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)
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.