|January 4, 2011, 09:49||
central difference approximation
Join Date: Jul 2010
Posts: 10Rep Power: 7
Where can I find the expression of the central difference approximation of the first and second derrivative (spatial) for a NON uniform grid?
|January 4, 2011, 19:00||
Join Date: Mar 2009
Posts: 74Rep Power: 9
For 3 points, (x1, f1), (x2, f2), (x3, f3), x1 < x2 <x3
Two methods (identical results for the approximation):
1. Expand f1 and f3 about x2 in Taylor series. Expand through the second derivatives.
You get two equations with unknowns df/dx and d^2f/dx^2 evaluated at x2. Solve those for your solution. Note: Expand through the 3rd and 4th derivatives, you have terms for the major errors you ignore by truncating the series after the 2nd derivatives.
2. Fit a parabola, f(x) = f2 + b(x - x2) + c(x - x2)^2 through the 3 points. b and c will be functions of x1, x2, x3 and f2 and f3.
|Thread||Thread Starter||Forum||Replies||Last Post|
|First order in time and Central Difference Convergence problem||RameshK||Main CFD Forum||7||July 17, 2010 14:13|
|central difference method||sudhir||FLUENT||6||May 6, 2008 09:17|
|Specified Blend factor =1 Vs Central Difference||Kushagra||CFX||4||May 2, 2008 13:14|
|Central DIfference||Glen||Main CFD Forum||9||May 27, 2005 02:06|
|Central Difference vs Upwind Defference||S. Balasubramanyam||Main CFD Forum||5||January 16, 2002 02:58|