Transcript Free surface flows in Code Saturne

Free surface flows in Code Saturne
Results 21/09/2009
Olivier Cozzi
Equations of the problem
Mass Conservation Law
Momentum Conservation Law
Scalar Conservation Law
+
Space Conservation Law  respected when the mesh just moves vertically
+
Kinetic boundary condition 
on the free surface, that is to
say:
Dynamic boundary condition 
(because, on the free surface, sheer stress, normal stress, and effect of the surface
tension can be neglected)
Test cases
From “Application du prototype de module ALE du solveur commun a des cas de surface
libre” (H2000H400170), by F. Archambeau
EDF : closed tank (and solitary wave, almost ready...)
Wave amplitude A = 2m
Wavelength λ = 0.5L
Mesh: 105*20*1
Initial shape and 2nd order theoretical solution
(Chabert d'Hieres formula):
Airy's formula:
 T = 6s period in this case
Computation of the free surface
ALE method used to move the mesh verticaly, according
to the free surface speeds calculated by:
 1) Non iterative explicit Euler scheme
 2) Non iterative RK4 scheme
 3) Iterative explicit Euler scheme
 4) Iterative Crank-Nicolson scheme
Non iterative explicit Euler scheme
On the free surface, the mesh vertical speeds at time step n+1, i.e. wn+1 are
calculated with the values of time step n
Results:
Increasing waveheight
Real period bigger than
theoretical one
Non iterative RK4 scheme
On the free surface, the mesh vertical speeds at time step n+1, i.e. wn+1 are
calculated with the values of time step n and predictions
where
Results better than Euler
time scheme but still:
Increasing waveheight
Real period bigger than
theoretical one
Iterative explicit Euler scheme
On the free surface, the mesh vertical speeds at time step n+1, i.e. wn+1 are calculated with
iteration moving the mesh before solving the Navier-Stokes equations
Start of time step
tn+1
Moving of the
mesh according to
new wn+1 values
Solution of NS
equations
Calculation of
wn+1 from values
of time step tn
Calculation of
wn+1 thanks to
new values
Etc…
Moving of the
mesh according to
wn+1 values
Solution of NS
equations
Final wn+1 values
Iterative explicit Euler scheme
In the end, the iterative scheme converge to a final solution of wn+1, which respects
the Navier Stokes equations in the new geometry
Results different:
Damping of waveheight
Real period bigger than
theoretical one
Iterative Crank-Nicolson scheme
where n+1* values are calculated iteratively and
converge to final values, and so to a final
solution of wn+1
Results better than Euler
time scheme:
Damping of waveheight
reduced
Real period bigger than
theoretical one
And now ?
New test case of the solitary wave
Verification of the mass flow values
Iterative RK4 scheme ?
Any ideas ?
…