Lecture 20.pptx

# Lecture 20.pptx - Lecture 20 CBE 218 Fluid Mechanics March...

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Lecture 20 CBE 218 Fluid Mechanics March 6, 2015

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Chapter 20 Computational Fluid Dynamics Branch of fluid mechanics that uses numerical methods and algorithms to solve problems with fluid flow. Fundamental basis of all problems are the Navier-Stokes Equations. Methods - Discretization - Finite volume - Finite element - Finite difference - Spectral element - Boundary element - High resolution discretization
REPLACING DIFFERENTIAL EQUATIONS WITH DIFFERENCE EQUATIONS y = x –x 4 dy/dx=1 - 4x 3 d 2 y/dx 2 = -12x 2 d 3 y/dx 3 =-24x d 4 y/dx 4 =-24 CFD programs replace the basic differential equations (mass, momentum, energy) with algebraic difference equations and then solve numerically. This is called discretization.

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REPLACING DIFFERENTIAL EQUATIONS WITH DIFFERENCE EQUATIONS n n n n forward x y n x x y y dx dy 1 1 1 1 n n n n backward x y n x x y y dx dy 2 backward
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