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By H. Versteeg, W. Malalasekera

This complete textual content provides the basics of computing device Fluid Dynamics easily and obviously.

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Extra info for An Introduction to Computational Fluid Dynamics: The Finite Volume Method (2nd Edition)

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9 we give a brief summary of direct numerical simulation (DNS). 1 What is turbulence? First we take a brief look at the main characteristics of turbulent flows. The Reynolds number of a flow gives a measure of the relative importance of inertia forces (associated with convective effects) and viscous forces. 1 WHAT IS TURBULENCE? 41 of fluid slide past each other in an orderly fashion. If the applied boundary conditions do not change with time the flow is steady. This regime is called laminar flow. At values of the Reynolds number above Recrit a complicated series of events takes place which eventually leads to a radical change of the flow character.

The value of discriminant (b2 − 4ac) is equal to −4y. 55) is of mixed type. The equation is locally hyperbolic, parabolic or elliptic depending on the value of y. For the non-linear case similar remarks apply. The classification of the PDE depends on the local values of a, b and c. Second-order PDEs in N independent variables (x1, x2, . . 56) k Fletcher (1991) explains that the equation can be classified on the basis of the eigenvalues of a matrix with entries Ajk. 54). 9 Classification of fluid flow equations Systems of first-order PDEs with more than two independent variables are similarly cast in matrix form.

The only exceptions are certain flows with strong shockwaves, but even some of those are often well enough approximated by equilibrium assumptions. 3 NAVIER---STOKES EQUATIONS FOR A NEWTONIAN FLUID 21 We can describe the state of a substance in thermodynamic equilibrium by means of just two state variables. Equations of state relate the other variables to the two state variables. 29) The assumption of thermodynamic equilibrium eliminates all but the two thermodynamic state variables. In the flow of compressible fluids the equations of state provide the linkage between the energy equation on the one hand and mass conservation and momentum equations on the other.

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