Transcription of Module 1: Introduction to Finite Difference …
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Module 1: Introduction to Finite Difference Method and fundamentals of CFD Lecture 2: The Lecture deals with:Elementary Finite Difference Quotients Objectives_templatefile:///D:/chitra/npt el_phase2/mechanical/cfd/lecture2 of 16/19/2012 4:36 PM Module 1: Introduction to Finite Difference Method and fundamentals of CFD Lecture 2: Elementary Finite Difference QuotientsFinite Difference representations of derivatives are derived from Taylor series example, if is the - component of the velocity, at point can beexpressed in terms of Taylor series expansion about point ( )Mathematically, Eq. ( ) is an exact expression for if the series practice, is small and any higher-order term of is smaller than . Hence, forany function Eq. ( ) can be truncated after a Finite number of :In terms of magnitude, and higher order are neglected, Eq. ( ) becomes( )Eq. ( ) is second-order accurate, because terms of order and higher have beenneglected.
Module 1: Introduction to Finite Difference Method and Fundamentals of CFD Lecture 2: Elementary Finite Difference Quotients In order to obtain a finite difference for the second-order partial derivative
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