|
[Sponsors] |
August 4, 2011, 04:57 |
1D Burgers euqation with 4th Runge Kutta
|
#1 |
Member
Dokeun, Hwang
Join Date: Apr 2010
Location: Korea, Republic of
Posts: 98
Rep Power: 16 |
Hello
Now i'm tring to apply 4 Stage Runge Kutta scheme to 1D Burgers euqation as a model equation like this. hear, At this point, the slop is suggested as central differencing. The Question is.. How to handle at the point i=2,3,IM-2,IM-1? Because 4 Stage Runge Kutta requires i-2 ~ i+2 points for next step value at i, I can't get at i=2,3,IM-2,IM-1. I got the answer using 3 stage RK to i=3,IM-2 and 2 stage RK to i=2,IM-1. inspite of complicate euqations used. But I guess there manybe more simple way for near the boundary points. Please let me know simple solution for this. Thank you in advance. |
|
August 5, 2011, 04:18 |
|
#2 |
Senior Member
cfdnewbie
Join Date: Mar 2010
Posts: 557
Rep Power: 20 |
maybe I'm misunderstanding you, but the classical RK schemes use stages/nodes that are INSIDE the interval you are trying to integrate....so you are integrating in time, and you need the evaluation at (say) 1/3 delta t, 1/2 delta t, 2/3 delta t and so on...
how you discretize your spatial domain is up to you, since you are using a method of lines approach.... |
|
August 8, 2011, 03:45 |
|
#3 |
Member
Dokeun, Hwang
Join Date: Apr 2010
Location: Korea, Republic of
Posts: 98
Rep Power: 16 |
Dear cfdnewbie
Thank you for your reply. Would please review my spreading out of the equations. Becasue is defined as , refers . And, in turn, refers . Here, comes from and is derived from . As a result, to get , I need the values of at i+2~i-2. As the same manner, requires the value of at i-3~i+3. I feel that something is wrong with my equations but I'm in trouble to figure out it cleary. I attached my F90 code for fixing..(it works any way) I appreciate that again. |
|
August 8, 2011, 07:34 |
|
#4 |
Member
Dokeun, Hwang
Join Date: Apr 2010
Location: Korea, Republic of
Posts: 98
Rep Power: 16 |
dear cfdnewbie
I understood my problem. my original program was... DO i=2,IM-1 u1(i) = function of u(n,i) u2(i) = function of u(n,i) u3(i) = function of u(n,i) u4(i) = function of u(n,i) END DO but the right one should be DO n=1,NM-1 DO i=2,IM-1 u1(i) = function of u(n,i) END DO DO i=2,IM-1 u2(i) = function of u1(i) END DO DO i=2,IM-1 u3(i) = function of u2(i) END DO DO i=2,IM-1 u4(i) = function of u3(i) END DO DO i=2,IM-1 u(n+1,i) = u(n,i) + ~~~ END DO END DO at first i tred to write all u1, u2, u3, u4 as functions of u(n) along just one iteration, but now there are each iteration for u1~u4, and in another iteration I calculate u(n+1) |
|
Tags |
burgers equation, runge kutta |
Thread Tools | Search this Thread |
Display Modes | |
|
|
Similar Threads | ||||
Thread | Thread Starter | Forum | Replies | Last Post |
Runge Kutta 4th Order Source Code | sugu | Main CFD Forum | 4 | October 26, 2012 04:15 |
Using Runge kutta 4th order scheme in FSI using CFX | vmlxb6 | CFX | 0 | April 26, 2011 15:55 |
Runge Kutta Optimization | vasanth | Main CFD Forum | 6 | December 2, 2005 14:07 |
2N Storage runge kutta | Vasanth | Main CFD Forum | 3 | August 2, 2005 11:44 |
Diagonally Dominate Runge Kutta Method | Anthony Iannetti | Main CFD Forum | 0 | January 23, 2001 22:27 |