  In this work, we propose a SPH interpolating Kernel reformulation suitable
also to treat free edge boundaries in the computational domain. Application to
both inviscid and viscous stationary low compressibility accretion disc models
in Close Binaries (CB) are shown. The investigation carried out in this paper
is a consequence of the fact that a low compressibility modelling is crucial to
check numerical reliability.
  Results show that physical viscosity supports a well-bound accretion disc
formation, despite the low gas compressibility, when a Gaussian-derived Kernel
(from the Error Function) is assumed, in extended particle range - whose Half
Width at Half Maximum (HWHM) is fixed to a constant $h$ value - without any
spatial restrictions on its radial interaction (hereinafter GASPHER). At the
same time, GASPHER ensures adequate particle interpolations at the boundary
free edges. Both SPH and adaptive SPH (hereinafter ASPH) methods lack accuracy
if there are not constraints on the boundary conditions, in particular at the
edge of the particle envelope: Free Edge (FE) conditions. In SPH, an
inefficient particle interpolation involves a few neighbour particles; instead,
in the second case, non-physical effects involve both the boundary layer
particles themselves and the radial transport.
  Either in a regime where FE conditions involve the computational domain, or
in a viscous fluid dynamics, or both, a GASPHER scheme can be rightly adopted
in such troublesome physical regimes. Despite the applied low compressibiity
condition, viscous GASPHER model shows clear spiral pattern profiles
demonstrating the better quality of results compared to SPH viscous ones.
Moreover a successful comparison of results concerning GASPHER 1D inviscid
shock tube with analytical solution is also reported.
