Zienkiewicz O.C., Taylor R.L. Vol. 3. The finite - tiera.ru

12 Introduction and the equations of ¯uid dynamics
The reader will note that the above equations, with the exception of the convective
acceleration terms, are identical to those governing the problem of incompressible (or
slightly compressible) elasticity, which we have discussed in Chapter 12 of Volume 1.
1.4 Concluding remarks
We have observed in this chapter that a full set of Navier±Stokes equations can be
written incorporating both compressible and incompressible behaviour. At this
stage it is worth remarking that
1. More specialized sets of equations such as those which govern shallow-water ¯ow
or surface wave behaviour (Chapters 5, 7 and 8) will be of similar forms and need
not be repeated here.
2. The essential di€erence from solid mechanics equations involves the non-selfadjoint
convective terms.
Before proceeding with discretization and indeed the ®nite element solution of the
full ¯uid equations, it is important to discuss in more detail the ®nite element
procedures which are necessary to deal with such convective transport terms.
We shall do this in the next chapter where a standard scalar convective±di€usive±
reactive equation is discussed.
References
1. C.K. Batchelor. An Introduction to Fluid Dynamics, Cambridge Univ. Press, 1967.
2. H. Lamb. Hydrodynamics, 6th ed., Cambridge Univ. Press, 1932.
3. C. Hirsch. Numerical Computation of Internal and External Flows, Vol.1,Wiley,Chichester,
1988.
4. P.J. Roach. Computational Fluid Mechanics, Hermosa Press, Albuquerque, New Mexico,
1972.
5. H. Schlichting. Boundary Layer Theory, Pergamon Press, London, 1955.
6. L.D. Landau and E.M. Lifshitz. Fluid Mechanics, Pergamon Press, London, 1959.
7. R. Temam. The Navier±Stokes Equation, North-Holland, 1977.
8. I.G. Currie. Fundamental Mechanics of Fluids, McGraw-Hill, 1993.