Bacigaluppi, Paola

Kazolea, Maria

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HAL Id: hal-03860569https://hal.inria.fr/hal-03860569Submitted on 18 Nov 2022HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.Introduction to the special issue on numerical methodsand applications for waves in coastal environmentsMaria Kazolea, Paola BacigaluppiTo cite this version:Maria Kazolea, Paola Bacigaluppi. Introduction to the special issue on numerical methods and appli-cations for waves in coastal environments. Water Waves, 2022. ￿hal-03860569￿Introduction to the special issue on numerical methods and applications for waves in coastal environments. Paola Bacigaluppi1  and Maria Kazolea21Department of Aerospace Science and Technology, Politecnico di Milano, Via La Masa 34, 20156 Milan, Italy, paola.bacigaluppi@poilimi.it2INRIA, Univ. Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, 200 Avenue de la Vieille Tour, 33405 Talence cedex, France, maria.kazolea@inria.frThe goal  of  this  special  issue is  to provide an overview of recent  progress in the area of numerical  methods and applications for ocean waves in the coastal environment, to identify current challenges and to present and discuss approaches for performing accurate predictions of nonlinear and dispersive water  waves and our ability to understand and predict impacts on coastal structures and urban areas. Over 1.6 million kilometers of coastlines occur on the earth’s surface. These areas are subject to hazardscreated by a range of natural events, such as earthquakes and hurricanes which are a source for largewaves and have a negative economic and social impact on the affected areas. In recent decades,mathematical and numerical modeling of free surface flows in realistic coastal environments has becomean active research field and has been developed to the point where it is possible to provide operational  information.  In  many  situations,  simulations  with  numerical  coastal  models  represent  a  necessary complement to laboratory experiments for both site assessment and coastal design. Numerical modeling  has  also  become an  essential  complement  to  experimental  investigations  at  small  scales,  due  to  the potential of providing a more complete description of the underlying physics.Significant research efforts have been put into advancing the understanding of important coastal processes such as wave propagation, shoaling, diffraction, refraction, wave breaking and run-up over the shoreline;  see for example [1,14] and references therein. These advances improve our ability to understand and  predict impacts on coastal structures and urban areas. In this framework, a review of some of the most  relevant modeling approaches and numerical discretization techniques can be found in [15].The collected papers of this issue are directed to discuss modern developments and trends in the accurate  numerical modeling of free surface flows. We can divide the contributions into two main categories. The first one involves papers dealing with the discretisation of dispersive equations and the second includes the  works  on  wave  breaking.  Indeed,  in  the  last  decades,  asymptotic  depth  average  models  like  Boussinesq type models that involve dispersive terms, are widely used to simulate the coastal processes. The discretization of these models usually lead to numerical models that are of practical use in design  compared to the ones produced by more complicated mathematical models like the Euler equations. A review on the history and all fundamental aspects of the Boussinesq type (BT) models can be found in [3,15]. The works in the first category of this issue aims to answer some open problems concerning the  discetisation of this type of models such as the absorbing boundary conditions for the simulation of waves on bounded domains [2] , the reduction of the computational cost which arise from the multi-step time  schemes used to discretise the BT models [4] and the efficient discretisation of fully dispersive models  with source terms [7]. The second category of this special issue deals with the topic of wave breaking. This is a very wide and active field of research [12]. The contributions in this issue are concerned with wave breaking at the  surface of the ocean and not with the breaking of internal waves which is also an important phenomenon and is connected to global ocean circulation [19].  Problems arising from fundamental research and real  applications in coastal  environments demand accurate descriptions of both breaking inception and the  details of the breaking process [1,12-14,16,18].  The directions of research that the works of this issue attempt to contribute are the identification and classification of different type of wave breaking [6], the reduction of the computational cost in the accurate description of wave breaking using non hydrostatic Reynolds Averaged Navier-Stokes equations [10], and the understanding of the wave breaking closures  for Boussinesq type models [11].  Contributions in this issue:In the work entitled Perfectly matched layers methods for mixed hyperbolic-dispersive equations [2], the authors deal with absorbing boundary conditions for the simulation of propagation of waves on bounded numerical domains. They study the stability of classical perfectly matched layer (PML) equations for  different types of linear dispersive water wave models.  They apply the PML strategy to the linearized Korteweg-de Vries equation,  and show analytically and numerically that  this  approach is  not  always stable.  They  introduce  a  hyperbolic  system  with  a  source  term  which  formally  approximates  the Korteweg-de  Vries  equation  and  show  its  ability  to  mimic  most  of  the  classical  properties  of  the  Korteweg-de Vries equation. Finally they consider a class of more realistic water wave model,  namely mixed BBM-Boussinesq systems that describe the evolution of a shallow layer of inviscid fluid, The authors prove a complete stability for the associated PML equations and illustrate numerically that the PML technique works in this caseThe  paper  of  Cauquis,  Ricchiuto  and  Heinrich  [3]  entitled  Lax-Wendroff  schemes  with  polynomial extrapolation and simplified Lax-Wendroff schemes for dispersive waves: a comparative study  focuses on novel  approaches based on the classical  Lax-Wendroff  strategy to achieve single step high order  schemes in  time for  the  Boussinesq and the enchanted Boussinesq equations.  To reduce the cost  of  evaluating the complex correction terms arising in the Lax-Wendroff procedure for Boussinesq equations,  the authors propose several simplified strategies which allow to reduce the computational time at fixed accuracy.  To  evaluate  these  qualities,  they  perform a  spectral  analysis  to  assess  the  dispersion  and damping error. They then evaluate the schemes on several benchmarks involving dispersive propagation  over flat and non-flat bathymetries, and perform numerical grid convergence studies on two of them.  Their  results show a potential  for  a CPU reduction between 35% and 40% to obtain accuracy levels comparable to those of the classical RK3 method.The paper by Desmons and Lubin [6] investigates a new type of breaker, proposed by [20] by detailing several geometric aspects which lead to the unusual size and behavior of some very large plunging jets  generated when waves break above some drastic  changes of  bathymetry.  The authors  investigate  all geometrical aspects of the breaking process, to propose a classification of the breaker types which were observed in the numerical results. They  indicate the influences of the reef parameters (steps heights and  lengths) on the subsequent breaking process. They also show that the air entrainment was indeed much larger during the composite breaker occurrence.In the contribution of Guermond, Kees, Popov, and Tovar [7] a numerical method for approximating the dispersive Serre Green-Naghdi equations with topography using continuous finite elements, is presented. The method is an extension of the hyperbolic relaxation technique introduced in [8]. It is explicit, second-order accurate in space, third-order accurate in time, and is invariant domain preserving. It is also well-balanced and parameter free. Special attention is given to the convex limiting technique when physical source terms are added in the equations. The method is verified with academic benchmarks and validated by comparison with laboratory experimental data.  The contribution by Iravani, Badiel and Brocchini proposes a method to improve the performance of a  novel  RANS model  for breaking water waves.  More precisely the method uses a differential  grid to  reduce the computational cost  while maintaining a good accuracy. In this “sub grid” approach [10] the  pressure values are computed on a coarse grid while the velocities are solved on a finer grid. The grid  resolution is increased near the surface and bottom boundaries. The results show how the computational effort can be reduced up to 70% while providing more than satisfactory results for properties of interest for the coastal engineering practice, like wave height decay and mean water elevation.In the  Parameter  sensitivity  for  wave breaking closures  in  Boussinesq-type models [11],  the  authors Joshi, Kazolea and Ricchiuto are considering the issue of wave breaking closure for the weakly dispersive  fully nonlinear equations of Green-Naghdi. The authors make use of the sensitivity indices computed by means of Analysis of Variance (ANOVA) to provide the sensitivity of wave breaking simulation, using  two  different  wave breaking closures,  to the variation of parameters such as the mesh size and the  breaking parameters for each breaking model. The first wave breaking closure used  is a hybrid method consisting of suppressing the dispersive terms in the breaking region and the second one is  an eddy viscosity approach based on the solution of a turbulent kinetic energy model. In the contribution  Efficient numerical computations of long-wave run-up and their sensitivity to grid nesting [17], Mihami, Roeber and Morichon present a novel numerical approach to the shallow-water equations based on an explicit  second-order finite-volume scheme with a staggered grid. The authors  implement their method and demonstrate that  the code is  well  balanced and can handle shock fronts  efficiently.  Grid  nesting  is  used  to  improve  computational  efficiency,  and  it  is  shown that  accurate predictions of long-wave run-up can be achieved with less computational effort than would be necessary in existing codes.Acknowledgments We are grateful to H. Kalisch and M. Groves, the editors-in-chief of this journal for providing a forum for this collection of papers, and we thank the journal staff for providing support throughout the preparation of  this  Special  Issue.  Finally,  we  would  like  to  thank  the  authors  for  submitting  high-quality contributions, and the reviewers for their valuable service.References [1] Bacigaluppi, P., Ricchiuto, M. and Bonneton, P. Implementation and evaluation of breaking detection criteria for a hybrid boussinesq model. Water waves 2, 207-241, 2020.[2] Besse, C., Gavrilyuk, S., Kazakova, M. and Noble, P., 2022. Perfectly Matched Layers Methods for Mixed Hyperbolic–Dispersive Equations. Water Waves, pp.1-31.[3] Brocchini, M. A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics, Proc. R. Soc. A, 469, 2013.[4] Cauquis, A., Ricchiuto, M. and Heinrich, P., 2022. Lax–Wendroff Schemes with Polynomial Extrapolation and Simplified Lax–Wendroff Schemes for Dispersive Waves: A Comparative Study. Water Waves, pp.1-33.[5] Derakhti, M., Kirby, J.T., Banner, M.L., Grilli, S.T. and Thomson, J., 2020. A unified breaking onset criterion for surface gravity water waves in arbitrary depth. Journal of Geophysical Research: Oceans, 125(7), p.e2019JC015886.[6] Desmons, F. and Lubin, P., 2022. Numerical Simulations of Waves Breaking over a Rectangular Submerged Reef Consisting of a Double Step: Analogies with massive Natural Wave Breaking over Abrupt Bathymetries. Water Waves, pp.1-29.[7] Guermond, J.L., Kees, C., Popov, B. and Tovar, E., 2022. Well-Balanced Second-Order Convex Limiting Technique for Solving the Serre–Green–Naghdi Equations. Water Waves, pp.1-37.[8] Guermond, J.-L. Maier, M., Popov, B. and Tomas, I. Second-order invariant domain preserving approximation of the compressible Navier–Stokes equations. Computer Methods in Applied Mechanics and Engineering, 375(1):113608, 2021.[9] Hatland, S. and Kalisch, H. Wave breaking in undular bores generated by a moving weir. Physics of Fluids, 31, 033601, 2021.[10] Iravani, N., Badiei, P., and Brocchini, M. Novel free surface boundary conditions for spilling breaking waves. “Coastal Engineering”, 159, 103717, 2020.[11] Joshi, S., Kazolea, M. and Ricchiuto, M., 2022. Parameter sensitivity for wave breaking closures in Boussinesq-type models. Water Waves, pp. [12] Kalisch, H., Ricchiuto, M., Bonneton, P., Colin, M., and Lubin, P. Introduction to the special issue on breaking waves. European Journal of Mechanics-B/Fluids, 73, 1-5, 2019.[13] Kazolea, M., Delis, A.I., Synolakis, C.E. Numerical treatment of wave breaking on unstructured Finite Volume approximations for extended Boussinesq-type equations. J. Comput. Phys. 271, 281–305, 2014.[14] Kazolea, M. and Ricchiuto, M. On wave breaking for Boussinesq-type models, Ocean Modelling 123:16-39, 2018.[15] Kirby, J.T. Recent advances in nearshore wave, circulation and sediment transport modelling. Journal of Marine Research 75 : 263-300, 2017.[16] Lubin, P. and Chanson, H. Are breaking waves, bores, surges and jumps the same flow? Environ. Fluid Mech. 17, 47–77, 2017.[17] Mihami, F.-Z., Roeber, V. and Morichon, D. Efficient numerical computations of long-wave run-up and their sensitivity to grid nesting, Water Waves, to appear.[18] Robertson, B., Hall, K., Zytner, R., and Nistor, I. Breaking waves: review of characteristic relationships. Coast. Eng. J. 55(1), 13500021–135000240, 2013.[19] Wunsch, C. and Ferrari, R., Vertical mixing, energy, and the general circulation of the oceans, Annual Review of Fluid Mechanics 36, 281–314, 2004.[20] Yasuda, T., Mutsuda, H., Oya, A., Tada, A., and Fukumoto, T. A new type breaker forming a giant jetand its decaying properties. Proc. 25th International Conferences Coastal Engineering, 300–313, 1996.

Introduction to the special issue on numerical methods and applications for waves in coastal environments

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Introduction to the special issue on numerical methods and applications for waves in coastal environments

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