  In the non viscous fluid dynamics, Smooth Particle Hydrodynamics (SPH), as a
free Lagrangian "shock capturing" method adopts either an artificial viscosity
contribution or an appropriate Riemann solver technique. An explicit or an
implicit dissipation, introduced in such techniques, is necessary to solve the
Euler equations to solve flow discontinuities (the Riemann problem).
Dissipation is useful to smooth out spurious heating and to treat transport
phenomena. A simple, effective solution of the Riemann problem is here
proposed, based on an empirical reformulation of the equation of state (EoS) in
the Euler equations in fluid dynamics, whose limit for a motionless gas
coincides with the classic EoS of ideal gases. Results on 1D shock tube tests
are here shown, as well as a 3D transport application on accretion discs in
close binaries (CBs).
