OceanWave3D - Fully Nonlinear and Dispersive free surface wave modelling


Research, improve and develop robust, fast and accurate methodologies for large-scale fully nonlinear and dispersive free surface modelling, highly accurate kinematics in the entire fluid domain and nonlinear wave-structure and moving wave-body methods for marine offshore engineering applications.

OceanWave3D newsletter

Sign up the the OceanWave3D newsletter to get the latest information about OceanWave3D. Sign up here: LINK.


For efficient simulation of free surface flow over variable depth in coastal and offshore engineering a first Boussinesq model was derived by Peregrine (1976). This model was restricted to accurate simulations in shallow waters. The equations were 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). Engsig-Karup et al. (2008) developed a robust and efficient flexible-order finite difference model based on a fully nonlinear and dispersive potential flow model which was thereafter referred to The OceanWave3D model. The OceanWave3D model addresses the limitations in practical application ranges of most Boussinesq-type models and is inspired by the original work by Li and Fleming (1997) who were the first to propose a low-order multigrid method for efficient and scalable solution of the fully nonlinear potential flow equations for water wave applications. Extensions to the work of Li and Fleming (1997) focusing on improved efficiency via high-order discretizations have been analyzed and demonstrated by Bingham et al. (2007). Further improvements in both efficiency and robustness is described in Engsig-Karup et al. (2008) for a complete model in three space dimension. These developments led to the original algorithmic strategy due to Li and Fleming be generalized to a flexible-order finite difference discretization in three space dimensions that could be mapped with high efficiency to Graphics Processing Units (GPUs) by Engsig-Karup, Madsen and Glimberg (2011). This work was aimed at closing the performance gap between traditional Boussinesq-type models and volumen-based solvers such as the fully nonlinear potential flow model and enabled for the first time fast (near) real-time nonlinear hydrodynamics calculations at unpreceedented speed for such a model, cf. Engsig-Karup, Madsen and Glimberg (2011) on the feasibility of real-time computations. The model was developed to enable efficient massively parallel computations for arbitrary sized (large-scale) problems on modern heterogeneous many-core hardware and analyzed with benchmarks in more detail by Engsig-Karup (2014) confirming robustness and efficiency of the model. Several novel improvements of the above-mentioned developments of the work are described in Ducrozet et al. (2012), Ducrozet et al. (2013), Engsig-Karup et al. (2014), Paulsen et al. (2014), Bigoni et al. (2015) and Engsig-Karup et al. (2016) and Duz et al (2016). In particular, the work of Engsig-Karup et al. (2016) represents a breakthrough in the development of a robust multi-domain methodology using the Spectral Element Method for simulation of highly nonlinear and dispersive wave propagation giving opportunity for accurate wave propagation and kinematics together with use of flexible (possibly adapted) unstructured meshes for fully nonlinear wave-body interactions applications as described in Engsig-Karup et al. (2017) aimed at realistic marine settings and engineering purposes.

The OceanWave3D model can be viewed as merely a 'discrete free surface model' of the Fully Nonlinear and Dispersive Potential Flow equations with application range limited only by the truncation errors introduced in the discretization procedure and the assumptions behind the model, namely, that it is potential flow. The novel parallel numerical algorithms and efficient implementations combined with the use of modern technology makes it possible to achieve high performance making it feasible as a base solver for novel engineering analysis and engineering applications. To advocate reproducible science and contribute to stimulate fundamental research and collaborations aimed at delivering more advanced engineering tools, the software is delivered as open source (see licensing terms below).


The OceanWave3D model has been developed at Technical University of Denmark as a part of ongoing research efforts with Allan P. Engsig-Karup as lead architect and main developer.

The research activities at DTU Compute focus on development, benchmarking and application of new algorithms and new analysis techniques for the development of robust and fast numerical tools and enabling proper use of modern technology for scientific calculations directed towards advanced engineering applications.

Model features

The model has been designed to enable fast(!) engineering analysis of wave problems.

Some key Oceanwave3D model features are given below.

The model has been designed and implemented to enable

Source code

The OceanWave3D software exist in several versions (Fortran 90 and C++) and currently the Fortran 90 version has been prepared to be used freely under the terms of the GNU Lesser General Public License v3. For any use of the OceanWave3D source code in your environment and reporting proper reference must be made to the origin of the software.

Please cite the following reference(s) to support the work.

The OceanWave3D or OceanWave3D-CPU version is first presented in
@ARTICLE{EngsigKarupEtAl08, AUTHOR = "Engsig-Karup, A.P. and Bingham, H.B. and Lindberg, O.", TITLE = "An efficient flexible-order model for {3D} nonlinear water waves", YEAR = "2009", JOURNAL = "Journal of Computational Physics", VOLUME = "228", PAGES = "2100-2118" }

DOWNLOAD from GITHUB: OceanWave3D-Fortran90.

The GPU-accelerated version OceanWave3D-GPU is first presented in
@article {EngsigKarupEtAl2011, author = {Engsig-Karup, A. P. and Madsen, Morten G. and Glimberg, Stefan L.}, title = {A massively parallel GPU-accelerated model for analysis of fully nonlinear free surface waves}, journal = {International Journal for Numerical Methods in Fluids}, volume = {70}, number = {1}, publisher = {John Wiley & Sons, Ltd}, year = {2012}, }

A library implementation of the OceanWave3D-GPU version has been done in the GPULAB Library which is presented in
@INPROCEEDINGS{GlimbergEtAl13, AUTHOR = "Glimberg, L. S. and Engsig-Karup, A. P. and Nielsen, A. S. and Dammann, B.", TITLE = "Development of software components for heterogeneous many-core architectures", EDITOR = "Raphael Couturier", BOOKTITLE = "Designing Scientific Applications on GPUs", SERIES = "Lecture notes in computational science and engineering", PAGES = "73--104", PUBLISHER = "CRC Press / Taylor \& Francis Group", YEAR = "2013" }

   Commons licens
GPULAB library by DTU Compute is licensed by the Creative Commons Attribution 4.0 International License.

Request for direct access to the software can happen by E-mail apek @ dtu . dk with a statement of intended purpose of application. It is possible to contribute to the project.


The general-purpose fully nonlinear potential flow model is used in several academic/industrial applications for

Ongoing work seek to address or explore new types or aspects of next-generation applications.

If you have an application or a project described online somewhere, E-mail apek @ dtu . dk and give directions to proper referencing to get it listed here.

Recent talks

  1. Massively Parallel Computational Hydrodynamics for Sustainable Energy Source Applications, HPC Core Workshop, United Kingdom, April, 2016.
  2. On recent progres on the development of new general-purpose fully nonlinear marine hydrodynamics models for wave propagation and wave-body applications, Hydrodynamics of Wave Energy Converters (HYWEC), Bilbao, Spain, April, 2017.

Peer-Reviewed Publications related to the numerical model in this project

  1. Li, B. and Fleming, C. A. A three dimensional multigrid model for fully nonlinear water waves. 1997. Coastal Engineering, Vol 30: 235-258.
  2. H. B. Bingham and H. Zhang. On the accuracy of finite-difference solutions for nonlinear water waves. J. Engng. Math., 58:211-228, 2007.
  3. 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.
  4. 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. In International Journal of Numerical Methods in Fluids Volume 2012; 70(1):20-36.
  5. Ducrozet, G., Bingham, H. B., Engsig-Karup, A. P., Bonnefoy, F. and Ferrant, P. 2012 A comparative study of two fast nonlinear free-surface water wave models. In International Journal for Numerical Methods in Fluids 08/2012; 69(11):1818-1834.
  6. Ducrozet, G., Engsig-Karup, A. P., Bingham, H. B. and Ferrant, P. 2013 A non-linear wave decomposition model for efficient wave-structure interaction. Part A: Formulation, validations and analysis. In Journal of Computational Physics 09/2013; 257:863-883.
  7. Glimberg, S. L., Engsig-Karup, A. P., Dammann, B. and Nielsen, A. S. 2013. (ISBN: 978-1-4665-7162-4) In book: Designing Scientific Applications on GPUs, Chapter: Development of High-Performance Software Components for Emerging Architectures, Publisher: Taylor & Francis, Editors: Raphael Couturier, pp.73-104.
  8. Engsig-Karup, A. P., Glimberg, S. L., Nielsen, A. S. and Lindberg, O. 2013. (ISBN: 978-1-4665-7162-4) In book: Designing Scientific Applications on GPUs, Chapter: Fast hydrodynamics on heterogenous many-core hardware, Publisher: Taylor & Francis, Editors: Raphael Couturier, pp.251-294.
  9. Engsig-Karup, A. P. 2014 Analysis of efficient preconditioned defect correction methods for nonlinear water waves. Accepted for publication in International Journal of Numerical Methods in Fluids.
  10. Paulsen, B. T., Bredmose, H. and Bingham, H. B. 2014. An efficient domain decomposition strategy for wave loads on surface piercing circular cylinders. In Coastal Engineering, Volume 86, Pages 57-76.
  11. Bigoni, D., Engsig-Karup, A.P. and Eskilsson, C. A Stochastic Nonlinear Water Wave Model for Efficient Uncertainty Quantification. In http://arxiv.org. 2015.
  12. Engsig-Karup, A.P., Eskilsson, C. and D. Bioni. A Stabilised Nodal Spectral Element Method for Fully Nonlinear Water Waves. In Journal of Computational Physics, Volume 318, 1 August 2016, Pages 1-21.
  13. Duz, B., Bunnik, T., Kapsenberg, G. and Vaz, G. Numerical simulation of nonlinear free surface water waves - coupling of a potential flow solver to a URANS/VOF code. OMAE2016, 2016.
  14. Engsig-Karup, A.P., Eskilsson, C. and Bigoni, D. Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation. ISOPE2016, 2016.
  15. Engsig-Karup, A.P., Monteserin, C. and Eskilsson, C. A Stabilised Nodal Spectral Element Method for Fully Nonlinear Water Waves Part 2: Wave-body interaction. E-published at arXiv.org, 27 March, 2017.

PhD theses (Research on advanced Fully Nonlinear Potential Flow Modelling Tools at DTU)

  1. Engsig-Karup, A. P. Unstructured Nodal {DG-FEM} solution of high-order Boussinesq-type equations (2006), Department of Mechanical Engineering, Technical University of Denmark.
  2. Glimberg, S. L. Designing Scientific Software for Heterogeneous Computing - With application to large-scale water wave simulations (2013), Department of Applied Mathematics and Computer Science, Technical University of Denmark.
  3. Kontos, S. Robust Numerical Methods for Nonlinear Wave-Structure Interaction in a Moving Frame of Reference (2016), Department of Mechanical Engineering/Department of Applied Mathematics and Computer Science/FORCE Technology, Technical University of Denmark


  1. Stochastic benchmarks for Whalin's test case (Not officially published yet, figures via python scripts)