LGEP 2014 ID = 1529International audienceA semi-implicit approach is proposed for computing the current density in superconductors characterized by nonlinear vectorial power law. A nodal discontinuous Galerkin method is adopted for the spatial discretization of the nonlinear system satisfied by the components of the electric field. Explicit developments are used to construct boundary conditions to avoid the modeling of a volume around the superconducting sample. A modified Newton iterative method is introduced for solving the discrete system. Numerical examples on a 2-D superconducting plate and a 3-D superconducting cube are computed. Distributions of a component of the current density are presented and differences in the diffusive process are highlighted. The penetration time and losses are compared with those obtained with an A-V formulation solved by a finite-volume method

The fluid flow transport and hydrodynamic problems often take the form of hyperbolic systems of conservation laws. In this work we will present a new scheme of finite volume methods for solving these evolution equations. It is a family of finite volume Eulerian-Lagrangian methods for the solution of non-linear problems in two space dimensions on unstructured triangular meshes. The proposed approach belongs to the class of predictor-corrector procedures where the numerical fluxes are reconstructed using the method of characteristics, while an Eulerian method is used to discretize the conservation equation in a finite volume framework. The scheme is accurate, conservative and it combines advantages of the modified method of characteristics to accurately solve the non-linear conservation laws with a finite volume method to discretize the equations. The proposed Finite Volume Characteristics (FVC) scheme is also non-oscillatory and avoids the need to solve a Riemann problem. Several test examples will be presented for the shallow water equations. The results will be compared to those obtained with the Roe.

International audienceIn this paper, different formulations of Maxwell equations are combined for computing the shielding effectiveness of enclosures made from heterogeneous periodic materials. The validity of the homogenized parameters given by Maxwell-Garnett rules in the frequency domain are tested in the time domain by using a nodal DG method, which uses an interface condition based on analytical solution in the frequency domain to replace a conductive sheet. This interface condition allows to avoid meshing the thin sheet, thus reducing the computational cost. Results of scattering by composite enclosures are presented in the frequency domain thanks to a FFT