[liadpaskin]

Hello,
My name is Liad. I´m a naval architecture and marine engineering student, and a CFD researcher from Brazil.
Right now, we are developing a finite element software for solving Navier Stokes equations. I had a problem trying to develop a wave making model, and so I’ve modeled the same problem in CFX to compare the results. That´s when I found a very strange behavior from CFX v14.

The geometry consists of a rectangular area (1 m x 4 m), which is entirely filled with a homogeneous fluid. Since this should be a two-dimensional simulation, the rectangle was extruded for the size of an element and symmetry boundary conditions were imposed on those faces. There is no free surface model in this simulation; the free surface is obtained imposing null static pressure on the top edge. The wave should be sufficiently small to match the Airy`s wave simplifications, one of which states that the free surface is undisturbed. So, on the inlet we impose the theory´s velocities profile, i.e.:

Vx = ζ w * cosh⁡[k(z+d)] * cos⁡(wt-kx) / sinh⁡(kd)
Vz = -ζ w * sinh⁡[k(z+d)] * sin⁡(wt-kx) / sinh⁡(kd)

On the bottom is imposed a no-slip, no-penetration boundary condition and on the outlet a free-slip, no-penetration boundary condition.

The strange behavior observed is related to the “time initialization” option on the “transient scheme: Second Order Backward Euler” chosen. If “automatic” is picked, extrapolation is used whenever the solver finds convenient and the results are satisfactory: wave propagates as it should for time steps of 10^-2 s. If “previous timestep” is picked instead, wave length is highly increased (twice the size of the domain) so it does not propagates as it should, even for a time step of 10^-6 s.

Since CFX`s documentation says almost nothing about this extrapolation method, I’ve made some research and found an extrapolation method called Richardson Extrapolation that might be used together with the Backward Euler transient scheme as seen in the reference: http://www.cs.elte.hu/~faragois/pape...al_version.pdf.

Anyway, I don´t understand how this extrapolation method can converge a simulation that does not converge for MUCH smaller time steps. Does anyone have an idea of what´s happening here?

Thanks a lot for the patience on reading this question. There follows some images and the general settings resume as the "CFX Command Language for Run".

Velocities vector solution for “automatic” time step initialization with 10^-2 seconds time steps:
https://drive.google.com/file/d/0Bw-...ew?usp=sharing

Velocities vector solution for “previous” time step initialization with 10^-6 seconds time steps:
https://drive.google.com/file/d/0Bw-...ew?usp=sharing

Mesh used for both simulations (A mesh sensitivity analysis has already been made, concluding this mesh is fine).
https://drive.google.com/file/d/0Bw-...ew?usp=sharing

CFX Command Language for Run (This if for the “automatic” time step initialization, but the other one is exactly the same, except for the “previous” time step initialization chosen and the timestep size of 10^-6):
https://drive.google.com/file/d/0Bw-...ew?usp=sharing

With regards,
Liad.