In a prior work [CEMRACS10], a curvilinear bi-dimensional finite volume extension of
Lagrangian centered schemes GLACE [GLACE] on unstructured cells, whose edges are
parameterized by rational quadratic Bézier curves was proposed and we showed numerical
results for this scheme. Now, we extend the EUCCLHYD scheme [EUCCLHYD] to these
cells. To simulate flows with evolving large deformations, we write a formalism allowing
the time evolution of the conic parameter. As an example, this allows an edge changing
from an ellipse segment to a hyperbolic one. In this framework, we consider the case of a
mesh whose edges are circle segments with non fixed centers. We show that this formalism
extends also the previous work [GLACE CIRCLE] (which is equivalent to [CEMRACS10]
when conic edges are all circles). This is a necessary first step toward general conical
deformation
