Ensuring numerical stability of wave propagation by tuning model parameters using genetic algorithms and response surface methods

Abstract The effectiveness of a Metamodel-Embedded Evolution Framework for model parameter identification of a Smoothed Particles Hydrodynamic (SPH) solver, called DualSPHysics, is demonstrated when applied to the generation and propagation of progressive ocean waves. DualSPHysics is an open-source code that provides GP-GPU acceleration, allowing for highly refined simulations. The automatic optimization framework combines the global-convergence capabilities of a Multi-Objective Genetic Algorithm (MOGA) with Response Surface Method (RSM) based on a Kriging approximation. The proposed Metamodel-Embedded Evolutionary framework is used to find the set of SPH model parameters that ensures an accurate reproduction of a 2 n d order Stokes wave propagating in a numeric flume tank. In order to demonstrate the consistency of the obtained results, the optimum set of parameters found by the framework is finally used to reproduce other 2 n d and 3 r d order Stokes waves propagating over the same flume tank.

[1]  I. Losada,et al.  Simulating coastal engineering processes with OpenFOAM , 2013 .

[2]  Andy J. Keane,et al.  Engineering Design via Surrogate Modelling - A Practical Guide , 2008 .

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

[4]  Andrea Colagrossi,et al.  A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH , 2009, Comput. Phys. Commun..

[5]  Kwok-wing Chau.  Selection and Calibration of Numerical Modeling in Flow and Water Quality , 2004 .

[6]  Régis Duvigneau,et al.  Kriging‐based optimization applied to flow control , 2012 .

[7]  Alessandro Dal Palù,et al.  GPU-enhanced Finite Volume Shallow Water solver for fast flood simulations , 2014, Environ. Model. Softw..

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

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

[10]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[11]  Robert G. Dean,et al.  Water wave mechanics for engineers and scientists , 1983 .

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

[13]  Corrado Altomare,et al.  Long-crested wave generation and absorption for SPH-based DualSPHysics model , 2017 .

[14]  P. B. Smit,et al.  Non-hydrostatic modeling of surf zone wave dynamics , 2014 .

[15]  Emanuele Barca,et al.  An automated decision support system for aided assessment of variogram models , 2017, Environ. Model. Softw..

[16]  Raghavan Srinivasan,et al.  Efficient multi-objective calibration of a computationally intensive hydrologic model with parallel computing software in Python , 2013, Environ. Model. Softw..

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

[18]  Benedict D. Rogers,et al.  Towards accelerating smoothed particle hydrodynamics simulations for free-surface flows on multi-GPU clusters , 2012, J. Parallel Distributed Comput..

[19]  Patrizia Piro,et al.  On the use of surrogate-based modeling for the numerical analysis of Low Impact Development techniques , 2017 .

[20]  Benedict Leimkuhler,et al.  Integration Methods for Molecular Dynamics , 1996 .

[21]  Stefano Gaggero,et al.  Design of contracted and tip loaded propellers by using boundary element methods and optimization algorithms , 2016 .

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

[23]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[24]  Harry B. Bingham,et al.  A new Boussinesq method for fully nonlinear waves from shallow to deep water , 2002, Journal of Fluid Mechanics.

[25]  A. Colagrossi,et al.  On the filtering of acoustic components in weakly-compressible SPH simulations , 2017 .

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

[27]  J. Monaghan,et al.  A refined particle method for astrophysical problems , 1985 .

[28]  Christos Makropoulos,et al.  Multiobjective optimisation on a budget: Exploring surrogate modelling for robust multi-reservoir rules generation under hydrological uncertainty , 2015, Environ. Model. Softw..

[29]  P. Amparo López-Jiménez,et al.  Performance assessment of OpenFOAM and FLOW-3D in the numerical modeling of a low Reynolds number hydraulic jump , 2016, Environ. Model. Softw..

[30]  Giuliano Vernengo,et al.  Numerical investigation on the hydrodynamic performance of fast SWATHs with optimum canted struts arrangements , 2017 .

[31]  Bryan A. Tolson,et al.  Review of surrogate modeling in water resources , 2012 .

[32]  Stefano Brizzolara,et al.  Numerical Modeling of Breaking Periodical Waves on a Sloped Beach Profile by SPH , 2014 .

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

[34]  D. Ian Austin,et al.  A NUMERICAL MODEL OF WAVE/BREAKWATER INTERACTIONS , 1982 .

[35]  Daniel L. Clark,et al.  Engineering Design Exploration Using Locally Optimized Covariance Kriging , 2016 .

[36]  Farrokh Mistree,et al.  Kriging Models for Global Approximation in Simulation-Based Multidisciplinary Design Optimization , 2001 .

[37]  Hitoshi Gotoh,et al.  Lagrangian Particle Method for Simulation of Wave Overtopping on a Vertical Seawall , 2005 .

[38]  Jin Li,et al.  Application of machine learning methods to spatial interpolation of environmental variables , 2011, Environ. Model. Softw..

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

[40]  J. Monaghan,et al.  Solitary Waves on a Cretan Beach , 1999 .

[41]  George Em Karniadakis,et al.  A multi-fidelity framework for investigating the performance of super-cavitating hydrofoils under uncertain flow conditions , 2017 .

[42]  Jérémy Rohmer,et al.  A meta-modelling strategy to identify the critical offshore conditions for coastal flooding , 2012 .

[43]  Paolo Mignosa,et al.  3D SPH numerical simulation of the wave generated by the Vajont rockslide , 2013 .

[44]  Corrado Altomare,et al.  Hybridization of the Wave Propagation Model SWASH and the Meshfree Particle Method SPH for Real Coastal Applications , 2015 .

[45]  Giuliano Vernengo,et al.  Simulation based design of a fleet of ships under power and capacity variations , 2016 .

[46]  Per A. Madsen,et al.  Simulation of nonlinear wave run-up with a high-order Boussinesq model , 2008 .

[47]  Student,et al.  THE PROBABLE ERROR OF A MEAN , 1908 .

[48]  Jonathan L. Goodall,et al.  Design and implementation of a general software library for using NSGA-II with SWAT for multi-objective model calibration , 2016, Environ. Model. Softw..

[49]  C. Friedland,et al.  Isotropic and anisotropic kriging approaches for interpolating surface-level wind speeds across large, geographically diverse regions , 2017 .

[50]  G. Matheron.  Principles of geostatistics , 1963 .

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

[52]  A. Colagrossi,et al.  δ-SPH model for simulating violent impact flows , 2011 .

[53]  George Keith Batchelor,et al.  An Introduction to Fluid Dynamics. , 1969 .

[54]  A. O'Hagan,et al.  Predicting the output from a complex computer code when fast approximations are available , 2000 .

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

[56]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[57]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

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

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

[60]  Robert A. Dalrymple,et al.  3D SPH Simulation of large waves mitigation with a dike , 2007 .

[61]  J. Kirby,et al.  BOUSSINESQ MODELING OF WAVE TRANSFORMATION, BREAKING, AND RUNUP. II: 2D , 2000 .

[62]  Tomohiro Suzuki,et al.  The applicability of SWASH model for wave transformation and wave overtopping: A case study for the Flemish coast , 2011 .

[63]  M. Gómez-Gesteira,et al.  Smoothed particle hydrodynamics applied in fluid structure interactions , 2013 .

[64]  J. Winter.  Practical Assessment, Research, and Evaluation Practical Assessment, Research, and Evaluation Using the Student's t-test with extremely small sample sizes Using the Student's t-test with extremely small sample sizes , 2022 .

[65]  Francesca Pianosi,et al.  A Matlab toolbox for Global Sensitivity Analysis , 2015, Environ. Model. Softw..