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A numerical model for the three-dimensional simulation of liquid-gas flows with free surfaces is presented. The incompressible Navier-Stokes equations are assumed to hold in the liquid domain. In the gas domain, the velocity is disregarded, the pressure is ...

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 to the volume of fluid (VOF) method, the numerical schemes used to solve the problem are different. A splitting method is used for the time discretization. At each time step, two advection problems and a generalized Stok

We present a numerical model for the simulation of 3D sediment transport in a Newtonian flow with free surfaces. The Navier-Stokes equations are coupled with the transport, deposition, and resuspension of the particle concentrations, and a volume-of-fluid ...

An a posteriori error estimate is derived for the approximation of the transport equation with a time dependent transport velocity. Continuous, piecewise linear, anisotropic finite elements are used for space discretization, the Crank-Nicolson scheme schem ...

This paper describes the use of an a posteriori error estimator to control anisotropic mesh adaptation for computing inviscid compressible flows. The a posteriori error estimator and the coupling strategy with an anisotropic remesher are first introduced. ...

In this paper we derive two a posteriori upper bounds for the heat equation. A continuous, piecewise linear finite element discretization in space and the Crank-Nicolson method for the time discretization are used. The error due to the space discretization ...

The p-Laplacian problem -del & sdot; ((mu + |del u|(p-2))del u) = f is considered, where mu is a given positive number. An anisotropic a posteriori residual-based error estimator is presented. The error estimator is shown to be equivalent, up to higher ord ...

We consider finite element error approximations of the steady incompressible Navier-Stokes equations defined on a randomly perturbed domain, the perturbation being small. Introducing a random mapping, these equations are transformed into PDEs on a fixed re ...

An anisotropic a posteriori error estimate is derived for a finite element discretization of the wave equation in two space dimensions. Only the error due to space discretization is considered, and the error estimates are derived in the nonnatural L-2(0, T ...

Two:dimensional time-dependent calculations for a molecular model of finite extensibility in the journal-bearing geometry are presented. The flow is considered to be incompressible and isothermal. The momentum conservation equation is integrated using a time-marching procedure in which local ensembles of dumbbells act as stress calculators. The calculations are based on the Calculation of non-Newtonian flows: finite elements and stochastic simulation technique (CONNFFESSIT) and combine deterministic (finite

We present a numerical model for the simulation of 3D poly-dispersed sediment transport in a Newtonian flow with free surfaces. The physical model is based on a mixture model for multiphase flows. The Navier-Stokes equations are coupled with the transport ...

The elliptic problem - div(mu del u) = f is considered, where mu > 0 is smooth but strongly varying. Anisotropic a posteriori error estimates are derived, the effectivity index being bounded above and below by two constants independent of the data f, mu, t ...

A space-time adaptive algorithm to solve the motion of a rigid disk in an incompressible Newtonian fluid is presented, which allows collision or quasi-collision processes to be computed with high accuracy. In particular, we recover the theoretical result p ...

In the last decade, the cell productivity has been dramatically improved as demonstrated on AP30 technology with amperage increase from 350 kA to 440 kA. At the same time, available liquid bath volume in the pots has been drastically reduced by the anode surface enlargement. In order to achieve such impressive step change, management of alumina dissolution is a key point to optimize both cell design and process control algorithms. Rio Tinto Aluminium and EPFL have developed a 3D model taking into account th

The capability of calculation of non-Newtonian flows: finite elements and stochastic simulation technique (CONNFFESSIT) to compute transient free surface flows is extended to deal with transient viscoelastic flows for domains in which the topology (connectivity) can change in time and also to deal with multivalued free surfaces, i.e. those that cannot be described by a single-valued height function nor be mapped onto an equivalent problem. Such flows are of great practical relevance as they are prevalent in

This work deals with the numerical modeling of laser surface treatments, particularly laser remelting (a laser beam melts part of a moving work piece) and laser cladding (injection of powder in the melt pool produces a thin metallic layer on the work piece). A two-dimensional stationary model is presented for laser cladding. This model takes into account the solid-liquid phase change process and the important velocity field in the melt pool. A pure thermal problem is studied, which corresponds to a laser re

A numerical model is presented for the simulation of complex fluid flows with free surfaces in three space dimensions. The model described in Maronnier et al. (J. Comput. Phys. 1999; 155(2):439) is extended to three dimensional situations. The mathematical formulation of the model is similar to that of the volume of fluid (VOF) method, but the numerical procedures are different. A splitting method is used for the time discretization. At each time step, two advection problems-one for the predicted velocity f

A stabilized semidiscrete finite element discretization of the transient transport equation is studied in the framework of anisotropic meshes. A priori and a posteriori error estimates are derived, the involved constants being independent of the mesh aspec ...

In this paper, a finite element error analysis is performed on a class of linear and nonlinear elliptic problems with small uncertain input. Using a perturbation approach, the exact (random) solution is expanded up to a certain order with respect to a parameter that controls the amount of randomness in the input and discretized by finite elements. We start by studying a diffusion (linear) model problem with a random coefficient characterized via a finite number of random variables. A priori and a posteriori

The aim of this paper is to study the well-posedness and finite element approximation of the electrostatic shear Alfvén wave equations, a coupled system of two partial differential equations arising in plasma physics as a simplified sub-model of the drift-reduced Braginskii equations. To this end, anisotropic Sobolev spaces depending on the normalized magnetic field b are introduced, together with a Poincaré-type inequality along the integral curves of b, which holds under a geometric directedness condition

Marco Picasso

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Numerical simulation of free surface incompressible liquid flows surrounded by compressible gas

Numerical simulation of free surface flows

A splitting method for the numerical simulation of free surface flows with sediment deposition and resuspension

An adaptive algorithm for the transport equation with time dependent velocity

On the use of anisotropic a posteriori error estimators for the adaptative solution of 3D inviscid compressible flows

An Anisotropic Error Estimator For The Crank-Nicolson Method: Application To A Parabolic Problem

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem

A posteriori error estimation for the steady Navier-Stokes equations in random domains

Numerical Study Of An Anisotropic Error Estimator In The L-2(H-1) Norm For The Finite Element Discretization Of The Wave Equation

2-D time-dependent viscoelastic flow calculations using CONNFFESSIT

A semi-Lagrangian splitting method for the numerical simulation of sediment transport with free surface flows

Anisotropic Adaptive Finite Elements for an Elliptic Problem with Strongly Varying Diffusion Coefficient

A Space-Time Adaptive Algorithm to Illustrate the Lack of Collision of a Rigid Disk Falling in an Incompressible Fluid

Alumina Dissolution Modeling in Aluminium Electrolysis Cell Considering MHD Driven Convection and Thermal Impact

Calculation of variable-topology free surface flows using CONNFFESSIT

Simulation numérique des traitements de surface par laser

Numerical simulation of three-dimensional free surface flows

Anisotropic Error Estimates And Space Adaptivity For A Semidiscrete Finite Element Approximation Of The Transient Transport Equation

MATHICSE Technical Report : A posteriori error estimations for elliptic partial differential equations with small uncertainties

Well-posedness and finite element approximation of the electrostatic shear Alfvén wave equations