verifying second order

vahidmech · November 20, 2009, 14:56

hi
I have written a code for wave equation with RK2.
now I want to know how I can be sure that my code is second order?
the error must be smaller than what?

jed · November 20, 2009, 16:34

Which wave equation? In any case, you choose a smooth solution ( $\cos$ is good) and compare your code's results at successively finer resolution (refine in both space and time). Now plot $\log(\text{error})$ versus $\log(\Delta x)$ , the resulting slope is the order of accuracy of your method. If you don't have an exact solution available, you can manufacture one by introducing a distributed source term that makes something simple a solution, or (generally a worse option) compute a reference solution at very high resolution (preferably with a proven code).

CFDtoy · November 23, 2009, 16:51

Hi there,
Do richardson extrapolation test for grid convergence! 3 sets of results at time steps or spatial step h, h/2 ,h 4 is needed (basically 3 grids). works for structured mesh straight up ! Unstructured meshes are tricky. Since yours is a simple RK based integration procedure method..this works very well.

/CFDtoy

Quote:

Originally Posted by vahidmech

hi
I have written a code for wave equation with RK2.
now I want to know how I can be sure that my code is second order?
the error must be smaller than what?

November 20, 2009, 14:56	verifying second order	#1
vahidmech New Member vahid Join Date: Nov 2009 Posts: 6 Rep Power: 16	hi I have written a code for wave equation with RK2. now I want to know how I can be sure that my code is second order? the error must be smaller than what?

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
IS calc. with 2nd order discret. always necessary?	Azman	FLUENT	2	March 14, 2013 04:28
1st order vs 2nd order	ken	FLUENT	8	March 14, 2013 03:43
Unstable flow simpleFoam 2nd order	Valle	OpenFOAM	0	August 26, 2009 08:12
CFL condition for higher order schemes	Shyam	Main CFD Forum	2	February 14, 2008 14:24
SECOND ORDER DON'T CONVERGE, WHY??????????	naus	FLUENT	10	March 13, 2006 07:21

November 20, 2009, 16:34		#2
jed Member Jed Brown Join Date: Mar 2009 Posts: 56 Rep Power: 19	Which wave equation? In any case, you choose a smooth solution ( $\cos$ is good) and compare your code's results at successively finer resolution (refine in both space and time). Now plot $\log(\text{error})$ versus $\log(\Delta x)$ , the resulting slope is the order of accuracy of your method. If you don't have an exact solution available, you can manufacture one by introducing a distributed source term that makes something simple a solution, or (generally a worse option) compute a reference solution at very high resolution (preferably with a proven code).