Depth Integrated Non Hydrostatic Finite Element Model for Wave Propagation
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ISSN: 1680-8894
E-ISSN: 2219-6714
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Nov 21, 2017
Published: Nov 21, 2017
Published: Nov 21, 2017
Abstract
A depth integrated non hydrostatic finite element model for the propagation and transformation of waves in coastal areas was developed with success from the hydrostatic model SisBahia®. The model use quadratic quadrilateral finite element for horizontal velocities approximation and linear quadrilateral finite elements for water surface elevations and non hydrostatic pressures approximations. Because the model does not require the use of staggered grids it can be used on non structured finite element meshes.
Keywords
Waves propagation, non hydrostatic, finite element method, SisBahiaDownloads
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How to Cite
Calvo Gobbetti, L., & Colonna Rosman, P. (2017). Depth Integrated Non Hydrostatic Finite Element Model for Wave Propagation. I+D Tecnológico, 13(2), 55-65. Retrieved from https://revistas.utp.ac.pa/index.php/id-tecnologico/article/view/1715
References
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(2) Stansby P. K., Zhou J. G. “Shallow-water flow solver with non-hydrostatic pressure: 2D vertical plane problems”. International Journal for Numerical Methods in Fluids, Vol. 28, No. 3, pp. 541–563, 1998.
(3) Stelling G., Zijlema M. “An accurate and efficient finite difference algorithm for non-hydrostatic free surface flow with application to wave propagation”. International Journal for Numerical Methods in Fluids, Vol. 43, No. 1, pp. 1–23, 2003.
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(5) Yamazaki Y., Kowalik Z., Cheung K. F. “Depth-integrated, non-hydrostatic model for wave breaking and run-up”. International Journal for Numerical Methods in Fluids, Vol. 61, No. 5, pp. 473–497, 2008.
(6) Walters R. A. “A semi implicit finite element model for non- hydrostatic (dispersive) surface waves”. International Journal for Numerical Methods in Fluids, Vol. 49, No. 7, pp.721–737, 2005.
(7) Wei Z., Jia Y. “A depth-integrated non-hydrostatic finite element model for wave propagation”. International Journal for Numerical Methods in Fluids, Vol. 73, July, 2013.
(8) Rosman P. C. Referência Técnica do SisBahia©.(href="http://www.sisbahia.coppe.ufrj.br/SisBAHIA_RefTec_V95.p df), 2015.
(9) Brooks A., Hughes T. “Stream-line upwind/Petrov Galerkin formulation for Convection dominated flows with particular emphasis on the incompressible Navier-Stokes equation”. Comp. Meth. Appl. Mech. Eng., 32:199–259, 1982.
(10) Zijlema M., Stelling G. S. “Further experiences with computing non-hydrostatic free-surface flows involving water waves.” International Journal for Numerical Methods in Fluids, Vol. 48, No. 2, pp.169–197, 2005.
(11) Beji S., Battjes J. A. “Experimental investigation of wave propagation over a bar”. Coastal Engineering, Vol. 19, No. 1, pp. 151–162, 1993.
(12) Luth H. R., Klopman G., Kitou N. “Project 13G: kinematics of waves breaking partially on an offshore bar; LDV measurements for waves with and without a net onshore current.” Technical Report H1573, Delft Hydraulics, Delft, The Netherlands, 1994.
(13) Roeber V, Cheung K. F., Kobayashi M. H. “Shock-capturing Boussinesq-type model for nearshore wave processes”. Coastal Engineering, Vol. 57, No. 4, pp. 407–423, 2010.
(14) Briggs, M.J., Synolakis, C.E., Harkins, G.S., Green, D.R., 1995. Laboratory experiments of tsunami runup on a circular island. Tsunamis: 1992–1994, Springer, pp. 569–593, 1995.
(15) Yeh, H.H.J., Liu, P.L.F., Synolakis, C.E. Long-wave Runup Models, World Scientific, Singapore, 1996.
(16) Fuhrman, D.R., Madsen, P.A. “Simulation of nonlinear wave run-up with a high order Boussinesq model”. Coastal Engineering 55, 139–154, 2008.
(17) Zijlema, M., Stelling, G.S., Smit, P. “SWASH: an operational public domain code for simulating wavefields and rapidly variedflows in coastal waters”. Coastal Engineering 58, 992– 1012, 2011.
(18) Watson, G., Barnes, T.C.D. Peregrine, D.H “Numerical modelling of solitary wave propagation and breaking on a beach and runup on a vertical wall”. In: Yeh, H.H.J., Liu, P.L.F., Synolakis, C.E. (Eds.), Long-wave Runup Models. World Scientific, Singapore, pp. 291–297, 1996.
(19) Wei Z., Jia Y., “Simulation of nearshore wave processes by a depth-integrated non-hydrostatic finite element model”. Coastal Engineering 83, 93-107, 2014.
(2) Stansby P. K., Zhou J. G. “Shallow-water flow solver with non-hydrostatic pressure: 2D vertical plane problems”. International Journal for Numerical Methods in Fluids, Vol. 28, No. 3, pp. 541–563, 1998.
(3) Stelling G., Zijlema M. “An accurate and efficient finite difference algorithm for non-hydrostatic free surface flow with application to wave propagation”. International Journal for Numerical Methods in Fluids, Vol. 43, No. 1, pp. 1–23, 2003.
(4) Casulli V. A. “Semi-implicit finite difference method for non- hydrostatic free surface flows”. International Journal for Numerical Methods in Fluids, Vol. 30, No. 4, pp. 425–440, 1999.
(5) Yamazaki Y., Kowalik Z., Cheung K. F. “Depth-integrated, non-hydrostatic model for wave breaking and run-up”. International Journal for Numerical Methods in Fluids, Vol. 61, No. 5, pp. 473–497, 2008.
(6) Walters R. A. “A semi implicit finite element model for non- hydrostatic (dispersive) surface waves”. International Journal for Numerical Methods in Fluids, Vol. 49, No. 7, pp.721–737, 2005.
(7) Wei Z., Jia Y. “A depth-integrated non-hydrostatic finite element model for wave propagation”. International Journal for Numerical Methods in Fluids, Vol. 73, July, 2013.
(8) Rosman P. C. Referência Técnica do SisBahia©.(href="http://www.sisbahia.coppe.ufrj.br/SisBAHIA_RefTec_V95.p df), 2015.
(9) Brooks A., Hughes T. “Stream-line upwind/Petrov Galerkin formulation for Convection dominated flows with particular emphasis on the incompressible Navier-Stokes equation”. Comp. Meth. Appl. Mech. Eng., 32:199–259, 1982.
(10) Zijlema M., Stelling G. S. “Further experiences with computing non-hydrostatic free-surface flows involving water waves.” International Journal for Numerical Methods in Fluids, Vol. 48, No. 2, pp.169–197, 2005.
(11) Beji S., Battjes J. A. “Experimental investigation of wave propagation over a bar”. Coastal Engineering, Vol. 19, No. 1, pp. 151–162, 1993.
(12) Luth H. R., Klopman G., Kitou N. “Project 13G: kinematics of waves breaking partially on an offshore bar; LDV measurements for waves with and without a net onshore current.” Technical Report H1573, Delft Hydraulics, Delft, The Netherlands, 1994.
(13) Roeber V, Cheung K. F., Kobayashi M. H. “Shock-capturing Boussinesq-type model for nearshore wave processes”. Coastal Engineering, Vol. 57, No. 4, pp. 407–423, 2010.
(14) Briggs, M.J., Synolakis, C.E., Harkins, G.S., Green, D.R., 1995. Laboratory experiments of tsunami runup on a circular island. Tsunamis: 1992–1994, Springer, pp. 569–593, 1995.
(15) Yeh, H.H.J., Liu, P.L.F., Synolakis, C.E. Long-wave Runup Models, World Scientific, Singapore, 1996.
(16) Fuhrman, D.R., Madsen, P.A. “Simulation of nonlinear wave run-up with a high order Boussinesq model”. Coastal Engineering 55, 139–154, 2008.
(17) Zijlema, M., Stelling, G.S., Smit, P. “SWASH: an operational public domain code for simulating wavefields and rapidly variedflows in coastal waters”. Coastal Engineering 58, 992– 1012, 2011.
(18) Watson, G., Barnes, T.C.D. Peregrine, D.H “Numerical modelling of solitary wave propagation and breaking on a beach and runup on a vertical wall”. In: Yeh, H.H.J., Liu, P.L.F., Synolakis, C.E. (Eds.), Long-wave Runup Models. World Scientific, Singapore, pp. 291–297, 1996.
(19) Wei Z., Jia Y., “Simulation of nearshore wave processes by a depth-integrated non-hydrostatic finite element model”. Coastal Engineering 83, 93-107, 2014.