An Introduction to Computational Fluid Dynamics: The Finite by H. Versteeg, W. Malalasekera

By H. Versteeg, W. Malalasekera

This entire textual content provides the basics of laptop Fluid Dynamics easily and obviously.

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

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Initial conditions are needed in the entire rod and conditions on all its boundaries are required for all times t > 0. This type of problem is termed an initial– boundary-value problem. e. ). The solutions move forward in time and diffuse in space. The occurrence of diffusive effects ensures that the solutions are always smooth in the interior at times t > 0 even if the initial conditions contain discontinuities. The steady state is reached as time t → ∞ and is elliptic. 46). The governing equation is now equal to the one governing the steady temperature distribution in the rod.

This complicates matters greatly when flows around and above M = 1 are to be computed. Such flows may contain shockwave discontinuities and regions of subsonic (elliptic) flow and supersonic (hyperbolic) flow, whose exact locations are not known a priori. 11 is a sketch of the flow around an aerofoil at a Mach number somewhat greater than 1. 5 Auxiliary conditions for viscous fluid flow equations The complicated mixture of elliptic, parabolic and hyperbolic behaviours has implications for the way in which boundary conditions enter into a flow problem, in particular at locations where flows are bounded by fluid boundaries.

9, which is again bounded by the characteristics. 10a shows the situation for the vibrations of a string fixed at x = 0 and x = L. For points very close to the x-axis the domain of dependence is enclosed by two characteristics, which originate at points on the x-axis. The characteristics through points such as P intersect the problem boundaries. The domain of dependence of P is bounded by these two characteristics and the lines t = 0, x = 0 and x = L. 10b and c) in parabolic and elliptic problems is different because the speed of information travel is assumed to be infinite.

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