For simulation of free surface flow over variable depth in coastal engineering a first Boussinesq model was derived by Peregrine (1976). This model was restricted to accurate simulation in shallow water. The equations was later extended for the adaption to deeper waters. This led to the development of several modified forms of Boussinesq-type equations, e.g. Madsen et al. (1992) and Nwogu (1993) and later Madsen et al. (2003). The OceanWave3D model addresses the limitations in practical application ranges of Boussinesq-type models and is based on the original work by Li and Fleming (1997) and has been extended and improved by Bingham Et al. (2007), Engsig-Karup et al. (2008), Engsig-Karup et al. (2011).

Our work focuses on developing in proofs-of-concept robust and fast state-of-the-art numerical tools for nonlinear free-surface water waves useful for application in coastal and offshore engineering. The OceanWave3D model currently exists in an optimized CPU version based on Fortran 90 code and in a massively parallel GPU version developed in C , cf. Engsig-Karup et al. (2011). The two figures below highlight the scalability and performance properties of the OceanWave3D model. The GPU version of the model can currently solve problems with close to 100.000.000 degrees of freedom in the volumetric mesh for the laplace problem in single precision and using 4GB RAM and process one iteration of the efficient iterative solver in less than 1 second on a Fermi GPU. The massively parallel and naive Fermi implementation has been found to be at least x42 faster (only measured at close to 3 million degrees of freedom) than the single-core CPU version in double precision in a naive implementation done using CUDA. These results have been achieved by complete redesign of the iterative solver, efficient memory access patterns and using a GPU with high onchip bandwidth.

Scaling and Performance results achieved in collaboration with Morten Gorm Madsen.

Selected project publications and presentations

  1. H. B. Bingham and H. Zhang. On the accuracy of finite-difference solutions for nonlinear water waves. J. Engng. Math., 58:211-228, 2007.
  2. A. P. Engsig-Karup, H. B. Bingham and O. Lindberg. An efficient flexible-order model for 3D nonlinear water waves. December, 2008. Journal of computational physics, 228, pp. 2100--2118.
  3. A. P. Engsig-Karup, H. B. Bingham and O. Lindberg. A high-order finite difference method for nonlinear wave-structure interaction. In 22nd Intl. Wrkshp. Water Waves and Floating Bodies, Croatia, 2007.
  4. H. B. Bingham, A. P. Engsig-Karup, and O. Lindberg. Multigrid preconditioning for efficient solution of the 3D Laplace problem for wave-body interaction. In 23rd Intl. Wrkshp. Water Waves and Floating Bodies, Jeju Island, South Korea, 2008.
  5. Bingham, H. B. and Engsig-Karup, A. P. Boundary-fitted solutions for 3D nonlinear water wave-structure interaction. In 24th Intl. Wrkshp. Water Waves and Floating Bodies, April, Russia, 2009.
  6. Engsig-Karup, A. P., Ducrozet, G., Bingham, H. B. and Dammann, B. 2009 Toward a scalable flexible-order model for 3D nonlinear water waves, International Conference On Spectral and High Order Methods, Norwegian University of Science and Technology, Trondheim, Norway, 2009.
  7. Engsig-Karup, A. P., Madsen, M. G. and Glimberg, S. L. 2011 A massively parallel GPU-accelerated model for analysis of fully nonlinear free surface waves. Accepted for publication in International Journal of Numerical Methods in Fluids.