By H. Versteeg, W. Malalasekera
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This ebook provides the basics of computational fluid mechanics for the amateur person. It presents an intensive but hassle-free advent to the governing equations and boundary stipulations of viscous fluid flows, turbulence and its modelling, and the finite quantity approach to fixing stream difficulties on computers.
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Extra resources for An introduction to computational fluid dynamics
The ﬁnal result is that the discontinuity remains undiminished due to the absence of a dissipation mechanism to remove the kink in the slope. Compressible ﬂuid ﬂows at speeds close to and above the speed of sound exhibit shockwaves and it turns out that the inviscid ﬂow equations are hyperbolic at these speeds. The shockwave discontinuities are manifestations of the hyperbolic nature of such ﬂows. Computational algorithms for hyperbolic problems are shaped by the need to allow for the possible existence of discontinuities in the interior of the solution.
Even in ﬂows where the mean velocities and pressures vary in only one or two space dimensions, turbulent ﬂuctuations always have a threedimensional spatial character. Furthermore, visualisations of turbulent ﬂows reveal rotational ﬂow structures, so-called turbulent eddies, with a wide range of length scales. 2, which depicts a cross-sectional view of a turbulent boundary layer on a ﬂat plate, shows eddies whose length scale is comparable with that of the ﬂow boundaries as well as eddies of intermediate and small size.
At these speeds the Reynolds number is usually very high and the viscous regions in the ﬂow are usually very thin. The ﬂow in a large part of the solution region behaves as an effectively inviscid ﬂuid. This gives rise to problems in external ﬂows, because the part of the ﬂow where the outer boundary conditions are applied behaves in an inviscid way, which differs from the (viscous) region of ﬂow on which the overall classiﬁcation is based. 4) needs to be modiﬁed. The transient version of the algorithm needs to be adopted to make use of the favourable character of parabolic/hyperbolic procedures.