Coupled boundary conditions


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11 weeks ago by
Dear Fenics community,

I have recently been working on the implementation of the linearized Euler equations with a discontinuous Galerkin discretization in Fenics. The unknowns are the perturbations in density  $\rho$ρ , the velocity vector u  and the pressure p. For an isothermal wall, the appropriate boundary condition for this kind of problem would read:

$\frac{\rho}{\rho_0}=\frac{p}{p_0}$ρρ0 =pp0

Where  $\rho_0$ρ0 and  $p_0$p0 can be treated as constants for the sake of clarity. This is what I would call a coupled boundary condition, because the value of one solution variable depends on the value of another unknown solution variable.

Is there a way to implement such coupled boundary conditions in Fenics? I was thinking, maybe via Lagrange multipliers?

Thank you in advance,
Max
Community: FEniCS Project
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