Energy-decomposition analysis for viscous free-surface flows

International Journal for Numerical Methods in Fluids, 2005

A semi-implicit, staggered ÿnite volume technique for non-hydrostatic, free-surface ow governed by the incompressible Euler equations is presented that has a proper balance between accuracy, robustness and computing time. The procedure is intended to be used for predicting wave propagation in coastal areas. The splitting of the pressure into hydrostatic and non-hydrostatic components is utilized. To ease the task of discretization and to enhance the accuracy of the scheme, a vertical boundary-ÿtted co-ordinate system is employed, permitting more resolution near the bottom as well as near the free surface. The issue of the implementation of boundary conditions is addressed. As recently proposed by the present authors, the Keller-box scheme for accurate approximation of frequency wave dispersion requiring a limited vertical resolution is incorporated. The both locally and globally mass conserved solution is achieved with the aid of a projection method in the discrete sense. An e cient preconditioned Krylov subspace technique to solve the discretized Poisson equation for pressure correction with an unsymmetric matrix is treated. Some numerical experiments to show the accuracy, robustness and e ciency of the proposed method are presented. surface level. We come back to this point later. In the same step, the free-surface condition is reconsidered to assure global mass conservation. From a computational point of view, this improvement implies no requirement of the ÿrst fractional step. Hence, this method has a reduced splitting error. An alternative is proposed by Chen [12], where the pressure Poisson equation is ÿrst solved to obtain the non-hydrostatic pressure and subsequently correct the velocities. Thereafter, the surface elevation followed by the velocity ÿeld is updated. However, the momentum equations must be solved twice per time step, whereas usually the momentum equations are solved once per time step as done in References .

Physics of Fluids, 2022

This study examines the mass and Lagrangian transport, kinematic and dynamic characteristics of shallow-water breaking waves, focusing on the wave breaking, and jet impingement processes. A multiphase Navier–Stokes flow model has been developed to track the origin and trajectory for the jet and the splash-up using both a geometric piece-wise linear interface calculation volume-of-fluid (PLIC-VOF) and the Lagrangian particle tracking approaches. The model is first validated both quantitatively and qualitatively against the experimental data for the plunging jet and the splash-up during wave breaking, in which a good agreement is obtained. The mass transport and the origin of the jet and splash-up are studied using the new multi-component PLIC-VOF approach, and the different regions in the interior of the wave are tracked in an Eulerian way. Both horizontal and vertical drifts for the interior and surface particles are shown using the Lagrangian particles. The location and origin of t...

Computers & Fluids, 2008

This paper focuses on the energy budget in the calculation of unsteady free-surface flows on moving grids with and without using the 'arbitrary Lagrangian-Eulerian' (ALE) formulation or hydrostatic-pressure assumption. The numerical tool is an in-house general-purpose solver for the unsteady, incompressible and homogeneous Navier-Stokes equations in a Cartesian domain. An explicit fractionalstep method and co-located finite-volume method are used for the second-order accurate integrations in time and space. The test cases are nonlinear and linear irrotational standing waves, which allow to characterise the impacts of an ALE or Eulerian formulation with moving grids by comparison with the anticipated energy conservation. The study is also extended to viscous waves for varying waveheight-to-water-depth and basin aspect ratios. The Eulerian viewpoint produces marked overdamping as early as in the first wave period for the range of relative wave heights g 0 /h > 0.01, where g 0 is the wave semi-amplitude and h is the undisturbed water depth. The hydrostatic calculations misrepresent the evolution of the potential and kinetic energies for h/L > 0.1, where L is the basin length, with spurious modes arising from different initial conditions.

This paper assesses some recent trends in the novel numerical meshless method smoothed particle hydrodynamics, with particular focus on its potential use in modelling free-surface flows. Due to its Lagrangian nature, smoothed particle hydrodynamics (SPH) appears to be effective in solving diverse fluid-dynamic problems with highly nonlinear deformation such as wave breaking and impact, multi-phase mixing processes, jet impact, sloshing, flooding and tsunami inundation, and fluid-structure interactions. The paper considers the key areas of rapid progress and development, including the numerical formulations, SPH operators, remedies to problems within the classical formulations, novel methodologies to improve the stability and robustness of the method, boundary conditions, multi-fluid approaches, particle adaptivity, and hardware acceleration. The key ongoing challenges in SPH that must be addressed by academic research and industrial users are identified and discussed. Finally, a roadmap is proposed for the future developments.

1 Ocean Engineering Laboratory, UCSB.

2010

arXiv: Numerical Analysis, 2013

We propose a unified approach to the formal long-wave reduction of several fluid models for thin-layer incompressible homogeneous flows driven by a constant external force like gravity. The procedure is based on a mathematical coherence property that univoquely defines one reduced model given one rheology and one thin-layer regime. For the first time, as far as we know, various known reduced models can thus be investigated within a single mathematical framework, for various rheologies (viscous and viscoelastic) and various limit regimes (fast inertial flows and slow viscous flows). Furthermore, our systematic procedure also produces new reduced models for viscoelastic non-Newtonian fluids and improves on our previous work [Bouchut & Boyaval, M3AS (23) 8, 2013].

International Journal for Numerical Methods in Fluids, 2013

In this paper, we study how accurately the Smoothed Particle Hydrodynamics (SPH) scheme accounts for the conservation and the generation of vorticity and circulation, in a low viscosity, weakly compressible, barotropic fluid in the context of free-surface flows. We consider a number of simple examples to clarify the processes involved and the accuracy of the simulations. The first example is a differentially rotating fluid where the integration path for the circulation becomes progressively more complicated, whereas the structure of the velocity field remains simple. The second example is the collision of two rectangular regions of fluid. We show that SPH accurately predicts the time variation of the circulation as well as the total vorticity for selected domains advected by the fluid. Finally, a breaking wave is considered. For such a problem we show how the dynamics of the vorticity generated by the breaking process is captured by the SPH model.

We study the break-down mechanism of smooth solution for the gravity water-wave equation of infinite depth. It is proved that if the mean curvature κ of the free surface Σt, the trace (V, B) of the velocity at the free surface, and the outer normal derivative ∂P ∂n of the pressure P satisfy

2013

The meshless method Smoothed Particle Hydrodynamics (SPH) is one of the primarily developed numerical methods in the meshless methods family. It has been proven to work well with problems of free surface fluid flows. For the purpose of this thesis, the Smoothed Particle Hydrodynamics method and its current capabilities were studied. Using the obtained knowledge from the literature, a free surface fluid flow application was implemented in the framework of KRATOS multiphysics. Some well known benchmark problems were reproduced using the generated SPH solver. The algorithm's ability to catch the correct free surface evolution and obtain an accurate pressure distribution of free surface problems were analyzed. Furthermore, some programming aspects of coding for meshless methods were discussed from the computational workload point of view. Using the developed application, it was demonstrated that in order to create a generic SPH fluid solver that is able to model any type of fluid, some additional corrections must be applied to the SPH solution. These corrections, although being very convenient to obtain good particle tracking of the fluid motion, affect the pressure distribution of the flow excessively and make the weakly compressible SPH method untrusted for the pressure results of fluid flow problems. Foremost, I would like to express my gratitude to my supervisors in this thesis, Antonia Larese and Riccardo Rossi, for making this work possible by all the guidance that they have provided. Without their contribution, obtaining this work would be impossible. I would also like to thank all the KRATOS and CIMNE staff for giving me all the help they could whenever I needed, especially to my collegues Carlos Roig Pina, Miquel Santasusana and Pablo Becker for not turning down my overwhelming questions even though they are already very busy themselves. Last but not the least, I would like to thank my parents, Ayşen and Sümer Karacaova for all the support that they have given me through all my studying life. Despite the distance between us throughout the development of this work, they have always provided me with the necessary ambition needed to comply my goals. Π ij Artificial viscosity term σ Stress Tensor