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Additional info for An introduction to computational fluid dynamics
3, which gives the energy spectrum of turbulence downstream of a grid. The spectral energy E(κ) is shown as a function of the wavenumber κ = 2π/λ, where λ is the wavelength of the eddies. The spectral energy E(κ) (units m3/s2) is the kinetic energy per unit mass and per unit wavenumber of ﬂuctuations around the wavenumber κ. The diagram shows that the energy content peaks at the low wavenumbers, so the larger eddies are the most energetic. They acquire their energy through strong interactions with the mean ﬂow.
A change in temperature due to the sudden appearance of a small local heat source, changes the solution everywhere else. Disturbance signals travel in all directions through the interior solution. Consequently, the solutions to physical problems described by elliptic equations are always smooth even if the boundary conditions are discontinuous, which is a considerable advantage to the designer of numerical methods. To ensure that information propagates in all directions, the numerical techniques for elliptic problems must allow events at each point to be inﬂuenced by all its neighbours.
For an incompressible viscous flow there are no conditions on the density, but all the other above conditions apply without modiﬁcation. Commonly outﬂow boundaries are positioned at locations where the ﬂow is approximately unidirectional and where surface stresses take known values. For high Reynolds number ﬂows far from solid objects in an external ﬂow or in fully developed ﬂow out of a duct, there is no change in any of the velocity components in the direction across the boundary and Fn = −p and Ft = 0.