Solving a system of nonlinear, discretized partial derivatives (mass balances) using FSOLVE
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Dear MATLAB community,
I have a few questions regarding the topic that I hope some of you could help me on. The problem to solve is as follows:
For my research, I want to numerically analyze a system of stationary, 2D mass balances (electrochemistry) which is made up of partial derivatives and boundary conditions. I have by now found no built-in MATLAB commands are suitable (the format of the equations are not suitable for the PDE-tool, and pdepe is for transient systems only). Now I intend to discretize all equations using the command gradient, and solve the resulting system of algebraic, nonlinear equations using FSOLVE. Overall, 12 unknown variables (arrays) are to be solved by a system of 21 equations & constraints. I have embedded the relevant pieces of code.
My questions are:
- Whenever I want to run the m.file for testing, the following error shows up: Undefined function or variable 'x'. Why? I've seen numerous examples on MATLAB where multiple variables are defined as a = x(1), b = x(2) after which they are used in an equation F. This is the code:
function EQNS = nernst_planck_ae(x)
% Define independent variables in terms of x
c = x(1);
d = x(2);
cTm = x(3);
etc. until x(12).
- In essence, I want the solver to give arrays as an output (the variable concentration along the x-axis amongst others). However, when giving the equations, which are also array valued, the following error introduces itself: In an assignment A(:) = B, the number of elements in A and B must be the same. I understand this, but how can I work around this? The relevant code of line is:
EQNS(4) = - J_ch - D_m * cTm(end) .* gradient(phi_iem)
- Although the command gradient allows me to take the central difference of the derivative for any array/matrix, I also want to implement some boundary constraints for the solver. More specifically, I want for f(x), df/fx at x = 0 to be 0. How do I implement such a constraint in the equations? Is the following line of code in the correct format?:
% Neumman conditions for the dcdx & J_ions
dcdx = gradient(c);
dddx = gradient(d);
EQNS(10) = dcdx(1) == 0;
EQNS(11) = dcdx(end) == -J_ions/(2*D_s);
EQNS(12) = dddx(1) == 0;
EQNS(13) = dddx(end) == -J_ions/(2*D_s);
The EQNS are objective functions for fsolve.
I realize this is quite some text, though I tried to ask as concise as possible without letting out relevant information. I can upload the entire script if that helps. Also, I can reference the academic paper if needed.
In any case, thanks a lot for the effort in advance,
Jair
0 comentarios
Respuestas (1)
Torsten
el 11 de Abr. de 2017
First question:
From what you post we can not tell the reason for the error message. Maybe your call to "fsolve" will tell us more.
Second question:
EQN(4) is a scalar whereas - J_ch - D_m * cTm(end) .* gradient(phi_iem) seems to be a vector. So setting them equal is not possible.
You will have to reserve one equation for each component of the vector.
Third question:
EQNS(10) = dcdx(1);
EQNS(11) = dcdx(end) - (-J_ions/(2*D_s));
EQNS(12) = dddx(1) ;
EQNS(13) = dddx(end) - (-J_ions/(2*D_s));
Best wishes
Torsten.
6 comentarios
Torsten
el 12 de Abr. de 2017
count1 = length(array1)
for i=1:count1
EQNS(8+i)=array1(i);
end
count2 = length(array2)
for i=1:count2
EQNS(8+count1+i)=array2(i)
end
...
Best wishes
Torsten.
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