Runge Kutta for unsteady flow

Hooman · August 2, 2011, 06:28

Hi,

I am writing a code to solve an unsteady flow problem and I need to use the Runge Kutta methods for my time stepping scheme. I am having problems understanding what the code should do. The variables vary with time (t) and space (x). Am I right in saying that for each t the variables are evaluated at all x's? So I need a loop for the space variation inside a time loop?

I hope my question is clear. Any hints would be appreciated.

Thank you in advance.

panou · August 2, 2011, 07:29

Yes , you need a spatial loop inside time. The Runge-Kutta scheme as other which exist (simple euler..) march the each DOF(variable) at time. Therefore each variable (at nodes for the case of finite dif or element or volume at finite element or volume respectively) you must apply the time runge kutta scheme so that you find the all variables at next time.

In the case of explicit Runge-kutta scheme this is obvious. In implicit used with same manner.

Hooman · August 3, 2011, 08:58

Thanks. I had another question regarding Runge Kutta, I was looking at the Matlab help and the ODE solver in there. Looking at the first example:

function dy = rigid(t,y)
dy = zeros(3,1); % a column vector
dy(1) = y(2) * y(3);
dy(2) = -y(1) * y(3);
dy(3) = -0.51 * y(1) * y(2);
options = odeset('RelTol',1e-4,'AbsTol',[1e-4 1e-4 1e-5]);
[T,Y] = ode45(@rigid,[0 12],[0 1 1],options);

I have my equations almost in this form now, apart from the fact that y (or my variables) also vary with x. So I was wondering if each y i.e. y(1) , y(2) ... could be column vectors themselves containing the variations of y for each element or cell centre?

Thanks very much.

August 2, 2011, 06:28	Runge Kutta for unsteady flow	#1
Hooman Senior Member Join Date: Jun 2010 Posts: 111 Rep Power: 15	Hi, I am writing a code to solve an unsteady flow problem and I need to use the Runge Kutta methods for my time stepping scheme. I am having problems understanding what the code should do. The variables vary with time (t) and space (x). Am I right in saying that for each t the variables are evaluated at all x's? So I need a loop for the space variation inside a time loop? I hope my question is clear. Any hints would be appreciated. Thank you in advance.

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Flow meter Design	CD adapco Group Marketing	Siemens	3	June 21, 2011 08:33
Mass flow and U-Mom flow in CFX	Zhihua Xie	CFX	0	September 3, 2007 09:49
transform navier-stokes eq. to euler-eq.	pxyz	Main CFD Forum	37	July 7, 2006 08:42
2N Storage runge kutta	Vasanth	Main CFD Forum	3	August 2, 2005 10:44
Runge Kutta Method	CFDtoy	Main CFD Forum	12	May 22, 2005 13:00

August 2, 2011, 07:29		#2
panou New Member aaaaaaaaaaaaaa Join Date: Apr 2011 Posts: 23 Rep Power: 15	Yes , you need a spatial loop inside time. The Runge-Kutta scheme as other which exist (simple euler..) march the each DOF(variable) at time. Therefore each variable (at nodes for the case of finite dif or element or volume at finite element or volume respectively) you must apply the time runge kutta scheme so that you find the all variables at next time. In the case of explicit Runge-kutta scheme this is obvious. In implicit used with same manner.

August 3, 2011, 08:58		#3
Hooman Senior Member Join Date: Jun 2010 Posts: 111 Rep Power: 15	Thanks. I had another question regarding Runge Kutta, I was looking at the Matlab help and the ODE solver in there. Looking at the first example: function dy = rigid(t,y) dy = zeros(3,1); % a column vector dy(1) = y(2) * y(3); dy(2) = -y(1) * y(3); dy(3) = -0.51 * y(1) * y(2); options = odeset('RelTol',1e-4,'AbsTol',[1e-4 1e-4 1e-5]); [T,Y] = ode45(@rigid,[0 12],[0 1 1],options); I have my equations almost in this form now, apart from the fact that y (or my variables) also vary with x. So I was wondering if each y i.e. y(1) , y(2) ... could be column vectors themselves containing the variations of y for each element or cell centre? Thanks very much.