Long-crested wave generation and absorption for SPH-based DualSPHysics model

Abstract The present work presents a fully comprehensive implementation of wave generation and active wave absorption for second-order long-crested monochromatic and random waves in a WCSPH-based (Weakly Compressible Smoothed Particle Hydrodynamics) model. The open-source code DualSPHysics is used for the scope. The numerical flume resembles a physical wave facility, so that, the moving boundaries mimic the action of a piston-type wavemaker. The second-order wave generation system, capable of generating both monochromatic (regular) and random (irregular) waves, is implemented jointly with passive and active wave absorption. A damping system is defined as solution for passive absorption and is used to prevent wave reflection from fixed boundaries in the numerical flume. The use of active wave absorption allows avoiding spurious reflection from the wavemaker. These implementations are validated with theoretical solutions and experimental results, in terms of water surface elevation, wave orbital velocities, wave forces and capacity for damping the re-reflection inside the fluid domain.

[1]  Robert A. Dalrymple,et al.  Analysis of the artificial viscosity in the smoothed particle hydrodynamics modelling of regular waves , 2014 .

[2]  Javier L. Lara,et al.  Reynolds averaged Navier–Stokes modelling of long waves induced by a transient wave group on a beach , 2011, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[3]  S. Shao,et al.  Corrected Incompressible SPH method for accurate water-surface tracking in breaking waves , 2008 .

[4]  M. Gómez-Gesteira,et al.  Boundary conditions generated by dynamic particles in SPH methods , 2007 .

[5]  Marcel Zijlema,et al.  SWASH: An operational public domain code for simulating wave fields and rapidly varied flows in coas , 2011 .

[6]  Philippe St-Germain,et al.  Smoothed-particle hydrodynamics numerical modeling of structures impacted by tsunami bores , 2014 .

[7]  Moncho Gómez-Gesteira,et al.  Smoothed Particle Hydrodynamics for coastal engineering problems , 2013 .

[8]  Hemming A. Schäffer,et al.  SECOND-ORDER WAVEMAKER THEORY FOR IRREGULAR WAVES , 1996 .

[9]  E.P.D. Mansard,et al.  Group bounded long waves in physical models , 1983 .

[10]  Robert T. Guza,et al.  Paddle Generated Waves in Laboratory Channels , 1980 .

[11]  Taro Arikawa,et al.  On enhancement of Incompressible SPH method for simulation of violent sloshing flows , 2014 .

[12]  Mostafa Safdari Shadloo,et al.  Numerical Simulation of Long Wave Runup for Breaking and Nonbreaking Waves , 2015 .

[13]  Corrado Altomare,et al.  Comparison of numerical models for wave overtopping and impact on a sea wall , 2014 .

[14]  P. Fontanet.  THÉORIE DE LA GÉNÉRATION DE LA HOULE CYLINDRIQUE PAR UN BATTEUR PLAN (2e ordre d'approximation) , 1961 .

[15]  Hemming A. Schäffer,et al.  Review of Multidirectional Active Wave Absorption Methods , 2000 .

[16]  Tim Pullen,et al.  The role of offshore boundary conditions in the uncertainty of numerical prediction of wave overtopping using non-linear shallow water equations. , 2014 .

[17]  T. Havelock,et al.  LIX.Forced surface-waves on water , 1929 .

[18]  Peter Stansby,et al.  Coupled wave action and shallow-water modelling for random wave runup on a slope , 2011 .

[19]  M. Christensen,et al.  An Absorbing Wave-maker Based on Digital Filters , 1994 .

[20]  S. Hughes.  Laboratory wave reflection analysis using co-located gages , 1993 .

[21]  Javier L. Lara,et al.  Three-dimensional numerical wave generation with moving boundaries , 2015 .

[22]  D. Peregrine.  Water-wave impact on walls , 2003 .

[23]  Edmond Y.M. Lo,et al.  Simulation of near-shore solitary wave mechanics by an incompressible SPH method , 2002 .

[24]  Di Wu,et al.  Numerical simulations of wave interactions with vertical wave barriers using the SPH method , 2014 .

[25]  Holger Wendland,et al.  Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree , 1995, Adv. Comput. Math..

[26]  Xin Liu,et al.  2D Numerical ISPH Wave Tank for Complex Fluid–Structure Coupling Problems , 2016 .

[27]  Ping Dong,et al.  A SPH numerical wave basin for modeling wave-structure interactions , 2016 .

[28]  J. Monaghan.  Smoothed particle hydrodynamics , 2005 .

[29]  Peter A. Troch,et al.  An improved calculation model for the wave-induced pore pressure distribution in a rubble-mound breakwater core , 2012 .

[30]  M. Zijlema,et al.  Efficient and robust wave overtopping estimation for impermeable coastal structures in shallow foreshores using SWASH , 2017 .

[31]  Benedict D. Rogers,et al.  SPHysics - development of a free-surface fluid solver - Part 1: Theory and formulations , 2012, Comput. Geosci..

[32]  F. Aristodemo,et al.  SPH numerical modeling of wave–perforated breakwater interaction , 2015 .

[33]  Curtis Smith,et al.  Large-scale solitary wave simulation with implicit incompressible SPH , 2016 .

[34]  Peter Stansby,et al.  Random wave runup and overtopping a steep sea wall: Shallow-water and Boussinesq modelling with generalised breaking and wall impact algorithms validated against laboratory and field measurements , 2013 .

[35]  A. Skillen,et al.  Incompressible smoothed particle hydrodynamics (SPH) with reduced temporal noise and generalised Fickian smoothing applied to body–water slam and efficient wave–body interaction , 2013 .

[36]  Benedict D. Rogers,et al.  SPH for 3D floating bodies using variable mass particle distribution , 2013 .

[37]  G. Wei,et al.  Time-Dependent Numerical Code for Extended Boussinesq Equations , 1995 .

[38]  Hitoshi Gotoh,et al.  Current achievements and future perspectives for projection-based particle methods with applications in ocean engineering , 2016 .

[39]  P. Lin,et al.  ISPH wave simulation by using an internal wave maker , 2015 .

[40]  Philippe Van Bogaert,et al.  Description of loading conditions due to violent wave impacts on a vertical structure with an overhanging horizontal cantilever slab , 2012 .

[41]  Benedict D. Rogers,et al.  Numerical Modeling of Water Waves with the SPH Method , 2006 .

[42]  Benedict D. Rogers,et al.  Wave body interaction in 2D using smoothed particle hydrodynamics (SPH) with variable particle mass , 2012 .

[43]  Benedict D. Rogers,et al.  Simulation of caisson breakwater movement using 2-D SPH , 2010 .

[44]  B. Lemehaute.  An introduction to hydrodynamics and water waves , 1976 .

[45]  R. Dalrymple,et al.  SPH modeling of dynamic impact of tsunami bore on bridge piers , 2015 .

[46]  R. G. Dean,et al.  Forced small-amplitude water waves: a comparison of theory and experiment , 1960, Journal of Fluid Mechanics.

[47]  Javier L. Lara,et al.  Realistic wave generation and active wave absorption for Navier–Stokes models: Application to OpenFOAM® , 2013 .

[48]  Xing Ye Ni,et al.  Numerical Simulation of Wave Overtopping Based on DualSPHysics , 2013 .

[49]  Hemming A. Schäffer,et al.  Second-order wavemaker theory for multidirectional waves , 2003 .

[50]  Ole Secher Madsen,et al.  On the generation of long waves , 1971 .

[51]  O. Nwogu.  Alternative form of Boussinesq equations for nearshore wave propagation , 1993 .

[52]  B. Rogers,et al.  Composite modelling of subaerial landslide–tsunamis in different water body geometries and novel insight into slide and wave kinematics , 2016 .

[53]  Damien Violeau,et al.  Fluid Mechanics and the SPH Method: Theory and Applications , 2012 .

[54]  Sauro Manenti,et al.  SPH simulation of a floating body forced by regular waves , 2008 .

[55]  Kuang-An Chang,et al.  Numerical Modeling of Wave Interaction with Porous Structures , 2001 .

[56]  Stephen M. Longshaw,et al.  DualSPHysics: Open-source parallel CFD solver based on Smoothed Particle Hydrodynamics (SPH) , 2015, Comput. Phys. Commun..

[57]  D. Goring,et al.  Tsunamis -- the propagation of long waves onto a shelf , 1978 .

[58]  Maria Graça Neves,et al.  A Semi-Infinite Numerical Wave Flume Using Smoothed Particle Hydrodynamics , 2012 .

[59]  Corrado Altomare,et al.  Towards simulating floating offshore oscillating water column converters with Smoothed Particle Hydrodynamics , 2017 .

[60]  Stig E. Sand,et al.  CORRECT REPRODUCTION OF GROUP-INDUCED LONG WAVES , 1980 .

[61]  P. A. Madsen,et al.  A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly-varying bathymetry , 1992 .

[62]  Julien De Rouck,et al.  An active wave generating–absorbing boundary condition for VOF type numerical model , 1999 .

[63]  D. Peregrine.  Long waves on a beach , 1967, Journal of Fluid Mechanics.

[64]  Henrik Bredmose,et al.  Violent breaking wave impacts. Part 1: Results from large-scale regular wave tests on vertical and sloping walls , 2007 .

[65]  Corrado Altomare,et al.  Numerical modelling of armour block sea breakwater with smoothed particle hydrodynamics , 2014 .

[66]  S. J. Lind,et al.  Incompressible smoothed particle hydrodynamics for free-surface flows: A generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves , 2012, J. Comput. Phys..

[67]  Corrado Altomare,et al.  Applicability of Smoothed Particle Hydrodynamics for estimation of sea wave impact on coastal structures , 2015 .

[68]  Pengzhi Lin,et al.  Internal Wave-Maker for Navier-Stokes Equations Models , 1999 .

[69]  On the internal wave generation in Boussinesq and mild-slope equations , 2006 .

[70]  Ping Dong,et al.  Numerical simulation of wave interaction with porous structures using an improved smoothed particle hydrodynamic method , 2014 .

[71]  Stig E. Sand,et al.  Long waves in directional seas , 1982 .

[72]  Salvatore Marrone,et al.  Free-surface flows solved by means of SPH schemes with numerical diffusive terms , 2010, Comput. Phys. Commun..

[73]  K. Taylor.  Summarizing multiple aspects of model performance in a single diagram , 2001 .