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Lecture 21.pptx

Lecture 21.pptx - Lecture 21 CBE 218 Fluid Mechanics Grids...

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Lecture 21 CBE 218 Fluid Mechanics March 16, 2015
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Grids To apply difference equations to multidimensional problems, we divide the space into many points located on a mathematical grid. ∆x ∆y x y node i-1, j+1 i-1, j i-1, j-1 i+1, j+1 i+1, j i+1, j-1 i, j i, j+1 i, j-1
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Grids If we assume that there is a known value of ‘z’ at every intersection (or node), we can write central difference- You can extend this to 2-3 dimensional system…… j i j i j i j i y const central n x x z z x z x z , 1 , 1 , 1 , 1 ' ' 1 , 1 , 1 , 1 , ' ' j i j i j i j i x const central n y y z z y z y z
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Using grids and difference equations, we can transform working differential equation into algebraic form.
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One dimensional flow equation – unsteady state Explicit equation 2 2 y V t V x x
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