state two-fluid model equations describing boiling flow in heated channels.

ISSN:0149-5720    

DOI:10.1080/01495728408961821

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

The complex variable boundary-element method (CVBEM) is expanded into a finite series of analytic functions. For the special case of linear polynomial basis functions assumed on each boundary element, the CVBEM and the analytic function method (AFM) results in a similar numerical modeling approximation.

ISSN:0149-5720    

DOI:10.1080/01495728408961822

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

ISSN:0149-5720    

DOI:10.1080/01495728408960281

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor