Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2009.08937

Development and validation of a numerical wave tank based on the Harmonic Polynomial Cell and Immersed Boundary methods to model nonlinear wave-structure interaction

Fabien Robaux·Michel Benoit
View original source ↗Read source document ↗Export metadata ↓

Abstract

A fully nonlinear potential Numerical Wave Tank (NWT) is developed in two dimensions, using a combination of the Harmonic Polynomial Cell (HPC) method for solving the Laplace problem on the wave potential and the Immersed Boundary Method (IBM) for capturing the free surface motion. This NWT can consider fixed, submerged or wall-sided surface piercing, bodies. To compute the flow around the body and associated pressure field, a novel multi overlapping grid method is implemented. Each grid having its own free surface, a two-way communication is ensured between the problem in the body vicinity and the larger scale wave propagation problem. Pressure field and nonlinear loads on the structure are computed by solving a boundary value problem on the time derivative of the potential. The stability and convergence properties of the solver are studied basing on extensive tests with standing waves of large to extreme wave steepness, up to $H/\lambda=0.2$ ($H$ is the crest-to-trough wave height and $\lambda$ the wavelength). Ranges of optimal time and spatial discretizations are determined and high-order convergence properties are verified, first without using any filter. For cases with either high level of nonlinearity or long simulation duration, the use of mild Savitzky-Golay filters is shown to extend the range of applicability of the model. Then, the NWT is tested against two wave flume experiments, analyzing forces on bodies in various wave conditions. First, nonlinear components of the vertical force acting on a small horizontal circular cylinder with low submergence below the mean water level are shown to be accurately simulated up to the third order in wave steepness. The second case is a dedicated experiment with a floating barge of rectangular cross-section. This very challenging case (body with sharp corners in large waves) allows to examine the behavior (...to continue...)

Explore related subjects

physics.flu-dyn

Keep this discovery

BibTeXRIS

Fabien Robaux, Michel Benoit. 2020-09-18. Development and validation of a numerical wave tank based on the Harmonic Polynomial Cell and Immersed Boundary methods to model nonlinear wave-structure interaction. https://doi.org/10.1016/j.jcp.2021.110560

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Correlative effects of induced magnetic field-buoyancy on reactive solute dispersion dynamics in couple-stress fluids

We investigate the dispersion of a reactive solute in a couple-stress fluid flowing between two parallel plates under the combined effects of pressure-driven flow, buoyancy, and an induced magnetic field. The model incorporates first-order heterogeneous reactions at both channel walls alongside a bulk reaction. Using Mei's multiscale homogenization technique accurate to third order, we develop a higher-order asymptotic formulation to determine the effective longitudinal dispersion coefficient and concentration field. Analytical predictions are complemented by Brownian dynamics simulations and finite-difference solutions, while the Aris method of moments quantifies transient mean displacement, spatial variance, and effective dispersivity. The hydrodynamic analysis reveals a singular branch in the velocity solution when the Hartmann number equals half the couple-stress parameter and identifies a characteristic quarter-power scaling between the Hartmann number and couple-stress parameter, separating couple-stress- and magnetically dominated regimes. The model recovers classical Taylor-dispersion behavior in the non-reactive Newtonian limit and agrees well with experimental measurements. Couple-stress rheology and magnetic damping suppress shear-induced dispersion, whereas buoyancy enhances dispersion through additional transverse velocity gradients. A distinct saturation regime of the dispersion coefficient emerges with an increasing couple-stress parameter, while unequal wall absorption induces persistent transverse asymmetry, and stronger absorption enhances solute removal near the source. Numerical and stochastic results validate the analytical framework while resolving higher-order concentration structures and particle-scale wall adsorption.

physics.flu-dyn↗
arXiv2026

DiffSWE2d: a differentiable Shallow Water Equations solver for end-to-end flood and tsunami modelling

Solving inverse and optimisation problems with traditional shallow water equations (SWE) solvers can be computationally expensive, particularly when gradients with respect to model inputs or parameters must be estimated through repeated forward simulations. In this paper, we introduce DiffSWE2d, an open-source differentiable shallow water equations solver for end-to-end flood and tsunami modelling implemented in PyTorch. By leveraging automatic differentiation, DiffSWE2d represents the time-marching physics as a differentiable computational graph, enabling gradients to be propagated directly through the numerical solver. We validate the solver against two established benchmark cases and demonstrate its application to tsunami waveform inversion, showing its ability to infer model inputs through gradient-based optimisation. DiffSWE2d provides a flexible framework for integrating physics-based hydrodynamic modelling with modern optimisation and machine learning methods. The source code and reproducible examples are publicly available at: https://github.com/ZhonghouXu/DiffSWE2d

physics.flu-dyn↗
arXiv2026

Low inertia limit of elasto-inertial turbulence

Pipe and channel flows of viscoelastic fluids display chaotic dynamics at unusually low speeds, a phenomenon referred to as elasto-inertial turbulence, EIT. First reported in experiments a century ago, recent theoretical studies and model computations predict a variety of scenarios for the phenomenon's origin, ranging from hoop stress modes to center modes and to Tollmien-Schlichting waves. Lacking experimental confirmation, the relevant scenario in actual flows of polymer solutions remains unknown. We here determine the transition threshold of EIT in pipe experiments, covering three decades in elasticity number. Across this entire parameter range, the transition features center mode structures at onset. Eventually the instability diverges at a lower inertia (upper elasticity) limit, which is a robust signature of this center mode scenario. Finally, we report the first experimental observation of a traveling wave in viscoelastic pipe flow, and the sequences of localized structures found, are in excellent agreement with a center mode traveling wave, the "arrowhead" solution, discovered in model simulations.

physics.flu-dyn↗