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Frank Hartly (frank_h)
New member
Username: frank_h

Post Number: 1
Registered: 12-2009
Posted on Wednesday, December 09, 2009 - 02:56 am:   

Hello,

Thanks in advance for your advice and assistance.

I'm having difficulty trying to setup a 1D coupled system.

My domain spans time 0<t<100 and 1-dimension 0<x<300.

I have 1 PDE, 1 ODE, 2 integrals over x at t, and 1 alg. exn:

variables

Q { Q is a function of x and t }
U { U is a function of t }
T { single-integral of Q(x,t)dx from 0<x<300 at t }
G { single-integral of x*Q(x,t)dx from 0<x<300 at t }
S { S is a function of t }

equations

Q: dt(Q) = S*(1-T)*exp(-x) + (U/T)*dx(Q) {PDE}
U: dt(U) = (T-U)+U*F/T {ODE}
T: <------ help no idea how to define this yet {integral}
G: <------ help no idea how to define this yet {integral}
S: (1-S)=T*((S*U/T)-1)/(S^3) {algebraic}

I do not know how to handle equations for T and G, specifying a single-integral over x @ t. T and G are single-integrals for Q(x,t)dx or x*Q(x,t)dx from x=0 to x=300 with t fixed at each time point. Also, I'm unclear whether I need to define some of these variables as global variables--they evolve only with time but include the spatial integrals from T and G.

All comments greatly appreciated.

Thanks again!

Frank
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Robert G. Nelson (rgnelson)
Moderator
Username: rgnelson

Post Number: 1310
Registered: 06-2003
Posted on Wednesday, December 09, 2009 - 03:05 pm:   

If T = integral(Q(x,t)*dx) from 0 to X, then you can define the equation for T(x) as dx(T)=Q(x,t) and VAL(T,300) will be the value you want. You will need to set VALUE(T)=0 along x=0.

Define a similar equation for G.

In version 6 you can define the T and G equations in a THEN clause to avoid possible troubles with simultaneous solution of all variables.

S does not want to be defined as a VARIABLE, as it is simply an algebraic combination of U and T(300).
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Frank Hartly (frank_h)
New member
Username: frank_h

Post Number: 2
Registered: 12-2009
Posted on Wednesday, December 09, 2009 - 06:53 pm:   

Thank you.

I tried to implement this as follows below.

I keep getting the error 'Timestep has fallen below 1e-009 of starting value! You may have a temporal discontinuity in parameters'

Any ideas on what I'm doing incorrectly?

I tried removing and uncoupling the exn for S (the algebraic one) and also setting boundary values for R and G--to no success. I also changed the time step significantly with no success.

I would greatly, greatly appreciate any advice.

title
"force system"

select
nodelimit=100
coordinates
cartesian1

variables
Q (threshold=4) { Q is a function of x and t }
U (threshold=2000) { U is a function of t }
R (threshold=3500) { integral Q(x,t)dx from 0<x<100 at t }
G (threshold=125) { integral x*Q(x,t)dx from 0<x<100 at t }
S (threshold=2000) { S is a function of t }

definitions
C1 = 8.79646e-5
C2 = 4
C3 = 24600
C4 = 3.5
C5 = 0.13
C6 = 54
C7 = 1000
C8 = 48000
C9 = 0.08

equations
Q: dt(Q) = C1*S*(C2-VAL(R,100)/C3)*exp(-x/30)+C4*(U/VAL(R,100))*dx(Q)
U: dt(U) = C5*(VAL(R,100)-U) + C4*U*VAL(G,100)/VAL(R,100)
R: dx(R) = x*Q
G: dx(G) = Q
S: C6*(1-S/C7)=C8*VAL(R,100)*((C9*S*U/VAL(R,100))-1)/(S^3)

initial value
Q = 0
U = 0
R = 0
G = 0
S = 3000

boundaries
region 1
start(0)
line to (100)

time 0 to 100 by 0.01

end
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Marek Nelson (mgnelson)
Moderator
Username: mgnelson

Post Number: 169
Registered: 07-2007
Posted on Sunday, December 20, 2009 - 07:09 pm:   

There are several discussions about what this error report means and what to do about it:

http://www.pdesolutions.com/discus/messages/4/11913.html
http://www.pdesolutions.com/discus/messages/4/1608.html
http://www.pdesolutions.com/discus/messages/4/1552.html
http://www.pdesolutions.com/discus/messages/4/748.html

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