SUMMARY An unstructured grid, finite volume method is presented for the solution of two-dimensional viscous, incompressible flow. The method is based on the pressure-correction concept implemented on a semi-staggered grid. The computational procedure can handle cells of arbitrary shape, although solutions presented herein have been obtained only with meshes of triangular and quadrilateral cells. The discretization of the momentum equations is effected on dual cells surrounding the vertices of primary cells, while the pressure-correction equation applies to the primary-cell centroids and represents the conservation of mass across the primary cells. A special interpolation scheme s used to suppress pressure and velocity oscillations in cases where the semi-staggered arrangement does not ensure a sufficiently strong coupling between pressure and velocity to avoid such oscillations. Computational results presented for several viscous flows are shown to be in good agreement with analytical and experimental data reported in the open literature.

A pressure-correction method for the solution of incompressible viscous flows on unstructured grids

Modeling turbulent recirculating flows by finite-volume methods—current status and future directions☆

Experimental heat transfer and temperature correlations are presented for a steel beam installed beneath a ceiling when exposed to a localized fire source. The heat flux distribution on every part of the beam is formulated as a function of flame length and the distance from the fire source. A specially written finite volume code CV-FEM, as well as the general-purpose finite element code ANSYS were used for the numerical simulation. Experimental values of heat fluxes were applied as boundary conditions for the surfaces exposed to fire. The results of the three-dimensional transient thermal analysis obtained are compared with the experimental data. The program CV-FEM was found to be very effective for this type of problem. The experimental correlations obtained and numerical procedure developed can be used to predict the heating mechanism and thermal response of practical building members exposed to a localized fire.

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Experimental And Numerical Study On The Behaviour Of A Steel Beam Under Ceiling Exposed To A Localized Fire

A numerical method for calculating two-dimensional turbulent incompressible flow on unstructured triangular meshes is developed. A primitive variable formulation is used. The Helmholtz pressure equation algorithm is used to enforce the velocity continuity relation for incompressible flow. A careful treatment of the pressure dissipation model is presented. A standard k-ϵ turbulence model with wall functions is used to provide closure for the governing equations. A backward-facing step turbulent flow is calculated using an unstructured triangular mesh and the results are compared to experimental and computational data.

The Solution of the Two-Dimensional Incompressible Flow Equations on Unstructured Triangular Meshes

The control volume-based finite-element method for solution of the Navier-Stokes equations in vortex-streamfunction formulation is presented. The exponential interpolation function suggested by Baliga and Patankar is used for the vortex, whereas the linear interpolation function refers to the streamfunction. The new feature of the method lies in the formulation of boundary conditions for the vortex on a solid surface.

Control volume finite-element method for navier-stokes equations in vortex-streamfunction formulation

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.

C. Prakash

Papers

A control-volume finite-element method for predicting flow and heat transfer in ducts of arbitrary cross sections—part i: description of the method