LEADER 05576nam 2200745Ia 450 001 9910465621003321 005 20200520144314.0 010 $a9786610903979 010 $a1-4294-7019-4 010 $a0-19-151374-1 010 $a1-280-90397-X 035 $a(CKB)2560000000296346 035 $a(EBL)3052124 035 $a(OCoLC)137241535 035 $a(SSID)ssj0000088220 035 $a(PQKBManifestationID)11395633 035 $a(PQKBTitleCode)TC0000088220 035 $a(PQKBWorkID)10071231 035 $a(PQKB)11650742 035 $a(StDuBDS)EDZ0000073178 035 $a(MiAaPQ)EBC3052124 035 $a(Au-PeEL)EBL3052124 035 $a(CaPaEBR)ebr10167502 035 $a(CaONFJC)MIL90397 035 $a(EXLCZ)992560000000296346 100 $a20060127d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMathematical methods for the magnetohydrodynamics of liquid metals$b[electronic resource] /$fJean-Fre?de?ric Gerbeau, Claude la Bris and Tony Lelie?vre 210 $aOxford $cOxford University Press$d2006 215 $a1 online resource (325 p.) 225 1 $aNumerical mathematics and scientific computation 225 1 $aOxford science publications 300 $aDescription based upon print version of record. 311 $a0-19-856665-4 311 $a0-19-171801-7 320 $aIncludes bibliographical references and index. 327 $aContents; 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 327 $a2.1.1 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 327 $a3.1.3 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 327 $a3.5 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 327 $a3.8.3 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 327 $a5.1 Numerical approximations in the ALE formulation 330 8 $aAimed at research mathematicians, engineers and physicists, as well as those in industry, the approach of this text is highly mathematical and based on solid numerical analysis. It focuses on mathematical and numerical techniques for the simulation of magnetohydrodynamic phenomena, with an emphasis on industrial applications. 410 0$aNumerical mathematics and scientific computation. 410 0$aOxford science publications. 606 $aLiquid metals 606 $aMagnetohydrodynamics$xMathematics 608 $aElectronic books. 615 0$aLiquid metals. 615 0$aMagnetohydrodynamics$xMathematics. 676 $a538.6 700 $aGerbeau$b Jean-Fre?de?ric$0945617 701 $aLe Bris$b Claude$055696 701 $aLelie?vre$b Tony$0921320 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910465621003321 996 $aMathematical methods for the magnetohydrodynamics of liquid metals$92135401 997 $aUNINA