Discontinuous Galerkin method

For more info about our services contact : help@bestpfe.com

Table of contents

1 Superconductivity and numerical modelling 
1.1 Introduction
1.2 Superconductors : types I and II
1.2.1 Type-I superconductors
1.2.2 Type-II superconductors
1.3 HTS: macroscopic models
1.3.1 Critical state model : Bean model
1.3.2 E-J power law
1.3.3 Kim model
1.3.4 AC losses
1.4 HTS applications
1.5 Mathematical models
1.5.1 H formulation
1.5.2 E formulation
1.5.3 A 􀀀 V formulation
1.5.4 T 􀀀 formulation
1.6 Numerical methods
1.6.1 Minimization of an energy functional
1.6.2 Integral methods
1.6.3 Finite element method
1.6.4 Finite volume method
1.6.5 Finite element – Finite volume hybrid method
1.6.6 Discontinuous Galerkin method
1.7 Conclusion
2 3D modelling of high-temperature superconductors 
2.1 Introduction
2.2 Problem formulation
2.2.1 Constitutive laws
2.2.2 Differential formulation
2.2.3 Variational formulation
2.3 Finite element method
2.3.1 Mesh definition
2.3.2 Discrete variational formulation
2.3.3 Numerical treatment of the non-linearities arising from E =0
2.4 Discontinuous Galerkin method
2.4.1 Mesh definition
2.4.2 Discrete Variational formulation
2.4.3 Spatial approximation
2.4.4 Numerical fluxes terms on the faces of the mesh Th
2.4.5 Boundary conditions
2.4.6 Numerical treatment of the non-linearities arising from E = (J)J
2.5 Comparisons and validations
2.5.1 Straight superconducting filament embedded in a Niobium matrix carrying a sinusoidal transport current
2.5.2 Superconducting cube subjected to an alternating transverse magnetic field
2.6 Conclusion
3 3D modelling of twisted multi-filamentary superconducting wires 
3.1 Introduction
3.2 Influence of a transverse magnetic field on a twisted mono-filament wire
3.3 Mapping from a twisted mono-filament wire to a straight monofilament wire
3.4 Mapping validation on a twisted bi-filaments wire
3.4.1 Twisted bi-filaments superconducting wire subjected to a transverse magnetic field along the y-axis
3.4.2 Twisted bi-filaments superconducting wire subjected to an axial magnetic field along the z-axis
3.5 Mapping validation on a twisted six-filaments wire
3.5.1 Twisted six-filaments superconducting wire subjected to a transverse magnetic field along the y-axis
3.5.2 Twisted six-filaments superconducting wire subjected to an axial magnetic field along the z-axis
3.6 Study of multi-filamentary wires with multiple twist pitch
3.6.1 Influence of the number of twist pitch
3.6.2 Model-order reduction of a twisted multi-filamentary wire with multiple twist pitch
3.6.3 Analysis of the impact of elliptical fields on magnetization losses
3.7 Perspective : homogenization of multi-filamentary superconducting wire
3.8 Conclusion
General conclusion
Bibliography