Inspired by recent works of Zang Liu, Alan Weinstein and Ping Xu, we introduce the notions of CC algebroids and non asymmetric Courant algebroids and study these structures. It is shown that CC algebroids of rank greater than 3 are the same as Courant algebroids up to a constant factor, though the definition of CC algebroids is much simpler than that of Courant algebroids,requiring only 2 axiom...

We introduce Courant 1-derivations, which describe a compatibility between algebroids and linear (1,1)-tensor fields lead to the notion of Courant-Nijenhuis algebroids. provide examples 1-derivations on exact show that holomorphic can be viewed as special types By considering Dirac structures, one recovers Dirac-Nijenhuis structures previously studied by authors (in case standard algebroid) obt...

An implicit Lagrangian hydrodynamics code for general relativistic spherical collapse is presented. This scheme is based on an approximate linearized Riemann solver (Roe type scheme) and needs no artificial viscosity. This code is aimed especially at the calculation of the late phase of collapse-driven supernovae and the nascent neutron star, where there is a remarkable contrast between the dyn...

The conservative cascade scheme (CCS) combines a one-dimensional mass-conserving finite-volume method with an efficient semi-Lagrangian scheme over the sphere. Major limitations of this scheme are a breakdown in the polar region due to the coordinate singularity and a restriction to polar meridional Courant number Cu # 1. The proposed scheme is an extension of the CCS over the sphere for Cu . 1...