  In a previous paper, we have achieved the performance analysis of staggered
Lagrange-remap schemes, a class of solvers widely used for Hydrodynamics
applications. This paper is devoted to the rethinking and redesign of the
Lagrange-remap process for achieving better performance using today's computing
architectures. As an unintended outcome, the analysis has lead us to the
discovery of a new family of solvers -- the so-called Lagrange-flux schemes --
that appear to be promising for the CFD community.
