SPH weekly meeting Free surface flows in Code Saturne Results 23/11/2009 Olivier Cozzi
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
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)
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
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
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
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
100 time step of 100ms per period, ~100 cells per spatial period, courant max : ~0.6, time steps Free surface height at the left side wall as function of time Remarks: - Good height
100 time step of 100ms per period, ~100 cells per spatial period, courant max : ~0.6, 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
100 time step of 100ms per period, ~100 cells per spatial period, courant max : ~0.6, time steps Global relative volume as function of time Remarks: - Loss of volume… -0,018% per hour Results: 1. Standing wave
100 time step of 100ms per period, ~100 cells per spatial period, courant max : ~0.6, time steps Global relative energy as function of time Remarks: - Loss of energy… -0,05% per hour Results: 1. Standing wave
Wave amplitude A = 2m Mesh: 400*15*1Gaussian shape: Results: 2. Solitary wave
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
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
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
Experimental surface height (cm) as function of horizontal distance (cm) My results… so far Results: 3. Naca hydrofoil
Test case from “Nonlinear forces on a horizontal cylinder beneath waves”, by JOHN R. CHAPLIN Results: 4. Submerged cylinder
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 ?!?