Journal ArticleDOI
Corner problems and global accuracy in the boundary element solution of nonlinear wave flows
Stephan T. Grilli,Ib A. Svendsen +1 more
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In this article, a more stable free surface representation based on quasi-spline elements and an improved corner solution combining the enforcement of compatibility relationships in the double-nodes with an adaptive integration was proposed.Abstract:
The numerical model for nonlinear wave propagation in the physical space, developed by Grilli, et al. 12,13 , uses a higher-order BEM for solving Laplace's equation, and a higher-order Taylor expansion for integrating in time the two nonlinear free surface boundary conditions. The corners of the fluid domain were modelled by double-nodes with imposition of potential continuity. Nonlinear wave generation, propagation and runup on slopes were successfully studied with this model. In some applications, however, the solution was found to be somewhat inaccurate in the corners and this sometimes led to wave instability after propagation in time. In this paper, global and local accuracy of the model are improved by using a more stable free surface representation based on quasi-spline elements and an improved corner solution combining the enforcement of compatibility relationships in the double-nodes with an adaptive integration which provides almost arbitrary accuracy in the BEM numerical integrations. These improvements of the model are systematically checked on simple examples with analytical solutions. Effects of accuracy of the numerical integrations, convergence with refined discretization, domain aspect ratio in relation with horizontal and vertical grid steps, are separately assessed. Global accuracy of the computations with the new corner solution is studied by solving nonlinear water wave flows in a two-dimensional numerical wavetank. The optimum relationship between space and time discretization in the model is derived from these computations and expressed as an optimum Courant number of ∼0.5. Applications with both exact constant shape waves (solitary waves) and overturning waves generated by a piston wavemaker are presented in detail.read more
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Journal ArticleDOI
A fully non‐linear model for three‐dimensional overturning waves over an arbitrary bottom
TL;DR: In this article, an accurate three-dimensional numerical model, applicable to strongly non-linear waves, is proposed, where boundary geometry and field variables are represented by 16-node cubic ‘sliding’ quadrilateral elements, providing local inter-element continuity of the first and second derivatives.
Journal ArticleDOI
Modeling of waves generated by a moving submerged body. Applications to underwater landslides
Stephan T. Grilli,P. Watts +1 more
TL;DR: In this paper, a boundary element model of an underwater landslide is developed, and careful gridding and time stepping techniques are demonstrated that produce highly accurate simulation results based on conservation of volume.
Journal ArticleDOI
Development of a 3D numerical wave tank for modeling tsunami generation by underwater landslides
TL;DR: In this article, a three-dimensional numerical wave tank (NWT) solving fully nonlinear potential flow theory, with a higher-order boundary element method (BEM), is modified to simulate tsunami generation by underwater landslides.
Journal ArticleDOI
Shoaling of Solitary Waves on Plane Beaches
TL;DR: Shoaling of solitary waves on both gentle (1:35) and steeper slopes ( 1:6.50) is analyzed up to breaking using both a fully nonlinear wave model and high-accuracy laboratory experiments.
Journal ArticleDOI
Numerical Generation and Absorption of Fully Nonlinear Periodic Waves
Stephan T. Grilli,Juan Horrillo +1 more
TL;DR: In this article, permanent form periodic waves with zero-average mass flux are generated in a two-dimensional numerical wave tank solving fully nonlinear potential flow equations, and an absorbing beach is modeled at the end of the tank in which an external free-surface pressure absorbs energy from high frequency waves; and a piston-like condition absorbing energy from low-frequency waves.
References
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Journal ArticleDOI
The Deformation of Steep Surface Waves on Water. I. A Numerical Method of Computation
TL;DR: In this paper, the authors present a method for following the time-history of space-periodic irrotational surface waves, where the only independent variables are the coordinates and velocity potential of marked particles at the free surface at each time step an integral equation is solved for the new normal component of velocity.
DissertationDOI
Tsunamis -- the propagation of long waves onto a shelf
TL;DR: In this paper, a numerical method of solving the Boussinesq equations for constant depth using finite element techniques is presented, which is extended to the case of an arbitrary variation in depth (i.e., gradually to abruptly varying depth).
Journal ArticleDOI
An efficient boundary element method for nonlinear water waves
TL;DR: In this paper, a computational model for highly nonlinear 2D water waves in which a high-order Boundary Element Method is coupled with a high order explicit time stepping technique for the temporal evolution of the waves is presented.
Journal ArticleDOI
Numerical simulation of breaking waves
TL;DR: In this article, the authors present a similar method, but with the exception that the problem is solved in the physical plane and finite depth is introduced, whereas in this paper, the same problem is stated in the same way, except that certain other effects can be included without much modification of the program.
Journal ArticleDOI
The stability of solitary waves
TL;DR: In this article, the stability of finite amplitude, two-dimensional solitary waves of permanent form in water of uniform depth with respect to 2D infinitesimal disturbances is investigated and numerically confirmed that the results obtained by Saffman (submitted to J. Fluid Mech.) for the superharmonic instability of periodic waves hold also in the case of solitary waves.