Is it possible to impose only a left boundary condition?

[HannoSpreeuw]

I am trying to mimic work from a paper where only a left boundary condition is specified for a 1D depth grid, i.e. only a condition at the surface is specified for two particular PDEs and not at the bottom.

Btw, the other three PDEs - this is about solving a set of five coupled PDEs - do have boundary conditions specified at the bottom.

Is it possible to do this in py-pde?
It seems you always have to specify both a left and right boundary condition.

[david-zwicker]

You are correct that py-pde always requires boundary conditions on both sides since this was most natural for the use cases for which we developed the package. However, if you use one-sided approximations in the finite-difference scheme (e.g., forward or backward derivatives), one of the boundary condition will not be used, so you can set it to an arbitrary value. It might be a good idea to use absurdly large values or even np.nan to ensure that the boundary condition does not spill into the simulation.

[david-zwicker]

No currently, there is no way to do this. I guess we could implement a no-op boundary condition, but I still don't really see the use case. If you only use one-sided derivatives, you know that one of the boundary conditions will not be used and so the chosen condition will not affect the simulation.

[HannoSpreeuw]

Yes, I understand, but a one-sided derivative is only first order accurate.

[NiklasHohmann]

What about the case of a linear transport equation, whose solution is a wave propagating into one direction? Analytically there should only be boundary condition specified on the upwind side. I know that numerically this should be approached with an upwind(-biased) scheme, but for any scheme that uses information from the downwind side, the bc will spill into the integration.

[david-zwicker]

I agree with your statements. What is your concrete question?

[NiklasHohmann]

I just wanted to make sure I understood correctly, thanks for your answer!

[aminih01]

It might not be relevant, but how can we separately define left/right boundaries for different fields in a coupled problem? I am trying to set different boundary types by saying bc_x_left = {"value" :0} for one field, but I don't know how to prevent that from being applied to both fields as I need bc_x_left to be set to derivative for my second field.

[david-zwicker]

This is certainly possible. If you use the PDE class, you need to specify boundary conditions using the bc_ops argument; see the documentation.