An introduction to computational fluid dynamics by H. Versteeg, W. Malalasekera

By H. Versteeg, W. Malalasekera

This tested, best textbook, is acceptable for classes in CFD. the recent variation covers new thoughts and techniques, in addition to significant growth of the complicated subject matters and functions (from one to 4 chapters).


This booklet offers the basics of computational fluid mechanics for the amateur consumer. It presents a radical but elementary advent to the governing equations and boundary stipulations of viscous fluid flows, turbulence and its modelling, and the finite quantity approach to fixing move difficulties on computers.


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Without density variations there is no linkage between the energy equation and the mass conservation and momentum equations. The flow field can often be solved by considering mass conservation and momentum equations only. The energy equation only needs to be solved alongside the others if the problem involves heat transfer. 3 Navier---Stokes equations for a Newtonian fluid The governing equations contain as further unknowns the viscous stress components τij. The most useful forms of the conservation equations for fluid flows are obtained by introducing a suitable model for the viscous stresses τij.

Fletcher (1991) noted that under-specification of boundary conditions normally leads to failure to obtain a unique solution. Over-specification, however, gives rise to flow solutions with severe and unphysical ‘boundary layers’ close to the boundary where the condition is applied. If the location of the outlet or far field boundaries is chosen far enough away from the region of interest within the solution domain it is possible to get physically meaningful results. Most careful solutions test the sensitivity of the interior solution to the positioning of outflow and far field boundaries.

The governing equation is linear so each of the individual Fourier components (and also their sum) would persist in time without change of amplitude. The final result is that the discontinuity remains undiminished due to the absence of a dissipation mechanism to remove the kink in the slope. Compressible fluid flows at speeds close to and above the speed of sound exhibit shockwaves and it turns out that the inviscid flow equations are hyperbolic at these speeds. The shockwave discontinuities are manifestations of the hyperbolic nature of such flows.

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