Numerical investigations of wave overtopping at coastal structures

Under the numerical modelling work package of the EU funded CLASH project, the time accurate, free surface capturing, incompressible Navier–Stokes solver AMAZON-SC has been applied to study impulsive wave overtopping at Samphire Hoe, near Dover in the United Kingdom. The simulations show that the overtopping process on this vertical, sheet pile, seawall is dominated by impulsive, aerated, near vertical overtopping jets. In order to perform the simulations AMAZON-SC has been extended to incorporate an isotropic porosity model and for validation purposes the solver has been applied to study overtopping of a low crested sea dike and a 10:1 battered wall. The results obtained for the battered wall and Samphire Hoe tests are in good agreement both with predicted overtopping discharges calculated using the UK overtopping manual and with available experimental results.

[1]  Lafayette K. Taylor,et al.  A time accurate calculation procedure for flows with a free surface using a modified artificial compressibility formulation , 1994 .

[2]  Clive G. Mingham,et al.  The applicability of the shallow water equations for modelling violent wave overtopping , 2004 .

[3]  M. Chung.  Cartesian cut cell approach for simulating incompressible flows with rigid bodies of arbitrary shape , 2006 .

[4]  David M. Ingram,et al.  Free-surface flows under impacting droplets , 2008, J. Comput. Phys..

[5]  Wojciech Sulisz,et al.  Wave reflection and transmission at permeable breakwaters of arbitrary cross-section , 1985 .

[6]  F. Gao.  Numerical Modelling of Wave Interaction with Porous Structures , 2007 .

[7]  Ling Qian,et al.  A free-surface capturing method for two fluid flows with moving bodies , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[8]  D. Durran.  Numerical Methods for Fluid Dynamics , 2010 .

[9]  William Allsop,et al.  Wave overtopping at vertical and steep seawalls , 2005 .

[10]  G. Tryggvason,et al.  A front-tracking method for viscous, incompressible, multi-fluid flows , 1992 .

[11]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[12]  Anat Arbhabhirama,et al.  Friction Factor and Reynolds Number in Porous Media Flow , 1973 .

[13]  Ching-Jer Huang,et al.  Structural permeability effects on the interaction of a solitary wave and a submerged breakwater , 2003 .

[14]  Tom Bruce,et al.  Violent wave overtopping - measurements at large and small scale , 2003 .

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

[16]  B. V. Leer,et al.  Towards the Ultimate Conservative Difference Scheme , 1997 .

[17]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[18]  Tim Pullen,et al.  Violent wave overtopping at Samphire Hoe: field and laboratory measurements , 2005 .

[19]  Bram van Leer,et al.  On the Relation Between the Upwind-Differencing Schemes of Godunov, Engquist–Osher and Roe , 1984 .

[20]  Javier L. Lara,et al.  2-D numerical analysis of near-field flow at low-crested permeable breakwaters , 2004 .

[21]  Hideaki Miyata,et al.  Fully non‐linear free‐surface simulations by a 3D viscous numerical wave tank , 1999 .

[22]  R. I. Issa,et al.  A Method for Capturing Sharp Fluid Interfaces on Arbitrary Meshes , 1999 .

[23]  S. Osher,et al.  A level set approach for computing solutions to incompressible two-phase flow , 1994 .

[24]  Derek M. Causon,et al.  A cartesian cut cell method for compressible flows Part A: static body problems , 1997, The Aeronautical Journal (1968).

[25]  Stuart E. Rogers,et al.  Upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations , 1990 .

[26]  Ole Secher Madsen,et al.  Wave Transmission through Porous Structures , 1974 .

[27]  P. Roache.  Verification of Codes and Calculations , 1998 .

[28]  Julien De Rouck,et al.  Wave Interaction with a Sea Dike using a VOF Finite Volume Method , 2003 .

[29]  Richard H. Pletcher,et al.  The Development of a Free Surface Capturing Approach for Multidimensional Free Surface Flows in Closed Containers , 1997 .

[30]  Tim Pullen,et al.  Field and laboratory measurements of mean overtopping discharges and spatial distributions at vertical seawalls , 2009 .

[31]  Patrick J. Roache,et al.  Verification and Validation in Computational Science and Engineering , 1998 .

[32]  Derek M. Causon,et al.  Developments in Cartesian cut cell methods , 2003, Math. Comput. Simul..

[33]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[34]  W. Rider,et al.  Reconstructing Volume Tracking , 1998 .

[35]  A. Gaitonde,et al.  A dual-time method for the solution of the unsteady Euler equations , 1994, The Aeronautical Journal (1968).

[36]  L YoungsD,et al.  Time-dependent multi-material flow with large fluid distortion. , 1982 .

[37]  Antony Jameson,et al.  Fast multigrid method for solving incompressible hydrodynamic problems with free surfaces , 1993 .

[38]  Dartzi Pan,et al.  A New Approximate LU Factorization Scheme for the Reynolds-Averaged Navier-Stokes Equations , 1986 .

[39]  Pengzhi Lin,et al.  A fixed-grid model for simulation of a moving body in free surface flows , 2007 .

[40]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[41]  J. Monaghan.  Simulating Free Surface Flows with SPH , 1994 .

[42]  Derek M. Causon,et al.  The development of a Cartesian cut cell method for incompressible viscous flows , 2007 .

[43]  Julien De Rouck,et al.  Wave overtopping over a sea dike , 2004 .

[44]  Derek M. Causon,et al.  A Cartesian cut cell method for shallow water flows with moving boundaries , 2001 .

[45]  S. Zaleski,et al.  Modelling Merging and Fragmentation in Multiphase Flows with SURFER , 1994 .

[46]  Ling Qian,et al.  Cartesian Cut Cell Two-Fluid Solver for Hydraulic Flow Problems , 2003 .