Numerical Solutions of the Basic Equations

Abstract

AbstractRapid developments of computers, of their computational speeds and of the data storage capacities, have resulted in powerful tools to solve the basic equations of fluid mechanics numerically. Computational results can be obtained that compare well with corresponding experimental data. Computer simulations of fluid flows have become an important sub-field of modern fluid mechanics. This importance will increase further in the future and for this reason an introduction to numerical fluid mechanics is given in this Chapter. The different types of differential equations, parabolic, hyperbolic and elliptic, are explained and it is outlined that their features are also observed in flows. It is also necessary to take their properties into account when methods for the numerical solutions of the basic equations of fluid mechanics are considered. The digitalization of the fluid mechanics equations is explained and the discretizations in space and time are outlined, and different methods such as the central difference method, upwind difference method, etc., are introduced. The implementations of boundary and initial conditions are discussed. Sample computations of flows are presented as examples of applications of numerical computer programs to practical fluid flows. Important contributions to this chapter were made by my son Dr.-Ing. Bodo Durst.