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Mathematical methods for the magnetohydrodynamics of liquid metals [[electronic resource] /] / Jean-Frédéric Gerbeau, Claude la Bris and Tony Lelièvre
| Mathematical methods for the magnetohydrodynamics of liquid metals [[electronic resource] /] / Jean-Frédéric Gerbeau, Claude la Bris and Tony Lelièvre |
| Autore | Gerbeau Jean-Frédéric |
| Pubbl/distr/stampa | Oxford, : Oxford University Press, 2006 |
| Descrizione fisica | 1 online resource (325 p.) |
| Disciplina | 538.6 |
| Altri autori (Persone) |
Le BrisClaude
LelièvreTony |
| Collana |
Numerical mathematics and scientific computation
Oxford science publications |
| Soggetto topico |
Liquid metals
Magnetohydrodynamics - Mathematics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
9786610903979
1-4294-7019-4 0-19-151374-1 1-280-90397-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; 1 The magnetohydrodynamics equations; 1.1 The general fluid equations; 1.1.1 The conservation equations; 1.1.2 Boundary and initial conditions; 1.1.3 Steady-state equations; 1.2 The electromagnetic description; 1.3 The MHD coupling; 1.3.1 The general MHD system; 1.3.2 A commonly used simplified MHD coupling; 1.3.3 The density-dependent case; 1.4 Other MHD models; 1.5 The MHD system considered in the sequel; 1.6 Non-dimensionalized equations; 2 Mathematical analysis of one-fluid problems; 2.1 Mathematical results on the incompressible homogeneous Navier-Stokes equations
2.1.1 Some basics2.1.2 The illustrative example of the two-dimensional case; 2.1.3 The three-dimensional hydrodynamic case; 2.1.4 Related issues; 2.2 Mathematical results on the one-fluid MHD equations; 2.2.1 A brief overview of the literature; 2.2.2 Mathematical analysis; 2.2.3 Back to the hyperbolic system; 2.2.4 Stationary problems; 2.2.5 A hybrid problem; 2.2.6 Other MHD models and formulations; 3 Numerical approximation of one-fluid problems; 3.1 A general framework for problems with constraints; 3.1.1 A model problem: the Stokes equations; 3.1.2 Abstract framework for a linear problem 3.1.3 Application to the Stokes problem3.1.4 The inf-sup condition; 3.1.5 The mixed Galerkin method; 3.1.6 Algebraic aspects; 3.1.7 Mixed finite element for the Stokes problem; 3.1.8 Extension to nonlinear problems; 3.2 A glance at stabilized finite elements; 3.3 Mixed formulations of the stationary MHD equations; 3.3.1 A formulation for convex polyhedra and regular domains; 3.3.2 A formulation for non-convex polyhedra; 3.4 Mixed finite elements for MHD; 3.4.1 Mixed finite elements on convex polyhedra and regular domains; 3.4.2 Mixed finite elements on non-convex polyhedra 3.5 Stabilized finite elements for MHD3.6 Solution strategy and algebraic aspects; 3.6.1 Fully coupled iterations for stationary problems; 3.6.2 Decoupled iterations for stationary problems; 3.6.3 Fully coupled iterations for transient problems; 3.6.4 MHD versus Navier-Stokes solvers; 3.7 Examples of test cases and simulations; 3.7.1 Hartmann flows; 3.7.2 A fluid carrying current in the presence of a magnetic field; 3.7.3 Convergence of nonlinear algorithms; 3.8 About the boundary conditions; 3.8.1 First set of boundary conditions; 3.8.2 Second set of boundary conditions 3.8.3 Practical implementation of the boundary conditions4 Mathematical analysis of two-fluid problems; 4.1 The difficulties of the non-homogeneous case; 4.1.1 A formal mathematical argument; 4.1.2 The major ingredient; 4.1.3 Short overview of the state of the art for the hydrodynamic case; 4.2 Weak solutions of the multifluid MHD system; 4.2.1 Mathematical setting of the equations; 4.2.2 Existence of a weak solution; 4.3 On the long-time behavior; 4.3.1 The nonlinear hydrodynamics case; 4.3.2 A detour by linearized models; 4.3.3 The MHD case; 5 Numerical simulation of two-fluid problems 5.1 Numerical approximations in the ALE formulation |
| Record Nr. | UNINA-9910465621003321 |
Gerbeau Jean-Frédéric
|
||
| Oxford, : Oxford University Press, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematical methods for the magnetohydrodynamics of liquid metals [[electronic resource] /] / Jean-Frédéric Gerbeau, Claude la Bris and Tony Lelièvre
| Mathematical methods for the magnetohydrodynamics of liquid metals [[electronic resource] /] / Jean-Frédéric Gerbeau, Claude la Bris and Tony Lelièvre |
| Autore | Gerbeau Jean-Frédéric |
| Pubbl/distr/stampa | Oxford, : Oxford University Press, 2006 |
| Descrizione fisica | 1 online resource (325 p.) |
| Disciplina | 538.6 |
| Altri autori (Persone) |
Le BrisClaude
LelièvreTony |
| Collana |
Numerical mathematics and scientific computation
Oxford science publications |
| Soggetto topico |
Liquid metals
Magnetohydrodynamics - Mathematics |
| ISBN |
9786610903979
1-4294-7019-4 0-19-151374-1 1-280-90397-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; 1 The magnetohydrodynamics equations; 1.1 The general fluid equations; 1.1.1 The conservation equations; 1.1.2 Boundary and initial conditions; 1.1.3 Steady-state equations; 1.2 The electromagnetic description; 1.3 The MHD coupling; 1.3.1 The general MHD system; 1.3.2 A commonly used simplified MHD coupling; 1.3.3 The density-dependent case; 1.4 Other MHD models; 1.5 The MHD system considered in the sequel; 1.6 Non-dimensionalized equations; 2 Mathematical analysis of one-fluid problems; 2.1 Mathematical results on the incompressible homogeneous Navier-Stokes equations
2.1.1 Some basics2.1.2 The illustrative example of the two-dimensional case; 2.1.3 The three-dimensional hydrodynamic case; 2.1.4 Related issues; 2.2 Mathematical results on the one-fluid MHD equations; 2.2.1 A brief overview of the literature; 2.2.2 Mathematical analysis; 2.2.3 Back to the hyperbolic system; 2.2.4 Stationary problems; 2.2.5 A hybrid problem; 2.2.6 Other MHD models and formulations; 3 Numerical approximation of one-fluid problems; 3.1 A general framework for problems with constraints; 3.1.1 A model problem: the Stokes equations; 3.1.2 Abstract framework for a linear problem 3.1.3 Application to the Stokes problem3.1.4 The inf-sup condition; 3.1.5 The mixed Galerkin method; 3.1.6 Algebraic aspects; 3.1.7 Mixed finite element for the Stokes problem; 3.1.8 Extension to nonlinear problems; 3.2 A glance at stabilized finite elements; 3.3 Mixed formulations of the stationary MHD equations; 3.3.1 A formulation for convex polyhedra and regular domains; 3.3.2 A formulation for non-convex polyhedra; 3.4 Mixed finite elements for MHD; 3.4.1 Mixed finite elements on convex polyhedra and regular domains; 3.4.2 Mixed finite elements on non-convex polyhedra 3.5 Stabilized finite elements for MHD3.6 Solution strategy and algebraic aspects; 3.6.1 Fully coupled iterations for stationary problems; 3.6.2 Decoupled iterations for stationary problems; 3.6.3 Fully coupled iterations for transient problems; 3.6.4 MHD versus Navier-Stokes solvers; 3.7 Examples of test cases and simulations; 3.7.1 Hartmann flows; 3.7.2 A fluid carrying current in the presence of a magnetic field; 3.7.3 Convergence of nonlinear algorithms; 3.8 About the boundary conditions; 3.8.1 First set of boundary conditions; 3.8.2 Second set of boundary conditions 3.8.3 Practical implementation of the boundary conditions4 Mathematical analysis of two-fluid problems; 4.1 The difficulties of the non-homogeneous case; 4.1.1 A formal mathematical argument; 4.1.2 The major ingredient; 4.1.3 Short overview of the state of the art for the hydrodynamic case; 4.2 Weak solutions of the multifluid MHD system; 4.2.1 Mathematical setting of the equations; 4.2.2 Existence of a weak solution; 4.3 On the long-time behavior; 4.3.1 The nonlinear hydrodynamics case; 4.3.2 A detour by linearized models; 4.3.3 The MHD case; 5 Numerical simulation of two-fluid problems 5.1 Numerical approximations in the ALE formulation |
| Record Nr. | UNINA-9910792234403321 |
|
Gerbeau Jean-Frédéric
|
||
| Oxford, : Oxford University Press, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||