Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics pp 60-68 | Cite as

# Two calculation procedures for steady, three-dimensional flows with recirculation

## Abstract

Two procedures are described for solving the Navier-Stokes equations for steady, fully three-dimensional flows: both are extensions of earlier methods devised for three-dimensional boundary layers, and have the following common features: (i) the main dependent variables are the velocities and pressure; (ii) the latter are computed on a number of staggered, interlacing grids, each of which is associated with a particular variable; (iii) a hybrid central-upwind difference scheme is employed; and (iv) the solution algorithms are sufficiently implicit to obviate the need to approach the steady state via the time evolution of the flow, as is required by wholly explicit methods.

The procedures differ in their manner of solving the difference equations. The SIVA (for SImultaneous Variable Adjustment) procedure, which is fully-implicit, uses a combination of algebraic elimination and point-successive substitution, wherein *simultaneous* adjustments are made to a point pressure, and the six surrounding velocities, such that the equations for mass and (linearised) momentum are locally satisfied.

The SIMPLE (for Semi-Implicit Method for Pressure-Linked Equations) method proceeds in a *successive* guess-and-correct fashion. Each cycle of iteration entails firstly the calculation of an intermediate velocity field which satisfies the linearised momentum equations for a guessed pressure distribution: then the mass conservation principle is invoked to adjust the velocities and pressures, such that all of the equations are in balance.

By way of an illustration of the capabilities of the methods, results are given of the calculation of the flow of wind around a building, and the simultaneous dispersal of the effluent from a chimney located upstream.

## Keywords

Difference Equation High Reynolds Number Sparse Grid Continuous Combustion Dimensional Boundary Layer## Preview

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