This paper describes the first steps of development of a new multidimensional
time implicit code devoted to the study of hydrodynamical processes in stellar
interiors. The code solves the hydrodynamical equations in spherical geometry
and is based on the finite volume method. Radiation transport is taken into
account within the diffusion approximation. Realistic equation of state and
opacities are implemented, allowing the study of a wide range of problems
characteristic of stellar interiors. We describe in details the numerical
method and various standard tests performed to validate the method. We present
preliminary results devoted to the description of stellar convection. We first
perform a local simulation of convection in the surface layers of a A-type star
model. This simulation is used to test the ability of the code to address
stellar conditions and to validate our results, since they can be compared to
similar previous simulations based on explicit codes. We then present a global
simulation of turbulent convective motions in a cold giant envelope, covering
80% in radius of the stellar structure. Although our implicit scheme is
unconditionally stable, we show that in practice there is a limitation on the
time step which prevent the flow to move over several cells during a time step.
Nevertheless, in the cold giant model we reach a hydro CFL number of 100. We
also show that we are able to address flows with a wide range of Mach numbers
(10^-3 < Ms< 0.5), which is impossible with an anelastic approach. Our first
developments are meant to demonstrate that the use of an implicit scheme
applied to a stellar evolution context is perfectly thinkable and to provide
useful guidelines to optimise the development of an implicit multi-D
hydrodynamical code.Comment: 21 pages, 18 figures, accepted for publication in A&