Free-Surface, Moving-Boundary and Multi-Phase Flows

2003

Mathematical and numerical aspects of free surface flows are investigated.

WIT transactions on engineering sciences, 2005

In this paper we will present a new computational approach to simulate free-surface flow problems efficiently. The finite element solution strategy is based on a combination approach derived from fixed-mesh and moving-mesh techniques. Here, the free-surface flow simulations are based on the Navier-Stokes equations written for two incompressible fluids where the impact of one fluid on the other one is extremely small. An interface function with two distinct values is used to locate the position of the free-surface in regions near the floating object, while mesh-moving is used to move the free-surface in regions where wave breaking is not expected. The stabilized finite element formulations are written and integrated in an arbitrary Lagrangian-Eulerian domain. In the mesh-moving scheme, we assume that the computational domain is made of elastic materials. The linear elasticity equations are solved to obtain the displacements for each computational node. The numerical example includes ...

2005

This work is the first step towards a multiphysics strategy for free-surface flows simulation. In particular, we present a strategy to couple one and two-dimensional hydrostatic free surface flow models. We aim to reduce the computational cost required by a full 2D model. After introducing the two models along with suitable a priori error estimates, we discuss the choice of convenient matching conditions stemming from the results obtained in Formaggia et al.[2001]. The numerical results in the last section confirm the soundness of our analysis.

Computers & Fluids, 2005

A numerical model for the simulation of three-dimensional liquid–gas flows with free surfaces and surface tension is presented. The incompressible Navier–Stokes equations are assumed to hold in the liquid domain, while the gas pressure is assumed to be constant in each connected component of the gas domain and to follow the ideal gas law. The surface tension effects are imposed as a normal force on the interface.An implicit splitting scheme is used to decouple the physical phenomena. Given the curvature of the liquid–gas interface, the method described in [Caboussat A, Picasso M, Rappaz J. Numerical simulation of free surface incompressible liquid flows surrounded by compressible gas. J Comput Phys 2005;203(2):626–49] is used to track the liquid domain and compute the velocity and pressure in the liquid and the pressure in the gas domain. Then the surface tension effects are added. A variational method for the computation of the curvature is presented by smoothing the characteristic function of the liquid domain and using a finite element unstructured mesh.The model is validated and numerical results in two and three space dimensions are presented for bubbles and/or droplets flows.

In this paper we present a summary of numerical methods for solving free surface and two fluid flow problems. We will focus the attention on level set formulations extensively used in the context of the finite element method. In particular, numerical developments to achieve accurate solutions are described. Specific topics of the algorithms, like mass preservation and interface redefinition, are evaluated. To illustrate these aspects, numerical strategies previously developed are applied to the solution of a sloshing and a water column collapse problems. To assess the capabilities of these techniques, the numerical results are compared against each other and with experimental data. Considering these aspects, the present work is aimed to outline some well reported aspects of level set-like formulations.

Computer Methods in Applied Mechanics and Engineering, 1998

A finite-element scheme based on a coupled arbitrary Lagrangian-Eulerian and Lagrangian approach is developed for the computation of interface flows with soluble surfactants. The numerical scheme is designed to solve the time-dependent Navier-Stokes equations and an evolution equation for the surfactant concentration in the bulk phase, and simultaneously, an evolution equation for the surfactant concentration on the interface. Secondorder isoparametric finite elements on moving meshes and second-order isoparametric surface finite elements are used to solve these equations. The interface-resolved moving meshes allow the accurate incorporation of surface forces, Marangoni forces and jumps in the material parameters. The lower-dimensional finite-element meshes for solving the surface evolution equation are part of the interface-resolved moving meshes. The numerical scheme is validated for problems with known analytical solutions. A number of computations to study the influence of the surfactants in 3D-axisymmetric rising bubbles have been performed. The proposed scheme shows excellent conservation of fluid mass and of the total mass of the surfactant.

Journal of Computational Physics, 1999

A numerical model is presented for the simulation of complex fluid flows with free surfaces. The unknowns are the velocity and pressure fields in the liquid region, together with a function defining the volume fraction of liquid. Although the mathematical formulation of the model is similar ...

2006

In this study, an interface-tracking method, NS-PFM, combining Navier-Stokes (NS) equations with a phase-field model (PFM) is applied to an incompressible two-phase free surface flow problem at a high density ratio equivalent to that of an air-water system, for examining the computational capability. Based on the Cahn-Hilliard free energy theory, PFM describes an interface as a finite volumetric zone across which physical properties vary steeply but continuously. Surface tension is defined as an excessive free energy per unit area induced by local density gradient. Consequently, PFM simplifies the interface-tracking procedure on a fixed spatial grid without any elaborating techniques in conventional numerical methods. It was confirmed through the numerical simulation that (1) the NS-PFM conducts self-organizing reconstruction of the interface with a certain thickness using volume flux driven by chemical potential gradient and (2) predicted collapse of two-dimensional liquid column in a gas under gravity agreed well with available data.

International Journal of Computational Fluid Dynamics, 2010

Transient free surface flows are numerically simulated by a finite element interface capturing method based on a level set approach. The methodology consists of the solution of two-fluid viscous incompressible flows for a single domain, where the liquid phase is identified by positive values of the level set function, the gaseous phase by negative ones, and the free surface by the zero level set. The numerical solution at each time step is performed in three stages: (i) a two-fluid Navier-Stokes stage, (ii) an advection stage for the transport of the level set function, and (iii) a bounded reinitialization with continuous penalization stage for keeping smoothness of the level set function. The proposed procedure, and particularly the renormalization stage, are evaluated in three typical two and three-dimensional problems.

International Journal for Numerical Methods in Fluids, 2012

This work describes a methodology to simulate free surface incompressible multiphase flows. This novel methodology allows the simulation of multiphase flows with an arbitrary number of phases, each of them having different densities and viscosities. Surface and interfacial tension effects are also included. The numerical technique is based on the GENSMAC front-tracking method. The velocity field is computed using a finite-difference discretization of a modification of the Navier-Stokes equations. These equations together with the continuity equation are solved for the two-dimensional multiphase flows, with different densities and viscosities in the different phases. The governing equations are solved on a regular Eulerian grid, and a Lagrangian mesh is employed to track free surfaces and interfaces. The method is validated by comparing numerical with analytic results for a number of simple problems; it was also employed to simulate complex problems for which no analytic solutions are available. The method presented in this paper has been shown to be robust and computationally efficient.