Problem with boundary conditions that change over time or other factors

[masuda-kazuki]

Hello,

I am confused about setting constraints, particularly when it comes to problems where boundary conditions change over time or other factors. What would be a smart way to write the code for such problems?

Here’s an example (omitting part of the equation for brevity):

I want to solve the following problem:

Input: x, z, t
Output: η, φ

Equations (where h is an arbitrary constant):
φ__z = 0 ; z = -h
φ__z - η__t - φ__x * η__x ; z = η

As mentioned earlier, the output (η) is used as a boundary condition for the input variable (z).

(Just to clarify, since I haven’t provided all the equations, it’s not possible to solve the problem with just this information. The example you provided is used for solving problems related to Stokes wave theory.)

Thank you in advance.

[ngeneva]

Hi @masuda-kazuki

Thanks for your interest in Modulus!
If I understood your problem correctly, I would parameterize the time dimension. We have an example of a 1D wave equation that may help with this. (see the forum post also for some info)

How to parameterize coefficients of PDEs?

Hi @cxi1 You can parameterize a PDE using a SymPy Symbol. While maybe not obvious, the 1D wave equation example can show how to go about this (here t is the parameterized variable). You can take these ideas and extend them to coefficients of other PDEs. Note inside the Wave equation we have: def __init__(self, c=1.0): # coordinates x = Symbol("x") # time t = Symbol("t") # make input variables input_variables = {"x": x, "t": t} ..…