A stabilised nodal spectral element method for fully nonlinear water waves

DOI10.1016/j.jcp.2016.04.060zbMath1349.76570arXiv1512.02548OpenAlexW2196462249WikidataQ57820583 ScholiaQ57820583MaRDI QIDQ726811

Allan P. Engsig-Karup, Claes Eskilsson, Daniele Bigoni

Publication date: 5 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.02548

zbMATH Keywords

spectral element methodfinite element methodsunstructured meshhydrodynamicshigh-order discretisationnonlinear and dispersive free surface waves

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Spectral methods applied to problems in fluid mechanics (76M22) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items

Development and validation of a numerical wave tank based on the harmonic polynomial cell and immersed boundary methods to model nonlinear wave-structure interaction, A mixed Eulerian-Lagrangian spectral element method for nonlinear wave interaction with fixed structures, A spectral/\(h p\) element depth-integrated model for nonlinear wave-body interaction, Implementation of a fully nonlinear Hamiltonian coupled-mode theory, and application to solitary wave problems over bathymetry, A coupled finite and boundary spectral element method for linear water-wave propagation problems, A conservative scheme for simulation of free-surface turbulent and wave flows, OpenMP parallelism in computations of three-dimensional potential numerical wave tank for fully nonlinear simulation of wave-body interaction using NURBS

Uses Software

• Nek5000

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On devising Boussinesq-type models with bounded eigenspectra: one horizontal dimension
• A harmonic polynomial cell (HPC) method for 3D Laplace equation with application in marine hydrodynamics
• Dealiasing techniques for high-order spectral element methods on regular and irregular grids
• A spectral element method for fluid dynamics: Laminar flow in a channel expansion
• Nodal DG-FEM solution of high-order Boussinesq-type equations
• An explicit construction of interpolation nodes on the simplex
• An efficient flexible-order model for 3D nonlinear water waves
• A finite element method for fully nonlinear water waves
• De-aliasing on non-uniform grids: algorithms and applications.
• Fully nonlinear wave interaction with freely floating non-wall-sided structures
• Free-surface flow simulation using \(hp\)/spectral elements
• Mesh update techniques for free-surface flow solvers using spectral element method
• Quasi ALE finite element method for nonlinear water waves
• On the accuracy of finite-difference solutions for nonlinear water waves
• Spectral Methods for Time-Dependent Problems
• Filtering in Legendre spectral methods
• Implementing Spectral Methods for Partial Differential Equations
• Taming the CFL Number for Discontinuous Galerkin Methods on Structured Meshes
• The deformation of steep surface waves on water - I. A numerical method of computation
• Basis Functions for Triangular and Quadrilateral High-Order Elements
• Numerical wave tank based on a ?-transformed finite element inviscid flow solver
• High-Order Methods for Incompressible Fluid Flow
• Local and global smoothing of discontinuous finite element functions using a least squares method
• A massively parallel GPU‐accelerated model for analysis of fully nonlinear free surface waves
• Analysis of efficient preconditioned defect correction methods for nonlinear water waves
• A comparison of gradient recovery methods in finite‐element calculations
• Finite element assembly strategies on multi‐core and many‐core architectures
• A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics
• The numerical computation of freely propagating time-dependent irrotational water waves
• Spectral Methods
• Spectral/hp Element Methods for Computational Fluid Dynamics
• A fast algorithm for particle simulations