[cxcxcx0505]

I am a newbie in CFD.I need to solve the one dimension linear wave problem.I have found some source from wiki here and wikipedia.
http://www.cfd-online.com/Wiki/Linea...Runga-Kutta.29

I need to solve using 6th compaq scheme,1st order upwind scheme,2th maccormack scheme and lax-wendroff scheme.And compare the results of this different schemes.The time derivative needs to be solve using 4th runge-kutta method.Can anybody explain more on how to do the numerical solution?Thanks.And,how to integrate the 4th runge-kutta into the equation?
I need more help and resource on how to do it.

[cxcxcx0505]

I have completed the numerical solution using maccormack scheme.Still need help for the other methods and on how to integrate the runge-kutta method into the time derivative.

[DoHander]

Hello,

have you checked your solution with the exact solution of the wave equation ?

Do

[cxcxcx0505]

hello,Do.Thanks for your advice and support.
I have consulted my professor,the above graph is the exact solution since the cfl number is equal to one.
I have solve the equation using lax-wendroff,maccormack,and upwind scheme.
Now,I need to solve the wave equation using sixth-order compact scheme and time-integrated by a four-stage runge-kutta method.I really dont have any idea how to do it.Is there anybody know how to do it?I need some materials and guidance.Thanks!

[DoHander]

Basically you need to "split" your problem in two parts:

1. Replace the spatial derivative with a 6th order finite difference formula and move this in the right hand term. You will have now a problem of this form:

df/dt=R(x)

where R(x) contains your discretized spatial terms.

2. For temporal discretization use any good book of numerical methods, or simply search Google for Runge-Kutta ...


Do

[DoHander]

About your professor confirmation that your solution is the "exact one" for CFL=1. This is true only if your implementation if faultless - this is exactly the point of comparing the "exact" analytical solution with the numerical one to prove that your implementation is correct.

From my experience the time spent in comparing a numerical solution with an analytical solution (when you have one) is always rewarded .

Do

[cxcxcx0505]

Thanks !

[cxcxcx0505]

when I solve for the runge-kutta equation,I use R(x) as the slope?