Time step size affects mesh deformation

[bobmyhill]

In tests/gmg_mesh_deform_topo.prm, there is a time-dependent function that controls deformation of the top boundary:

subsection Mesh deformation
  set Mesh deformation boundary indicators        = top: boundary function

  # The left and right boundary are allowed to move,
  # even though the Stokes velocity is zero along these boundaries.
  set Additional tangential mesh velocity boundary indicators = left,right

  subsection Boundary function
    set Variable names      = x,y,t
    set Function expression = 0;  if (x<0.5, 1e+2*sin(x*2*3.14159)*cos(t/0.001), 0)
  end
end

My assumption would be that at the fixed end time of this simulation, the top boundary should look the same, even if the velocity field inside the domain looks different. However, the mesh deformation appears to be dependent on the timestep size.

Edit: As @tjhei points out, the differences are because the function gives the boundary velocity, not position, and the velocity is treated as linear over a timestep, with the value taken from the start of the timestep. This can certainly be improved in a number of ways - for example, if the function could be given as displacement instead, the effective velocity over a tmestep could be calculated to give the exact deformation of the mesh.

t(6) = 0.0024, max timestep=0.0012

t(10) = 0.0024, max timestep=0.0006

t(14) = 0.0024, max timestep=0.0003

t(26) = 0.0024, max timestep=0.0001

The other timesteps are all shifted as well (i.e., this isn't just a problem with the last timestep).

These test results are using the version of the code in #6829 , but main branch shows the same behaviour.

[bobmyhill]

This feature is present using both AMG and GMG.

[tjhei]

I think we prescribe a velocity and not the displacement, right? I would expect it to converge to the same solution for dt going to zero.

[bobmyhill]

Ok, that's good. Should the velocity we select be time centered (either 1 sample or 2 point average)? I think at the moment it is taken from the beginning of the time step.

[tjhei]

the differences are because the function gives the boundary velocity, not position, and the velocity is treated as linear over a timestep,

Should the velocity we select be time centered (either 1 sample or 2 point average)? I think at the moment it is taken from the beginning of the time step.

That is an interesting question and pertains to all mesh deformation plugins. This is a question on how exactly the splitting scheme is defined. Maybe this plugin should convert the user provided displacement into a velocity?

@bangerth @gassmoeller