By Clive A.J. Fletcher, C. A. Fletcher
This famous 2-volume textbook presents senior undergraduate and postgraduate engineers, scientists and utilized mathematicians with the explicit options, and the framework to enhance talents in utilizing the concepts within the a variety of branches of computational fluid dynamics. A recommendations guide to the routines is in education.
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Extra resources for Computational Techniques for Fluid Dynamics 1: Fundamental and General Techniques
24); in practice a shock-wave occurs. 32 and 33) are based. 32 and 33) are valid. 3 Appropriate Boundary (and Initial) Conditions It has already been indicated (Sect. 4). It is also possible to specify boundary conditions (Sect. 2), for example as on CD and EF in Fig. 8. 22 and 23) is possible. 50) will be labelled r:x. and p characteristics. Three cases (shown in Fig. 6) are considered initially. The case shown in Fig. 6a is equivalent to that shown in Fig. 4. That is, data for both u and v on a non-characteristic curve, AB, uniquely determine the solution '....
4 Systems of Equations A consideration of Chap. 11 indicates that the governing equations for fluid dynamics often form a system, rather than being a single equation. 24) dv= G:)dx+G;)dY . 25) For the problem shown in Fig. 3 it is assumed that the solution has already been determined in the region ACPDB. As before, two directions, dy/dx, through Pare sought along which only total differentials, du and dv, appear. :::J C :::J o 1:0 Initial conditions Fig. 3. 23) ==> m1du+m 2 dv=(L 1E 1+L2E2) . 26) establishes the relationships L1Bll +L2B21 =m 1dy , L1B12+L2B22=m2dy .
I Background 19 and auxiliary (initial and boundary) conditions are well-posed mathematically if the following three conditions are met: i) the solution exists, ii) the solution is unique, iii) the solution depends continuously on the auxiliary data. The question of existence does not usually create any difficulty. An exception occurs in introducing exact solutions of Laplace's equation (Sect. 3) where the solution may not exist at isolated points. 53). g. inside the body in Fig. 7. The usual cause of non-uniqueness is a failure to properly match the auxiliary conditions to the type of governing POE.
Computational Techniques for Fluid Dynamics 1: Fundamental and General Techniques by Clive A.J. Fletcher, C. A. Fletcher