Control Volume Faces Research Articles

THE NORMALIZED WEIGHTING FACTOR METHOD: A NOVEL TECHNIQUE FOR ACCELERATING THE CONVERGENCE OF HIGH-RESOLUTION CONVECTIVE SCHEMES

This article deals with the development of a new method for accelerating the solution of flow problems discretized using high-resolution convective schemes. The technique is based on the normalized variable and space formulation (NVSF) methodology and is denoted here by the normalized weighting-factor (NWF) method. In contrast with the well-known deferred-correction (DC) procedure, the NWF method is fully implicit and is derived by directly replacing the control-volume face values by their Functional relationships in the discretized equation. The direct substitution is performed by the introduction of a variable, NWF, that accounts for the multiplicity of interpolation profiles in HR schemes. The new method is compared with the widely used DC procedure and is shown to be, on average, four times faster.

A fourth-order finite volume method with colocated variable arrangement

A finite volume solution method for the two-dimensional Navier-Stokes equations and temperature equation with 4th order discretization on cartesian grids is presented. The method uses colocated variable arrangement and the SIMPLE-kind of velocity-pressure coupling. The surface integrals (convection and diffusion fluxes through control volume faces) are approximated by Simpson's rule and polynomial interpolation, and the volume integrals (source terms) are approximated by fitting a fourth-order polynomial through nine points and integrating it analytically. Applications to the solution of a scalar transport on a known velocity field and to the lid-driven and buoyancy-driven cavity flows show superior accuracy as compared to the first and second order schemes. The approach can be readily extended to control volumes of arbitrary shape and unstructured grids.

One-dimensional ablation using Landau transformation and finite control volume procedure

A technique utilizing the Landau transformation has been developed to solve one-dimensional variable area ablation problems. It is based on applying the integral form of the conservation equations to control volumes that are moving with velocities consistent with the Landau transformation. Exponential temperature profiles are assumed to evaluate the conduction and convection fluxes at control volume faces. The technique has been applied to one-dimension al planar and cylindrical geometries with sample calculations presented to verify the accuracy of the method.

Calculation procedure for 3-D laminar flows in complex geometrics using a nonstaggered nonorthogonal grid system

In this paper the Navier-Strokes equations are solved for three-dimensional steady laminar flows in complex geometries using a nonorthogonal, nonstaggered coordinate system. The strong conservation form of the governing equations is discretized using a finite volume method. The pressure velocity coupling is ensured by using the pressure-weighted interpolation method to calculate the velocities at the faces of control volumes. The method was assessed by comparing the predicted results for six test cases in which analytical solutions or experimental data were available. They correspond to the transport of a scalar in a prescribed flow field, the flow through a square diffuser, the flow through a transforming elliptical duct, and the flow through an S-shaped duct. The predictions reveal good agreement with available data, demonstrating the accuracy and generality of the present method.

NUMERICAL TREATMENT OF DIFFUSION COEFFICIENTS AT INTERFACES

The main purpose of this work is to evaluate the values of diffusion coefficients at control-volume faces, using the finite-volume method, in transport problems that include diffusion processes. A heat conduction problem in a composite slab with linearly temperature-dependent conductivity, which has a closed-form solution, is selected for demonstration. It is found that the harmonic mean operation performs better than the arithmetic mean operation in evaluating the interface diffusion coefficients. Moreover, if we intend to obtain the information at some specific interfaces with abrupt changes of diffusion coefficients, the recommended grid layout is arranged such that each specific interface contains a grid node. This arrangement can give more accurate predictions at these unusual interfaces.

Cell vertex finite volume discretizations in three dimensions

AbstractThe cell vertex method is generalized to three dimensions. It is proved that there exists a one‐parameter family of eight‐point three‐dimensional methods with second‐order truncation error on parallelepipeds. Using different triangulations of control volume faces, various finite volume methods are derived. Some of these are identified as members of the aforementioned one‐parameter family and may be regarded as second‐order upwind schemes. A Fourier analysis is used to investigate the spectral properties of these discretizations.Numerical experiments illustrate that second‐order global accuracy is achieved on parallelepiped grids, as suggested by the theory. Randomly perturbed, stretched, sheared meshes are used to test these methods to destruction. It is found that upwinding improves both the accuracy on distorted meshes and the spectrum of the discretization.