Discussion Forum

Posted: 1 decade ago 27 janv. 2010, 04:20 UTC−5

Hi Sorry but I have some problems to understand you, could you be somewhat more explicit about your variables: I understand that you have : space variables and time: x, t dependent variables : a, c, s all functions of (x,t) constants: k1, k2, d1, d2, D1, D2, D3, Ta, n, m to use COMSOL notations: da/dt = at, da/dx = ax, d^2s/dx^2 = sxx, etc. You rewrite your expression to the type "something = 0" to be plug-in compatible with COMSOL Now remains the "ax(dotprduct)cx" but if a=a(x,t) and the same for c, then isn't the "dotproduct" simply the scalar product ? If not isnt it just to write it out related to the variables I may have missed ? I'm missing something essential here I believe ;) Good luck Ivar

Posted: 1 decade ago 27 janv. 2010, 15:54 UTC−5

Thank you so much for your response. Your assumptions are all correct except T is a constant and a is the depedent variable. The term here in question is the dot product between the gradient of a and the gradient of c with D2/c being the coefficient. So, yes, this does give you a scalar, but this scalar is dependent on both space (since it depends on the gradients) and time (since both variables vary with time). My problem is that I do not know if there is a built-in module of this PDE type or if I need to do it from scratch. If I do it from scratch, I am not sure the proper notation as I have not seen anything like this in the manual. Any help would be greatly appreciated, Stephen

Posted: 1 decade ago 27 janv. 2010, 16:44 UTC−5

Hi great then the "Ta" is a typo and should be read "T*a" with "T" a constant. so the three equations become: at=k1*(1/(1+s^m))*(a^n/(1+a^n))-a-d1/(1+T*a)*a*(1-c)+D1/c*ax*cx st=k2*c*(a^n/(1+a^n))-d2*s*D2*sxx ct=d1/(1+T*a)*c*(1-c)+D3*cxx space variables: x,t dependent variables: a,s,c k1,d1,T,D1,k2,d2,D2,D3,m,n all constants and with implicit: a=a(x,t) at=da(x,t)/dt ax=da(x,t)/dx ... s=s(x,t) st=ds(x,t)/dt sx=ds(x,t)/dx sxx=d^2s(x,t)/dx^2 ... c=c(x,t) ct=dc(x,t)/dt cx=dc(x,t)/dx cxx=d^2c(x,t)/dx^2 ... So far I understand it, one must now reorder the equations with some algebra to get them to fit the canonical coefficient form of COMSOL, unfortunately I have not been playing that much with arbitrary PDEs and COMSOL so I would need some time to sort it out (if possible), and it's getting late form me just now. Furthermore, I still havnt catched the reason why the dotproduct, in this case makes it so much worse (I find it awfull enough as is, OK ;) In anycase I would typically start to read through my copy of : http://www.comsol.com/academic/books/mmwfem/ to be inspired. There are some good exercices therein starting from the PDE's and reordering them to be COMSOL compliant, so I can only propose that you borrow this book, or perhaps you have it already ? Good luck Ivar

Posted: 1 decade ago 27 janv. 2010, 16:55 UTC−5

Thank you so much for your help. One small thing: st=k2*c*(a^n/(1+a^n))-d2*s*D2*sxx should be st=k2*c*(a^n/(1+a^n))-d2*s+D2*sxx (maybe it was a typo). Anyways, the book you mentioned: is this available for free online? Thank you again for your help, and I hope to hear from you regarding getting the equations in the canonical coefficient form of COMSOL. Stephen [QUOTE] Hi great then the "Ta" is a typo and should be read "T*a" with "T" a constant. so the three equations become: at=k1*(1/(1+s^m))*(a^n/(1+a^n))-a-d1/(1+T*a)*a*(1-c)+D1/c*ax*cx st=k2*c*(a^n/(1+a^n))-d2*s*D2*sxx ct=d1/(1+T*a)*c*(1-c)+D3*cxx space variables: x,t dependent variables: a,s,c k1,d1,T,D1,k2,d2,D2,D3,m,n all constants and with implicit: a=a(x,t) at=da(x,t)/dt ax=da(x,t)/dx ... s=s(x,t) st=ds(x,t)/dt sx=ds(x,t)/dx sxx=d^2s(x,t)/dx^2 ... c=c(x,t) ct=dc(x,t)/dt cx=dc(x,t)/dx cxx=d^2c(x,t)/dx^2 ... So far I understand it, one must now reorder the equations with some algebra to get them to fit the canonical coefficient form of COMSOL, unfortunately I have not been playing that much with arbitrary PDEs and COMSOL so I would need some time to sort it out (if possible), and it's getting late form me just now. Furthermore, I still havnt catched the reason why the dotproduct, in this case makes it so much worse (I find it awfull enough as is, OK ;) In anycase I would typically start to read through my copy of : http://www.comsol.com/academic/books/mmwfem/ to be inspired. There are some good exercices therein starting from the PDE's and reordering them to be COMSOL compliant, so I can only propose that you borrow this book, or perhaps you have it already ? Good luck Ivar [/QUOTE]

Posted: 1 decade ago 4 févr. 2010, 11:27 UTC−5

I was wondering if you had any additional thoughts on this. We're really struggling trying to find a form which COMSOL can handle. Stephen