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Many variants of non-hydrostatic models have been proposed in the literature, exposing excellent features such as frequency dispersion and nonlinear effects. However, no advances have been made in assessing these models at an engineering level with observations under realistic nearshore conditions. Over the past 10 years, strong efforts have been made at Delft University to advance the state of wave modelling and flooding simulations for coastal engineering. Just to mention a few:
  • An implementation of the Keller-box scheme for vertical pressure gradients to resolve frequency dispersion accurately and efficiently (Stelling and Zijlema, 2003).
  • An efficient implementation of an advection scheme on staggered grids based on primitive variables enabling to conserve momentum, and a simple wet-dry algorithm (Stelling and Duinmeijer, 2003).
  • An efficient and stable implementation of a Poisson solver for non-hydrostatic pressure (Zijlema and Stelling, 2005).
  • Branch into more challenging wave features within the surf and swash zones by applying the aforementioned methods (Zijlema and Stelling, 2008, Zijlema et al., 2011).
Concerning the development of SWASH, the main achievements have been obtained in reliability, robustness, computational efficiency, and user-friendliness. SWASH has been extensively applied and validated. To date, over 60 journal publications and proceedings papers have outlined the numerical methodology as employed in SWASH, and have presented SWASH comparisons on topics such as wave propagation, dispersion, refraction, diffraction, flooding and drying, moving shoreline, hydraulic jumps, cross-shore motions of irregular breaking waves, wave runup, wave overtopping, surf beats, nearshore circulations, and setups induced by breaking waves. See also some examples of SWASH simulations.

Below are the key publications.
  1. Casulli, V. and Stelling, G.S., 1998. Numerical simulation of 3D quasi-hydrostatic, free-surface flows. J. Hydr. Eng. ASCE, 124, 678-686.
  2. Stelling, G.S. and Duinmeijer, S.P.A., 2003. A staggered conservative scheme for every Froude number in rapidly varied shallow water flows. Int. J. Numer. Meth. Fluids, 43, 1329-1354.
  3. Stelling, G. and Zijlema, M., 2003. An accurate and efficient finite-difference algorithm for non-hydrostatic free-surface flow with application to wave propagation. Int. J. Numer. Meth. Fluids, 43, 1-23.
  4. Zijlema, M. and Stelling, G.S., 2005. Further experiences with computing non-hydrostatic free-surface flows involving water waves. Int. J. Numer. Meth. Fluids, 48, 169-197.
  5. Cramer, S.C. and Stelling, G.S., 2008. A conservative unstructured scheme for rapidly varied flows. Int. J. Numer. Meth. Fluids, 58, 183-212.
  6. Zijlema, M. and Stelling, G.S., 2008. Efficient computation of surf zone waves using the nonlinear shallow water equations with non-hydrostatic pressure. Coast. Engng., 55, 780-790.
  7. Cea, L., Stelling, G. and Zijlema, M., 2009. Non-hydrostatic 3D free surface layer-structured finite volume model for short wave propagation. Int. J. Numer. Meth. Fluids, 61, 382-410.
  8. Stelling, G.S. and Zijlema, M., 2009. Numerical modeling of wave propagation, breaking and run-up on a beach. In: Advanced Computational Methods in Science and Engineering (B. Koren and C. Vuik, eds.), Lecture Notes in Computational Science and Engineering, 71, 373-401, Springer, Heidelberg.
  9. Cui, H., Pietrzak, J.D. and Stelling, G.S., 2010. A finite volume analogue of the P1NC - P1 finite element, with accurate flooding and drying. Ocean Model., 35, 16-30.
  10. Zijlema, M., Stelling, G. and Smit, P., 2011. SWASH: An operational public domain code for simulating wave fields and rapidly varied flows in coastal waters. Coast. Engng., 58, 992-1012.
  11. Smit, P., Zijlema, M. and Stelling, G., 2013. Depth-induced wave breaking in a non-hydrostatic, near-shore wave model. Coast. Engng., 76, 1-16.
Some other papers related to SWASH are
  1. Zijlema, M., Stelling, G. and Smit, P., 2011. Simulating nearshore wave transformation with non-hydrostatic wave-flow modelling. 12th International Workshop on Wave Hindcasting and Forecasting & 3rd Coastal Hazard Symposium, Oct 30-Nov 4, 2011, Kohala Coast, Hawaii.
  2. Torres-Freyermuth et al., 2012. Wave-induced extreme water levels in the Puerto Morelos fringing reef lagoon. Nat. Hazards Earth Syst. Sci., 12, 3765-3773.
  3. Vilani, M., Bosboom, J., Zijlema, M. and Stive, M.J.F., 2012. Circulation patterns and shoreline response induced by submerged breakwaters, in: P.J. Lynett and J.M. Smith (Eds.), Proc. 33th Int. Conf. on Coast. Engng., ASCE, World Scientific Publishing, Singapore, paper no. structures.25
  4. Zijlema, M., 2012. Modelling wave transformation across a fringing reef using SWASH, in: P.J. Lynett and J.M. Smith (Eds.), Proc. 33th Int. Conf. on Coast. Engng., ASCE, World Scientific Publishing, Singapore, paper no. currents.26
  5. Rijnsdorp, D.P., Smit, P.B. and Zijlema, M., 2012. Non-hydrostatic modelling of infragravity waves using SWASH, in: P.J. Lynett and J.M. Smith (Eds.), Proc. 33th Int. Conf. on Coast. Engng., ASCE, World Scientific Publishing, Singapore, paper no. currents.27
  6. Suzuki, T., Verwaest, T., Veale, W., Trouw, K. and Zijlema, M., 2012. A numerical study on the effect of beach nourishment on wave overtopping in shallow foreshores, in: P.J. Lynett and J.M. Smith (Eds.), Proc. 33th Int. Conf. on Coast. Engng., ASCE, World Scientific Publishing, Singapore, paper no. waves.50
  7. Tomas Van Oyen, Tomo Suzuki, Marcel Zijlema, Pieter Rauwoens, and Peter Troch, 2012. Modelling the finite amplitude dynamics of tidal sand waves with SWASH (poster), ICCE 2012: Proceedings of the 33rd International Conference on Coastal Engineering, Santander, Spain, 1-6 July 2012.
  8. Mao Xing Wei and Zhi Gang Bai, 2013. A new time domain analysis of the wave power. Applied Mechanics and Materials, Vols. 253-255, pp. 720-723.
  9. Guoliang Zou and Qinghe Zhang, 2013. Improvement of absorbing boundary conditions for non-hydrostatic wave-flow model SWASH. Applied Mechanics and Materials, Vols. 353-356, pp. 2676-2682.
  10. Brinkkemper, J.A., Torres-Freyermuth, A., Mendoza, E.T. and Ruessink, B.G., 2013. Parameterization of wave run-up on beaches in Yucatan, Mexico: a numerical study. Coastal Dynamics 2013, 7th Int. Conf. on Coast. Dyn., 24-28 June 2013, Arcachon, France.
  11. Mark Buckley and Ryan Lowe, 2013. Evaluation of nearshore wave models in steep reef environments. Coastal Dynamics 2013, 7th Int. Conf. on Coast. Dyn., 24-28 June 2013, Arcachon, France.
  12. Gerbrant Ph. van Vledder, Gerben Ruessink and Dirk P. Rijnsdorp, 2013. Individual wave height distributions in the coastal zone: measurements and simulations and the effect of directional spreading. Coastal Dynamics 2013, 7th Int. Conf. on Coast. Dyn., 24-28 June 2013, Arcachon, France.
  13. Simon H.C. Wong, Stephen G. Monismith, and Alexandria B. Boehm, 2013. Simple estimate of entrainment rate of pollutants from a coastal discharge into the surf zone. Environ. Sci. Technol., 47 (20), 11554-11561.
  14. P.B. Smit and T.T. Janssen, 2013. The evolution of inhomogeneous wave statistics through a variable medium. J. Phys. Oceanogr., 43, 1741-1758.
  15. Pieter Smit, Tim Janssen, Leo Holthuijsen and Jane Smith, 2014. Non-hydrostatic modeling of surf zone wave dynamics. Coast. Engng., 83, 36-48.
  16. de Bakker, A.T.M., Tissier, M.F.S. and Ruessink, B.G., 2014. Shoreline dissipation of infragravity waves. Continental Shelf Research, 72, 73-82.
  17. Dirk P. Rijnsdorp, Pieter B. Smit and Marcel Zijlema, 2014. Non-hydrostatic modelling of infragravity waves under laboratory conditions. Coast. Engng., 85, 30-42.
  18. Andrea Ruju, Javier L. Lara and Inigo J. Losada, 2014. Numerical analysis of run-up oscillations under dissipative conditions. Coast. Engng., 86, 45-56.
  19. N. Subasita, H. Latief and S.R. Pudjaprasetya, 2014. The SWASH model for soliton splitting due to decreasing depth. AIP Conf. Proc. 1589, 150-153.
  20. Mark Buckley, Ryan Lowe and Jeff Hansen, 2014. Evaluation of nearshore wave models in steep reef environments. Ocean Dynamics, 64, 847-862.
  21. Jishad, M., Vu, T. T. and Kumar, J. (2014). Modelling of wave propagation over a submerged sand bar using SWASH. Indian Journal of Marine Sciences, 43(7), 7.
  22. M. Zheleznyak, R. Demchenko, P. Diky and M. Sorokin (2014). Numerical simulation of harbor eigen frequencies by a nonlinear non-hydrostatic model SWASH. Ninth Int. Sci. Conf. "Mathematical modeling and simulation systems", June 23-27, 2014, Kiev, Ukraine.
  23. Pedro Veras Guimares et al, 2015. Numerical simulation of extreme wave runup during storm events in Tramanda Beach, Rio Grande do Sul, Brazil. Coast. Engng., 95, 171-180.
  24. Zijlema, M., 2014. Modelling vertical variation of turbulent flow across a surf zone using SWASH, in: P.J. Lynett (Eds.), Proc. 34th Int. Conf. on Coast. Engng., Seoul, Korea, published by the Coastal Engineering Research Council, paper no. waves.3
  25. Van Vledder, G. Ph. and Zijlema, M., 2014. Non-hydrostatic wave modelling in partly sheltered areas, in: P.J. Lynett (Eds.), Proc. 34th Int. Conf. on Coast. Engng., Seoul, Korea, published by the Coastal Engineering Research Council, paper no. waves.11
  26. Dusseljee, D.W., Klopman, G., Van Vledder, G. Ph. and Riezebos, H.J., 2014. Impact of harbor navigation channels on waves: a numerical modelling guideline, in: P.J. Lynett (Eds.), Proc. 34th Int. Conf. on Coast. Engng., Seoul, Korea, published by the Coastal Engineering Research Council, paper no. waves.58
  27. Altomare, C., et al., 2014. A hybrid numerical model for coastal engineering problems, in: P.J. Lynett (Eds.), Proc. 34th Int. Conf. on Coast. Engng., Seoul, Korea, published by the Coastal Engineering Research Council, paper no. waves.60
  28. Suzuki, T., Altomare, C., Verwaest, T., Trouw, K. and Zijlema, M., 2014. Two-dimensional wave overtopping calculation over a dike in shallow foreshore by SWASH, in: P.J. Lynett (Eds.), Proc. 34th Int. Conf. on Coast. Engng., Seoul, Korea, published by the Coastal Engineering Research Council, paper no. structures.3
  29. Vanneste D., et al., 2014. Comparison of numerical models for wave overtopping and impact on a sea wall, in: P.J. Lynett (Eds.), Proc. 34th Int. Conf. on Coast. Engng., Seoul, Korea, published by the Coastal Engineering Research Council, paper no. structures.5
  30. St-Germain, P., Nistor, I., Readshaw, J. and Lamont, G., 2014. Numerical modeling of coastal dike overtopping using SPH and non-hydrostatic NLSW equations, in: P.J. Lynett (Eds.), Proc. 34th Int. Conf. on Coast. Engng., Seoul, Korea, published by the Coastal Engineering Research Council, paper no. structures.10
  31. Van den Bos, J., Verhagen, H.J., Zijlema, M. and Mellink, B., 2014. Towards a practical application of numerical models to predict wave-structure interaction: an initial validation, in: P.J. Lynett (Eds.), Proc. 34th Int. Conf. on Coast. Engng., Seoul, Korea, published by the Coastal Engineering Research Council, paper no. structures.50
  32. Gracia, V., et al., 2014. A new generation of early warning system for coastal risk. The ICOAST project., in: P.J. Lynett (Eds.), Proc. 34th Int. Conf. on Coast. Engng., Seoul, Korea, published by the Coastal Engineering Research Council, paper no. management.18
  33. Guoxiang Wu, Jun Wang, Bingchen Liang, and Dong Young Lee, 2014. Simulation of Detailed Wave Motions and Coastal Hazards, Journal of Coastal Research: Special Issue 72 - The 3rd International Rip Current Symposium: pp. 127-132
  34. Jong Joo Yoon, 2014. Non-hydrostatic Modeling of Wave Transformation and Rip Current Circulation: A Case Study for Haeundae Beach, Korea, Journal of Coastal Research: Special Issue 72 - The 3rd International Rip Current Symposium: pp. 184-189
  35. Dirk Rijnsdorp, Gerben Ruessink and Marcel Zijlema, 2015. Infragravity-wave dynamics in a barred coastal region, a numerical study. J. Geophys. Res. Oceans, 120, 4068-4089.
  36. Lowe, R. J., A. S. Leon, G. Symonds, J. L. Falter and R. Gruber, 2015. The intertidal hydraulics of tide-dominated reef platforms. J. Geophys. Res. Oceans, 120.
  37. Oskamp, J. A. and Dababneh, A. (Jemie) A. (2015, July 27). A Proposed Approach for Two-dimensional Run-up Modeling. International Society of Offshore and Polar Engineers.
  38. Vyzikas, T., Stagonas, D., Buldakov, E. and Greaves, D. (2015, July 27). Efficient Numerical Modelling of Focused Wave Groups for Freak Wave Generation. International Society of Offshore and Polar Engineers.
  39. Altomare et al. (2015) Study of the overtopping flow impacts on multifunctional sea dikes in shallow foreshores with an hybrid numerical model. E-proceedings of the 36th IAHR World Congress, 28 June - 3 July, 2015, The Hague, the Netherlands
  40. Crespo et al. (2015) SPH modelling in coastal engineering. E-proceedings of the 36th IAHR World Congress, 28 June - 3 July, 2015, The Hague, the Netherlands
  41. De Roo et al. (2015) Numerical modelling of 2D wave transformation processes from nearshore to a shallow foreshore: comparison between the Mike21, SWASH and XBeach models. E-proceedings of the 36th IAHR World Congress, 28 June - 3 July, 2015, The Hague, the Netherlands
  42. Van Vledder (2015) Swell-wave island interaction and wave piloting in the Southern pacific ocean. E-proceedings of the 36th IAHR World Congress, 28 June - 3 July, 2015, The Hague, the Netherlands
  43. Miani et al. (2015) Sand dune breaching along the Emilia-Romagna littoral zone: a deterministic approach. E-proceedings of the 36th IAHR World Congress, 28 June - 3 July, 2015, The Hague, the Netherlands
  44. J-F. Filipot, 2015. Investigation of the bottom-slope dependence of the nonlinear wave evolution toward breaking using SWASH. Journal of Coastal Research, in press.
  45. Altomare et al., 2015. Hybridization of the wave propagation model SWASH and the meshfree particle method SPH for real coastal applications. Coastal Engineering Journal, Vol. 57, No. 4.
  46. Bingchen Lianga, Guoxiang Wua, Fushun Liua, Hairong Fana, Huajun Li, 2015. Numerical study of wave transmission over double submerged breakwaters using non-hydrostatic wave model. Oceanologia, Volume 57, Issue 4, Pages 308-317
  47. Medellin et al., 2016. Run-up parameterization and beach vulnerability assessment on a barrier island: a downscaling approach. Nat. Hazards Earth Syst. Sci., 16, 167-180, doi:10.5194/nhess-16-167-2016.
  48. Lia Yuliawati, Nugrahinggil Subasita, Didit Adytia and Wono Setya Budhi, 2016. Simulation of obliquely interacting solitary waves with a hard wall by using HAWASSI-VBM and SWASH model. AIP Conf. Proc. 1707, 040003
  49. de Bakker, A.T.M., Tissier, M.F.S. and Ruessink, B.G., 2016. Beach steepness effects on nonlinear infragravity-wave interactions: A numerical study. J. Geophys. Res. Oceans, 121, 554-570.
  50. Dirk Rijnsdorp and Marcel Zijlema, 2016. Simulating waves and their interactions with a restrained ship using a non-hydrostatic wave-flow model. Coastal Engineering, 114, 119-136.
  51. Na Zhang, Qinghe Zhang, Guoliang Zou and Xuelian Jiang, 2016. Estimation of the transmission coefficients of wave height and period after smooth submerged breakwater using a non-hydrostatic wave model. Ocean Engineering, 122, 202-214.
  52. Esther R. Gomes, Ryan P. Mulligan, Katherine L. Brodie and Jesse E. McNinch, 2016. Bathymetric control on the spatial distribution of wave breaking in the surf zone of a natural beach. Coastal Engineering, 116, 180-194.
  53. Alexandre Nicolae Lerma, Rodrigo Pedreros, and Nadia Senechal, 2016. Wave Set-up and Run-up Variability on a Complex Barred Beach During Highly Dissipative Storm Conditions. Journal of Coastal Research: Special Issue 75 - Proceedings of the 14th International Coastal Symposium, Sydney, 6-11 March 2016: pp. 882-886.
  54. Cao, H., Feng, W., and Chen, Y. (2016). Numerical modeling of wave transformation and runup reduction by the coastal vegetation of the South China Sea. Vila-Concejo, A.; Bruce, E.; Kennedy, D.M., and McCarroll, R.J. (eds.), Proceedings of the 14th International Coastal Symposium (Sydney, Australia). Journal of Coastal Research, Special Issue, No. 75, pp. 830-835. Coconut Creek (Florida), ISSN 0749-0208.
  55. Rohmer Jeremy, Deborah Idier, Thomas Bulteau and Franois Paris (2016). Tracking the critical offshore conditions leading to inundation via active learning of full-process based models. Proc. of 3rd European Conference on Flood Risk Management (FLOODrisk 2016), article number 04026.
  56. Sylvestre Le Roy, Alexis Stepanian, Rodrigo Pedreros, Thomas Bulteau, Alexandre Nicolae-Lerma and Yann Balouin (2016). Assessing coastal flooding hazard in urban areas: the case of estuarian villages in the city of Hyres-les-Palmiers. Proc. of 3rd European Conference on Flood Risk Management (FLOODrisk 2016), article number 01010.
  57. Ye Liu and Shao-Wu Li (2016). Resolution of Incident and Reflected Components of Nonlinear Regular Waves. Coast. Eng. J. 58, 1650012.
  58. Tomohiro Suzuki, Corrado Altomare, William Veale, Toon Verwaest, Koen Trouw, Peter Troch and Marcel Zijlema, 2017. Efficient and robust wave overtopping estimation for impermeable coastal structures in shallow foreshores using SWASH. Coast. Engng., 122, 108-123.
  59. Alexandre Nicolae Lerma, Rodrigo Pedreros, Arthur Robinet and Nadia SÚnÚchal, 2017. Simulating wave setup and runup during storm conditions on a complex barred beach. Coast. Engng., 123, 29-41.
Here, some MSc and PhD theses can be found where development and application of SWASH have been carried out.
  1. Dirk Rijnsdorp (2011). Numerical modelling of infragravity waves in coastal regions. TU Delft.
  2. Tom Bogaard (2012). Modelling the anisotropy of turbulence with the SWASH model: Heterogeneous roughness conditions in open channel flows. TU Delft.
  3. Bart Mellink (2012). Numerical and experimental research of wave interaction with a porous breakwater. TU Delft.
  4. Joost Brinkkemper (2013). Modeling the cross-shore evolution of asymmetry and skewness of surface gravity waves propagating over a natural intertidal sandbar. Utrecht University.
  5. Maurits Kruijt (2013). Resistance of submerged groynes. TU Delft.
  6. Victor Martnez Ps (2013). Validation of SWASH for wave overtopping. TU Delft.
  7. Menno Steensma (2014). Onderzoek naar het modelleren van gebonden lange golven in SWASH (in dutch). University of Twente.
  8. Pieter Bart Smit (2014). Deterministic and stochastic modelling of ocean surface waves. PhD thesis, Delft University of Technology.
  9. Meritxell Salas Prez (2014). Overtopping over a real rubble mound breakwater calculated with SWASH. TU Delft.
  10. Mohamed Al-Saady (2014). Numerical study of regular and irregular wave interaction with vertical breakwaters. TU Delft.
  11. Joao Hinke Dobrochinski (2014). A combination of SWASH and Harberth to compute wave forces on moored ships. TU Delft.
  12. Frank van Mierlo (2014). Numerical modelling of wave penetration in ports. TU Delft.
  13. Carolin Briele (2014). Assessment of the application of permeable pile groins as coastal protection. TU Delft.
  14. Xiaomin Liao (2015). Cross-shore velocity moments in the nearshore: validating SWASH. TU Delft.
  15. Nikolaos Alavantas (2015). Investigation of infragravity waves in a two-dimensional domain using a non-hydrostatic numerical model, SWASH. University of Twente.
  16. Floris de Wit (2016). Tide-induced currents in a phase-resolving wave model. TU Delft.
  17. Dennis Monteban (2016). Numerical modelling of wave agitation in ports and access channels. TU Delft.
  18. Panagiotis Vasarmidis (2016). Assessment of the influence of permeable pile groins on nearshore hydraulics. TU Delft.
  19. Dirk Pieter Rijnsdorp (2016). Modelling waves and their impact on moored ships. PhD thesis, Delft University of Technology.