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3D Coupled MHD and Thermo-Electrical Modelling Applied to AP Technology Pots
A suite of efficient modelling tools is critical to continuously improve the performance and robustness of aluminium electrolysis cells. Rio Tinto Alcan has developed a suite of chained models to provide a goo...
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Optimization Problem Coupled with Differential Equations: A Numerical Algorithm Mixing an Interior-Point Method and Event Detection
The numerical analysis of a dynamic constrained optimization problem is presented. It consists of a global minimization problem that is coupled with a system of ordinary differential equations. The activation ...
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Some Mathematical and Numerical Aspects in Aluminum Production
In this paper, we present a mathematical modeling of some magnetohydrodynamic effects arising in an aluminum production cell as well as its numerical approximation by a finite element method. We put the emphas...
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Numerical simulation of macrosegregation: a comparison between finite volume method and finite element method predictions and a confrontation with experiments
Micro-macrosegregation calculations have been performed for a rectangular cavity containing either a Pb-48 wt pct Sn alloy or a Sn-5 wt pct Pb alloy. The numerical results calculated with a finite volume metho...
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On spectral pollution in the finite element approximation of thin elastic “membrane” shells
The bending terms in a shell are small with respect to membrane ones as the thickness tends to zero. Consequently, the membrane approximation gives a good description of vibration properties of a thin shell. T...
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Modelling in numerical simulation of electromagnetic heating
This paper deals with numerical simulation of induction heating for tri-dimensional time-varying axisymmetric geometries. The modelling used for the eddy current solver is presented in detail, from physical eq...
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Induction Heating for Three-Dimensional Axisymmetric Geometries: Modeling and Numerical Simulation
Induction heating is widely used in industry, and has found an increasing number of applications during the last years. Its principle lies in heat generation by eddy currents resulting from a rapidly varying m...
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Consistency, stability, a priori and a posteriori errors for Petrov-Galerkin methods applied to nonlinear problems
In an abstract framework we present a formalism which specifies the notions of consistency and stability of Petrov-Galerkin methods used to approximate nonlinear problems which are, in many practical situation...
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A Numerical Model for Electromagnetic Casters
We briefly describe a numerical model we have developed to simulate electromagnetic casting processes. The model is two-dimensional. The set of partial differential equations is given and the numerical methods...
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On the rotating beam: Some theoretical and numerical results
A bifurcation analysis for a thin beam rotating about an axis is carried out by the Golubitsky-Schaeffer theory of singularities. The rotation velocity is the bifurcation parameter, while the constants describ...
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Approximation of Hopf Bifurcation for Semilinear Parabolic Equations
For a system of semilinear parabolic equations which presents a Hopf bifurcation, we define a general discrete problem which retains the bifurcation property and State an error estimate between the exact and a...
