*Jean-Frédéric Gerbeau, Claude Le Bris, and Tony Lelièvre*

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198566656
- eISBN:
- 9780191718014
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566656.001.0001
- Subject:
- Mathematics, Mathematical Physics

This text focuses on mathematical and numerical techniques for the simulation of magnetohydrodynamic phenomena, with an emphasis on the magnetohydrodynamics of liquid metals, on two-fluid flows, and ...
More

This text focuses on mathematical and numerical techniques for the simulation of magnetohydrodynamic phenomena, with an emphasis on the magnetohydrodynamics of liquid metals, on two-fluid flows, and on a prototypical industrial application. The approach is a highly mathematical one, based on the rigorous analysis of the equations at hand, and a solid numerical analysis of the discretization methods. Up-to-date techniques, both on the theoretical side and the numerical side, are introduced to deal with the nonlinearities of the multifluid magnetohydrodynamics equations. At each stage of the exposition, examples of numerical simulations are provided, first on academic test cases to illustrate the approach, next on benchmarks well documented in the professional literature, and finally on real industrial cases. The simulation of aluminium electrolysis cells is used as a guideline throughout the book to motivate the study of a particular setting of the magnetohydrodynamics equations.Less

This text focuses on mathematical and numerical techniques for the simulation of magnetohydrodynamic phenomena, with an emphasis on the magnetohydrodynamics of liquid metals, on two-fluid flows, and on a prototypical industrial application. The approach is a highly mathematical one, based on the rigorous analysis of the equations at hand, and a solid numerical analysis of the discretization methods. Up-to-date techniques, both on the theoretical side and the numerical side, are introduced to deal with the nonlinearities of the multifluid magnetohydrodynamics equations. At each stage of the exposition, examples of numerical simulations are provided, first on academic test cases to illustrate the approach, next on benchmarks well documented in the professional literature, and finally on real industrial cases. The simulation of aluminium electrolysis cells is used as a guideline throughout the book to motivate the study of a particular setting of the magnetohydrodynamics equations.

*Jean-Frédéric Gerbeau, Claude Le Bris, and Tony Lelièvre*

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198566656
- eISBN:
- 9780191718014
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566656.003.0006
- Subject:
- Mathematics, Mathematical Physics

This chapter is entirely devoted to one industrial application, the simulation of the industrial production of aluminium in electrolytic cells. The simulation of this specific problem has indeed ...
More

This chapter is entirely devoted to one industrial application, the simulation of the industrial production of aluminium in electrolytic cells. The simulation of this specific problem has indeed motivated the whole scientific strategy described in the first five chapters. It serves as an illustration of the efficiency of the approach presented throughout this book. A schematic description of the problem is as follows. An electric current of huge intensity runs downwards through two horizontal layers of incompressible non-miscible conducting fluids. Owing to the magnetohydrodynamics coupling, the interface between the fluids moves, and, in view of the very high intensity of the electric current, the system is very sensitive to instabilities. The industrial challenge is to model, understand, and control these instabilities. Numerical simulation of nonlinear systems can help to reach such a goal. Other techniques (such as a stability analysis for the linearized system) are also employed, and are overviewed for comparison.Less

This chapter is entirely devoted to one industrial application, the simulation of the industrial production of aluminium in electrolytic cells. The simulation of this specific problem has indeed motivated the whole scientific strategy described in the first five chapters. It serves as an illustration of the efficiency of the approach presented throughout this book. A schematic description of the problem is as follows. An electric current of huge intensity runs downwards through two horizontal layers of incompressible non-miscible conducting fluids. Owing to the magnetohydrodynamics coupling, the interface between the fluids moves, and, in view of the very high intensity of the electric current, the system is very sensitive to instabilities. The industrial challenge is to model, understand, and control these instabilities. Numerical simulation of nonlinear systems can help to reach such a goal. Other techniques (such as a stability analysis for the linearized system) are also employed, and are overviewed for comparison.