By Clive A.J. Fletcher, C. A. Fletcher

**From the reports **

"In precis, a ebook of substantial utlity either within the school room and as a reference quantity ... Fletcher's ebook is bound to develop into a useful device for pupil and researcher alike, and a relied on advent and consultant to the quickly evolving box of CFD."

(H. Aref in: magazine of Fluid Mechanics)

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**Additional info for Computational Techniques for Fluid Dynamics 1: Fundamental and General Techniques**

**Example text**

For the: potential equation governing inviscid, irrotational flows, and for the boundary layer equations, the appropriate initial and boundary conditions are well established. For the Navier-Stokes equations the proper boundary conditions at a solid surface are well known but there is some flexibility in making the correct choice for farfield boundary conditions. In general an underprescription of boundary conditions leads to nonuniqueness and an overprescription to unphysical solutions adjacent to the boundary in question.

As noted above, the steady Navier-Stokes equations and the steady energy equation are also elliptic. 232). Namely, both the maximum and minimum values of 4J must occur on the boundary l3R, except for the trivial case that 4J is a constant. The maximum principle is useful in testing that computational solutions of elliptic PDEs are behaving properly. e. 4AC < B 2 , the characteristics are complex and cannot be displayed in the (real) computational domain. For elliptic problems in fluid dynamics, identification of characteristic directions serves no useful purpose.

1). 8) where H contains all the first derivative terms etc. 1) and A, Band C may be functions of x, y. 8) involves only total differentials. The existence of these (characteristic) directions relates directly to the category of POE. 8). 11 ) 22 2. 12) AR+BS+CT+H=O. 10 and 11), dy/dx defines the slope of the tangent to K. 13) reduces to the simpler relationship between dP/dx and dQ/dx, dP) ] dy dQ [ A ( dx +H dx +C dx =0 . 15) holds. 8) is: i) a hyperbolic PDE, two real characteristics exist, ii) a parabolic PDE, one real characteristic exists, iii) an elliptic PDE, the characteristics are complex.