Solving 16 PDE's at once with COMSOL. (source terms are unknown)

[iamkratos]

Hi all:

The solution to my problem requires solving 16 PDE's at once. This shouldn't be hard - but you'll know what my problem is in a minute. The 16 PDE's :

∂/∂t (I⁺_i) + Kn*μ_i ∂/∂x (I⁺_i) + I⁺_i = I₀
∂/∂t (I^-_i) + Kn*μ_i ∂/∂x (I^-_i) + I^-_i = I₀
for i's ranging from 1 to 8.

That comes up to 16 PDE's.

My domain is x ∊ [0,1]

I have numerical values for all the coefficients except I₀ .
Also I have Dirichlet Boundary Conditions for I⁺_i at x=0 and I^-_i at x=1 (for all 8 of each of them)

The only problem that I do have, is that my source term I₀ is to be defined as:

I₀ = 0.5 * [ Σ w_i.I⁺_i + Σ w_i.I^-_i ] (summations are for i=1 to 8)

I also know the values for w_i . (which are different for each i)

How can I solve this problem with Comsol??
Any Suggestions?

Thank you.

 

[mmwave]

Hi there,

Solving 16 PDEs at once can definitely be a challenging task, but it is not impossible. One suggestion would be to use Comsol's multiphysics capabilities, which allow you to solve multiple PDEs simultaneously. In this case, you can set up a multiphysics model with the 16 PDEs and include the source term I0 as a function of the other variables. You can also use Comsol's built-in functions to define the source term based on the given values of wi. Additionally, you can use Comsol's built-in boundary conditions to specify the Dirichlet boundary conditions for I+i and I-i at x=0 and x=1, respectively.

Another suggestion would be to use Comsol's optimization capabilities to find the values of I0 that satisfy the given equation. You can set up an optimization study with the 16 PDEs and define the objective function as the difference between the left and right sides of the equation, with I0 as the variable to be optimized. This way, Comsol will automatically adjust the value of I0 to satisfy the equation.

I hope these suggestions help and good luck with your problem!