Vijaya Ambati
Simulations
All files are in (avi) format.Linear free surface waves
Test case: Linear Harmonic Waves in a wave basin with periodic boundaries.
Numerical Scheme: Space-time discontinuous Galerkin Scheme.
Description: Space-time discontinuous Galerkin Scheme accommodates deforming grids which has advantage to model nonlinear waves satisfying the geometric conservation laws to the discrete level. To test the space-time DG scheme on deforming grid, we randomly move the mesh nodes w.r.t time and simulate the linear free surface waves which propagate undisturbed by the mesh movement. This demonstrates that the method is conservative on deforming grids and gives confidence to simulate nonlinear free surface waves. Furthermore, it is a good nontrivial test case for testing the numerical scheme for deforming grids.
Nonlinear free surface waves
Test case: Standing waves in a wave basin with solid boundaries.
Numerical Scheme: Space-time discontinuous Galerkin Scheme for nonlinear free surface waves.
Description: Standing waves are exact solutions of linear free surface water wave equations. However, they can be tested with the nonlinear numerical scheme from low to high amplitude. Under low amplitudes, the numerical results must match with exact solutions and at high amplitudes, some nonlinear behavior must be seen.
Standing waves for one time period
Standing waves for ten time periods
Test case: Linear harmonic waves with periodic boundaries.
Numerical Scheme: Space-time discontinuous Galerkin Scheme for nonlinear free surface waves.
Description: Linear harmonic waves are exact solutions of linear free surface water wave equations. However, they can be tested with the nonlinear numerical scheme from low to high amplitude. Under low amplitudes, the numerical results must match with exact solutions and at high amplitudes, some nonlinear behavior must be seen. We actually observe steepening of waves due to nonlinearities. As the waves steepen, we stop our numerical algorithm as it is not designed to handle overturning waves.
- Simulation: Potential vorticity "Omega" and Stream function "Psi".
- Lab: Hybrid Rossby-shelf mode travelling through a cylindrical laboratory ocean.
- See Onno Bokhove's home page.
- Flow over a conical hump: Potential vorticity
- Flow over a Gaussian hump: Potential vorticity
- Breaking harmonic waves in a rectangular domain: Breaking waves, Potential vorticity
- Poincare waves in a circular domain
(low amplitude).
- Kelvin waves in a circular domain
(low amplitude).
- Poincare waves (two harmonic modes) simulated using hpGEM. (low amplitude, high amplitude)
- Waves generated by a harmonic wave maker: (3D simulation: water depth) and (2D simulation: contour of water depth).
- Plane waves obliquely incidented on beach: (3D Simulation).
- Run-up and back wash on a wave guide: (3D) and (Velocity field).