1. SPH weekly meeting Free surface flows in Code Saturne Results 23/11/2009 Olivier Cozzi

2. Presentation of Code_Saturne…  CFD code based on a co-located Finite Volume approach  Parallel code coupling capabilities … and its ALE module  New boundary conditions for the boundary faces  Diffusion equation solver to know the mesh velocities for all the internal and boundary faces  Move of the mesh at the end of the time step

3. Equations of the problem  Mass Conservation Law  Momentum Conservation Law  Scalar Conservation Law +  Space Conservation Law  respected in C_S 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)

4.  Dynamic boundary condition  use of the usual usclim.F routine: on the free surface  Kinetic boundary condition  use of the special ALE usalcl.F routine: on the free surface Free-surface module within C-S

5. End of t n, save of fluid values Start of t n+1 Use of last mfs n for v b NS solution, new mfs n+1 Load of t n values, except for mfs Use of last mfs n+1 for v b Etc., until convergence! Move of the free surface End of t n+1, save of fluid values Free-surface module within C-S

6.  Variable of activation  Choice of convergence accuracy and max iteration number  Selection of time scheme (second order Crank-Nicolson method, or first order implicit Euler method)  Parallel computation still available Free-surface module within C-S

7.  Wave amplitude A = 1m  Wavelength λ = 0.5L  Mesh: 105*20*1  Initial shape and 2 nd order theoretical solution (Chabert d'Hieres formula):  Airy's formula:  T = 9,8s period in this case Results: 1. Standing wave

9. 100 time step of 100ms per period, ~100 cells per spatial period, courant max : ~0.6, 16 000 time steps Free surface height at the left side wall as function of time Remarks: - Good height

10. 100 time step of 100ms per period, ~100 cells per spatial period, courant max : ~0.6, 16 000 time steps Free surface height at the left side wall as function of time Remarks: - Good height - Time period overestimated 9,84s > T th = 9,78 s Results: 1. Standing wave

11. 100 time step of 100ms per period, ~100 cells per spatial period, courant max : ~0.6, 16 000 time steps Global relative volume as function of time Remarks: - Loss of volume… -0,018% per hour Results: 1. Standing wave

12. 100 time step of 100ms per period, ~100 cells per spatial period, courant max : ~0.6, 16 000 time steps Global relative energy as function of time Remarks: - Loss of energy… -0,05% per hour Results: 1. Standing wave

13.  Wave amplitude A = 2m  Mesh: 400*15*1Gaussian shape: Results: 2. Solitary wave

15. Calculation of 2000 time step of 50ms, courant max : ~0.1 Maximal free surface height as function of time Remarks: - Good height - Solitary wave speed slightly underestimated Results: 2. Solitary wave

16. Calculation of 2000 time step of 50ms, courant max : ~0.1 Global relative volume as function of time Remarks: - Loss of volume… -0,014% per hour Results: 2. Solitary wave

17. Test case from “The breaking and non-breaking wave resistance of a two- dimensional hydrofoil” by JAMES H. DUNCAN Steady test case Results: 3. Naca hydrofoil

19. Experimental surface height (cm) as function of horizontal distance (cm) My results… so far Results: 3. Naca hydrofoil

20. Test case from “Nonlinear forces on a horizontal cylinder beneath waves”, by JOHN R. CHAPLIN Results: 4. Submerged cylinder

21.  Energy and volume losses  ALE module  negative volume… calculation aborted  Problem of period for the standing wave (STREAM has the right period!) Problems to be solved  Any comments or ideas about my work ?!?