  Current explicit integration techniques in fluid dynamics are deeply limited
by the Courant-Friedrichs-Lewy condition of the time step progression, based on
the adopted spatial resolution coupled with the maximum value between the
kinetic velocity or the signal transmission speed in the computational domain.
Eulerian implicit integration techniques, even though more time consuming, can
allow to perform stable computational fluid dynamics paying the price of a
relatively larger inaccuracy in the calculations, without suffering such a
strict temporal limitation. In this paper, we present a simple and effective
scheme to perform Free Lagrangian Smooth Particle Hydrodynamics (SPH) implicit
integrations in Semi-Lagrangian approach without any Jacobian matrix inversion
operations for viscous Navier-Stokes flows. Applications to SPH accretion disc
simulation around a massive black hole (MBH) in a binary stellar system are
shown, together with the comparison to the same results obtained according to
the traditional explicit integration techniques. Some 1D and 2D critical tests
are also discussed to check the validity of the technique.
