By Bengt Andersson; et al

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On looking at the expressions for aW , aE and aP , one may see that they are identical for all cells and do not change during the iterations. 0200, for all cells. g. aE means that cell (P) is highly influenced by it, whereas a low number means the opposite; see Eq. 18). As can be seen here, aW is larger than aE , meaning that the value for cell P is more influenced by its western neighbour than by its eastern one. This shouldn’t come as any surprise, knowing that the gas is flowing from west to east and, thus, the western cell should play a more dominant role in the calculation of cell P.

E. the second derivative of φ is ‘small’. Otherwise, the first-order upwind scheme, Eq. 32), is used. 4 Taylor expansions Before proceeding, a short mathematical review of Taylor expansions will be given. Taylor’s theorem for a 1D expansion of a real function f (x) about a point x = x0 is given without a proof: f (x) = f (x0 ) + (x − x0 ) f ′ (x0 ) + (x − x0 )n (n) f (x0 ) + + n! x (x − x0 )2 ′′ f (x0 ) + · · · 2! (x − u)n (n+1) f (u)du. n! 33) x0 The last term in Eq. 33) is called the Lagrange remainder.

40) For non-Newtonian fluids there are several models available. In this book we will cover only Newtonian fluids, but the interested reader can find additional theories in standard textbooks [2]. The standard models for turbulent flows assume Newtonian fluids, and empirical models are required for modelling turbulent viscosity. Questions (1) Why are diffusivity, kinematic viscosity and thermal diffusion similar in gases at low pressure? (2) What is the molecular mechanism for viscous transport of momentum in gases?

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