Selected Topics in the Theory and Practice of Computational Fluid Dynamics
Abstract
Computational fluid dynamics (CFD) is a large branch of scientific computing that lately has undergone explosive growth. It draws upon elements from related disciplines: fluid mechanics, numerical analysis, theory of partial differential equations, computer science, and computational geometry. By selecting certain topics we try to trace the way the dramatic growth came about and to illustrate the interplay of the related disciplines. The scope is broad and the emphasis is on discussing the underlying fundamentals in order to present an overall perspective on CFD. The focus is on the evolution of nonsmooth features in inviscid flows, primarily macroscale discontinuities like shock waves and vortex sheets admitted as solutions to the Euler equations, but also with some view to their possible unstable progression into smallscale features, ending ultimately in turbulence. Some of the current finitedifference methods, and the theory they are based upon, which are used to treat these problems are reviewed, and different grid generation techniques are introduced. Together with some principles for using advanced supercomputers, we also discuss how the methods are implemented on these machines. A number of computed results, some of them new and of large scale with up to one million grid points, are presented which reflect the limits of the theory and the current status of the field.
 Publication:

Journal of Computational Physics
 Pub Date:
 September 1987
 DOI:
 10.1016/00219991(87)900726
 Bibcode:
 1987JCoPh..72....1R
 Keywords:

 Computational Fluid Dynamics;
 Finite Difference Theory;
 Inviscid Flow;
 Afterbodies;
 Architecture (Computers);
 Computational Grids;
 Euler Equations Of Motion;
 Grid Generation (Mathematics);
 Shock Wave Interaction;
 Vortex Sheets;
 Vortex Streets;
 Fluid Mechanics and Heat Transfer