201-Lect 13 - MECH201 Engineering Analysis (2009) p. 70...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MECH201 Engineering Analysis (2009) p. 70 10.6 The Crank-Nicolson Scheme -- an Implicit method In the computation using the implicit method half of the spatial differentiation in the "future time" and thus have to be solved by iteration. The FDA is expressed as: ( ) ( ) , 1 , 1, 1 , 1 1, 1 1, , 1, 2 2 2 2 i j i j i j i j i j i j i j i j T T T T T T T T t x + + + +- + +-- =- + +- + We now sort the future time (j+1) to the LHS and the rest in RHS: ( ) 1, 1 , 1 1, 1 , 1, , 1, 2 2 2 2 1 2 2 2 2 2 2 i j i j i j i j i j i j i j t t t t T T T T T T T x x x x + + +- + +- - + +- = +- + The above equation can be solve by iteration process. We may simply write: ( ) 1, 1 , 1 1, 1 , 1 2 i j i j i j i j rT r T rT b + + +- +- + +- = where 2 2 t r x = and ( ) , , 1, , 1, 2 2 2 i j i j i j i j i j t b T T T T x +- = +- + is a value for each node which is constant during the iteration process. and the iteration scheme take the form: ( ) ( ) , 1 1, 1 1, 1 , 1 1 2 new i j i j i j i j T r T T b r + + +- + = + + + In a form more convenient for programming:...
View Full Document

Page1 / 5

201-Lect 13 - MECH201 Engineering Analysis (2009) p. 70...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online