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CFD lecture 24 - Computational Fluid Dynamics Lecture 24...

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Computational Fluid Dynamics Lecture 24 General Curvilinear Coordinates Computing flow around complex geometry is better accomplished by solving the PDE’s of the N.S. equations in a generalized coordinate system. Transfer to Cartesian grid. This causes the PDEs to be more complex but improves the treatment of the boundary conditions. This permits grid lines to be concentrated in parts of the physical domain where strong gradients occur. Complications: Changes PDE’s. - additional terms, x ξ , etc. usually discretized, and introduce additional errors. Physical space ( ) , , , x y z t Computational space ( ) , , , ξ η ζ τ Want a unique – single valued transform - ξ grid lines don’t cross (similar to no caustics). 1
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Consider first the 1-D transform problem. Physical space clustered physical uniform computational grid A variable mesh is often used to cluster computational nodes, in a no-slip boundary layer. One stretching function is This would be ideal for a laminar boundary layer, but a turbulent boundary layer may benefit from an even stronger clustering of grid points near the wall. 2 on 0 1, and are constants. z a b a b ζ ζ ζ = + A second commonly used analytical transformation function is: 1 ln 1 1 1 1 ln 1 z h z h β β ζ β β β + − + = <
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