Control Volume Finite Element Method Research Articles

EVALUATION AND ENHANCEMENTS OF SOME CONTROL VOLUME FINITE-ELEMENT METHODS—PART 1. CONVECTION-DIFFUSION PROBLEMS

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.

Evaluation and Enhancements of Some Control Volume Finite-Element Methods—Part 1. Convection-Diffusion Problems

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 obtaine...

A CONTROL-VOLUME FINITE-ELEMENT METHOD FOR PREDICTING FLOW AND HEAT TRANSFER IN DUCTS OF ARBITRARY CROSS-SECTIONS—PART II: APPLICATION TO SOME TEST PROBLEMS

In part I of the paper, a control-volume finite-element method for predicting flow and heat transfer through ducts of arbitrary cross sections was described. This paper, part II in the two-part sequence, discusses application of the proposed method to some test problems. Our main interest is in predicting flow through ducts of varying cross sections. However, unfortunately, for ducts of varying cross sections, nothing is available in literature that can be used as a benchmark. This recognition necessitated the adoption of an alternative approach. In this paper, a procedure is described for formulating problems involving flow through ducts of arbitrary cross sections for which the exact solution is known. Such problems, with known exact solutions, then serve as benchmarks to validate the numerical method. Cases considered include a square diffuser and a deforming elliptic duct.

CONTROL VOLUME FINITE-ELEMENT METHOD FOR HEAT TRANSFER AND FLUID FLOW USING COLOCATED VARIABLES— 2. APPLICATION AND VALIDATION

Abstract A novel control-volume finite-element method for heat transfer and fluid flow, in which all variables are colocated, is demonstrated and validated by application to a variety of test problems. The test problems are the convective scalar transport of a step profile at various angles to the grid and the fluid flow prediction for the driven cavity problem with Reynolds numbers of 100, 400, and 1000, for inviscid flow across a forward-facing step, and for rigid-body rotation discretized on a rectangular mesh with Reynolds numbers of 28.3 and infinity. The performance of the method is found to be excellent in terms of accuracy, providing excellent agreement with exact and grid-independent results, using only modest mesh discretization. The performance of the rigid-body rotation problem indicates that the scheme is “almost” second-order accurate.

Examination of the Upwind (Donor-Cell) Formulation in Control Volume Finite-Element Methods for Fluid Flow and Heat Transfer

Examination of the Upwind (Donor-Cell) Formulation in Control Volume Finite-Element Methods for Fluid Flow and Heat Transfer

Control Volume Finite-Element Method for Heat Transfer and Fluid Flow Using Colocated Variables—2. Application and Validation

Abstract A novel control-volume finite-element method for heat transfer and fluid flow, in which all variables are colocated, is demonstrated and validated by application to a variety of test problems. The test problems are the convective scalar transport of a step profile at various angles to the grid and the fluid flow prediction for the driven cavity problem with Reynolds numbers of 100, 400, and 1000, for inviscid flow across a forward-facing step, and for rigid-body rotation discretized on a rectangular mesh with Reynolds numbers of 28.3 and infinity. The performance of the method is found to be excellent in terms of accuracy, providing excellent agreement with exact and grid-independent results, using only modest mesh discretization. The performance of the rigid-body rotation problem indicates that the scheme is “almost” second-order accurate.

Control Volume Finite-Element Method for Heat Transfer and Fluid Flow Using Colocated Variables— 1. Computational Procedure

Control Volume Finite-Element Method for Heat Transfer and Fluid Flow Using Colocated Variables— 1. Computational Procedure

A Control-Volume Finite-Element Method for, Predicting Flow and Heat Transfer in Ducts of Arbitrary Cross-Sections—Part II: Application to Some Test Problems

A Control-Volume Finite-Element Method for, Predicting Flow and Heat Transfer in Ducts of Arbitrary Cross-Sections—Part II: Application to Some Test Problems

A Control-Volume Finite-Element Method for Predicting Flow and Heat Transfer in Ducts of Arbitrary Cross Sections—Part I: Description of the Method

A finite-element method for predicting flow through ducts of arbitrary and varying cross sections is presented. The governing differential equations are discretized using a control-volume approach. For this purpose, specially constructed three-dimensional control volumes are employed. The method is of the marching type and is based an a fully implicit formulation. Here, in part I of the paper, only the basic methodology is described; in the accompanying pan II, results of application of the method to some test problems are presented.

An Improved Control Volume Finite-Element Method for Heat and Mass Transfer, and for Fluid Flow Using Equal-Order Velocity-Pressure Interpolation

An Improved Control Volume Finite-Element Method for Heat and Mass Transfer, and for Fluid Flow Using Equal-Order Velocity-Pressure Interpolation

SOLUTION OF SOME TWO-DIMENSIONAL INCOMPRESSIBLE FLUID FLOW AND HEAT TRANSFER PROBLEMS, USING A CONTROL VOLUME FINITE-ELEMENT METHOD

Abstract The capabilities of a new control volume finite-element method (CVFEM) are demonstrated by its application to four different example problems. Whenever possible, the results are compared with exact solutions or with the results of independent numerical and experimental investigations available in the literature. These comparisons indicate that the proposed CVFEM can successfully solve two-dimensional elliptic fluid flow and heat transfer problems in regular- and irregular-shaped domains.

Solution of Some Two-Dimensional Incompressible Fluid Flow and Heat Transfer Problems, Using a Control Volume Finite-Element Method

Solution of Some Two-Dimensional Incompressible Fluid Flow and Heat Transfer Problems, Using a Control Volume Finite-Element Method

A Control Volume Finite-Element Method for Two-Dimensional Fluid Flow and Heat Transfer

A Control Volume Finite-Element Method for Two-Dimensional Fluid Flow and Heat Transfer