Jie,
I am solving time-dependent Navier-Stokes equations with varying
Dirichlet boundary conditions. Although I have read the "Constraints on
degrees of freedom" for many times, I am still not sure what the best
way to implement changing boundary conditions is. My time scheme is
fully implicit, so there is an outer time loop, plus an inner Newton
iteration, and I am solving for the* newton_increment*. My code works
fine when the Dirichlet boundary conditions are not changing in time.
The way I implemented it is that I have two ConstraintMatrix, one for
nonzero_constraints and one for zero_constraints. At the *first* Newton
iteration in the *first* time step, I apply nonzero_constraint in the
assembly process using distribute_local_to_global and after solving it
call distribute to recover the constrained values. At all the following
iterations, use zero_constraints to assemble. This gives me the correct
solution because I start with v = 0, so the first newton iteration will
correctly set the boundary values, and after that I do want the
newton_increment at the Dirichlet boundary to be 0 since the boundary
condition do not change in time.
My first question is, if the boundary conditions are time-dependent,
then I would have to use nonzero constraints at the *first* Newton
iteration in *every* time step, right?
Correct.
In addition, the value of those
constraints should *not* be the fluid velocity that I want, instead, it
should be the velocity *delta* between time steps, because the degrees
of freedom to be solved are the velocity increment, not the velocity
itself, right?
Yes, also correct. But you could always rewrite things in such a way
that in the first Newton iteration in each time step, you solve for the
velocity and not the increment. In that case, the boundary values are
the correct velocity at the boundary, not just the increment from the
previous time step.
This issue gets more complicated when not only the constrained values
change in time, but also the dofs to be constrained also change in time.
This issue arises in my fluid-structure interaction application with
immersed method: I need to force the fluid velocity in certain area to
be the same as the solid velocity, and the solid location always
changes. Therefore, I want to apply totally different Dirichlet boundary
conditions at different time steps. This means I have to 1. recreate the
ConstraintMatrix 2. recreate the sparsity pattern, which is related to
the constraints, and reinitialize the system matrix, solution vectors
etc. Is this reasonable?
Yes. But if you do not eliminate constrained degrees of freedom from the
sparsity pattern (there is a function argument to
make_sparsity_pattern()), then you also don't need to recreate the
sparsity pattern in each time step and don't need to reinitialize the
matrix -- you just need to set it to zero.
Best
W.
--
------------------------------------------------------------------------
Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
--
The deal.II project is located at http://www.dealii.org/
For mailing list/forum options, see
https://groups.google.com/d/forum/dealii?hl=en
---
You received this message because you are subscribed to the Google Groups "deal.II User Group" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
For more options, visit https://groups.google.com/d/optout.
