A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate the interactions of extreme waves and three‐dimensional structures. The present implementation follows the classic VOF implementation for the liquid–gas system, considering only the liquid phase. Extrapolation algorithms are used to obtain velocities and pressure in the gas region near the free surface. The VOF technique is validated against the classic dam‐break problem, as well as series of 2D sloshing experiments and results from SPH calculations. These and a series of other examples demonstrate that the ability of the present approach to simulate violent free surface flows with strong nonlinear behaviour.
Abstract
A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate the interactions of extreme waves and three‐dimensional structures. The present implementation follows [...]
We present an efficient technique for the solution of free surface flow problems using level set and a parallel edge‐based finite element method. An unstructured semi‐explicit solution scheme is proposed. A custom data structure, obtained by blending node‐based and edge‐based approaches is presented so to allow a good parallel performance. In addition to standard velocity extrapolation (for the convection of the level set function), an explicit extrapolation of the pressure field is performed in order to impose both the pressure boundary condition and the volume conservation. The latter is also improved with a modification of the divergence free constrain. The method is shown to allow an efficient solution of both simple benchmark cases and complex industrial examples
Abstract
We present an efficient technique for the solution of free surface flow problems using level set and a parallel edge‐based finite element method. An unstructured semi‐explicit solution [...]
In this paper, we present a finite element model for free surface flows on fixed meshes. The main novelty of the approach, compared with typical fixed mesh finite element models for such flows, is that we take advantage of the particularities of free surface flow, instead of considering it a particular case of two‐phase flow. The fact that a given free surface implies a known boundary condition on the interface, allows us to solve the Navier–Stokes equations on the fluid domain uncoupled from the solution on the rest of the finite element mesh. This, together with the use of enhanced integration allows us to model low Froude number flows accurately, something that is not possible with typical two‐phase flow models applied to free surface flow.
Abstract
In this paper, we present a finite element model for free surface flows on fixed meshes. The main novelty of the approach, compared with typical fixed mesh finite element models for such [...]
The simulation of low Froude number mould filling problems on fixed meshes presents significant difficulties. As the Froude number decreases, the coupling between the position of the interface and the resulting flow field increases. The usual two‐phase flow model provides poor results for such flow. In order to overcome the difficulties, a free surface model that applies boundary conditions at the interface accurately is used. Moreover, the use of wall laws on curved boundaries also fails in the case of low Froude number flows. To solve this second problem, we combine wall laws with ‘do nothing’ boundary conditions. A special feature of our approach is that ‘do nothing’ boundary conditions are only applied in the normal direction. These two key ingredients together with the Level Set method allow us to simulate three‐dimensional mould filling problems borrowed directly from the foundry.
Abstract
The simulation of low Froude number mould filling problems on fixed meshes presents significant difficulties. As the Froude number decreases, the coupling between the position of the interface [...]
The present work aims at handling uncertain materials in shape and topology optimisation applied to additive manufacturing. More specifically, we minimise an objective function combining the mean values of standard cost functions and assume that the uncertainties are small and generated by two random variables. These two variables representing the amplitude of the Young's modulus correspond to the zone of porosity inclusion and surface roughness defects. A deterministic approach that relies on a secondorder Taylor expansion of the cost function has been proposed by Allaire & Dapogny [2]. The present work proposes a general framework to handle uncertainties of the Young's modulus in which its amplitude is divided into N zones and then applied onto two zones corresponding to the porosity inclusion and surface roughness defects. We demonstrate the effectiveness of the approach in the context of the level-set-based topology optimisation for the robust compliance minimisation of three-dimensional cantilever test cases.
Abstract
The present work aims at handling uncertain materials in shape and topology optimisation applied to additive manufacturing. More specifically, we minimise an objective function combining the mean values of standard cost functions and assume that the uncertainties are small and [...]
Excessive erosion of sand beaches defines a serious problem worldwide and is particularly pronounced in the Mediterranean region. One of the typical measures for alleviating this erosion consists in building rigid breakwaters in the vicinity of the coast for diminishing sand transport. This solution, however, is often accompanied by undesirable alteration of the coastline. In this work we address the viability of using conceptually new structures with inflatable elements striving to improve the control over the sediment transport. The aim of the inflatable element is to adapt the breakwater configuration to the sea state. A preliminary design is proposed and tested in a number of storm scenarios using an in-house finite element/level set model. Influence of various breakwater design parameters upon its functionality is studied. Transmission coefficients and maximum pressures exerted upon the breakwater are estimated. Numerical study performed shows that for the considered range of storm scenarios the proposed design is characterized by transmission coefficients below 0.5. It is also shown that the use of inflatable elements facilitates adaptation of the breakwater functionality to a given sea state.
Abstract
Excessive erosion of sand beaches defines a serious problem worldwide and is particularly pronounced in the Mediterranean region. One of the typical measures for alleviating this erosion consists in building rigid breakwaters in the vicinity of the [...]
In this paper, we are going to present a high-order shock fitting approach based on a cut-cell method. We formulate a suitable Constraint Optimization Problem and develop an algorithm aiming to reconstruct the shock front represented by the zero iso-contour of a Level Set function.
Abstract
In this paper, we are going to present a high-order shock fitting approach based on a cut-cell method. We formulate a suitable Constraint Optimization Problem and develop an algorithm aiming to reconstruct the shock front represented by the zero iso-contour of a Level Set funct[...]
In this paper we propose a method to approximate flow problems in moving domains using always a given grid for the spatial discretization, and therefore the formulation to be presented falls within the category of fixed-grid methods. Even though the imposition of boundary conditions is a key ingredient that is very often used to classify the fixed-grid method, our approach can be applied together with any technique to impose approximately boundary conditions, although we also describe the one we actually favor. Our main concern is to properly account for the advection of information as the domain boundary evolves. To achieve this, we use an arbitrary Lagrangian–Eulerian framework, the distinctive feature being that at each time step results are projected onto a fixed, background mesh, that is where the problem is actually solved.
Abstract
In this paper we propose a method to approximate flow problems in moving domains using always a given grid for the spatial discretization, and therefore the formulation to be presented [...]