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An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations

Éric Boillat (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this article, we consider the initial value problem which is obtained after a space discretization (with space step h) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size h chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between h and the time...

An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations

Éric Boillat (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this article, we consider the initial value problem which is obtained after a space discretization (with space step h ) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size h chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between h and the time step size...

Fluid–particle shear flows

Bertrand Maury (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Our purpose is to estimate numerically the influence of particles on the global viscosity of fluid–particle mixtures. Particles are supposed to rigid, and the surrounding fluid is newtonian. The motion of the mixture is computed directly, i.e. all the particle motions are computed explicitly. Apparent viscosity, based on the force exerted by the fluid on the sliding walls, is computed at each time step of the simulation. In order to perform long–time simulations and still control the solid fraction,...

Fluid–particle shear flows

Bertrand Maury (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Our purpose is to estimate numerically the influence of particles on the global viscosity of fluid–particle mixtures. Particles are supposed to rigid, and the surrounding fluid is newtonian. The motion of the mixture is computed directly, i.e. all the particle motions are computed explicitly. Apparent viscosity, based on the force exerted by the fluid on the sliding walls, is computed at each time step of the simulation. In order to perform long–time simulations and still control the solid fraction,...

Fully adaptive multiresolution schemes for strongly degenerate parabolic equations in one space dimension

Raimund Bürger, Ricardo Ruiz, Kai Schneider, Mauricio Sepúlveda (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We present a fully adaptive multiresolution scheme for spatially one-dimensional quasilinear strongly degenerate parabolic equations with zero-flux and periodic boundary conditions. The numerical scheme is based on a finite volume discretization using the Engquist-Osher numerical flux and explicit time stepping. An adaptive multiresolution scheme based on cell averages is then used to speed up the CPU time and the memory requirements of the underlying finite volume scheme, whose first-order...

Numerical simulation of gluey particles

Aline Lefebvre (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We propose here a model and a numerical scheme to compute the motion of rigid particles interacting through the lubrication force. In the case of a particle approaching a plane, we propose an algorithm and prove its convergence towards the solutions to the gluey particle model described in [B. Maury, ESAIM: Proceedings 18 (2007) 133–142]. We propose a multi-particle version of this gluey model which is based on the projection of the velocities onto a set of admissible velocities. Then, we describe...

Numerical simulation of gluey particles

Aline Lefebvre (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose here a model and a numerical scheme to compute the motion of rigid particles interacting through the lubrication force. In the case of a particle approaching a plane, we propose an algorithm and prove its convergence towards the solutions to the gluey particle model described in [B. Maury, ESAIM: Proceedings18 (2007) 133–142]. We propose a multi-particle version of this gluey model which is based on the projection of the velocities onto a set of admissible velocities. Then, we describe...

Numerical simulation of suspension induced rheology

Rodolphe Prignitz, Eberhard Bänsch (2010)

Kybernetika

Flow of particles suspended in a fluid can be found in numerous industrial processes utilizing sedimentation, fluidization and lubricated transport such as food processing, catalytic processing, slurries, coating, paper manufacturing, particle injection molding and filter operation. The ability to understand rheology effects of particulate flows is elementary for the design, operation and efficiency of the underlying processes. Despite the fact that particle technology is widely used, it is still...

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