Author |
Message |
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 |
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 |
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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