Abstract
Some authors have concluded that spiral structures and shocks do not develop if an adiabatic index $\gamma$ > 1.16 is adopted in accretion disc modelling, whilst others have claimed that they obtained well defined spirals and shocks adopting a $\gamma$ = 1.2 and a $M_2/ M_1$ = 1 stellar mass ratio. In our opinion, it should be possible to develop spiral structures for low compressibility gas accretion discs if the primary component is a black hole. We considered a primary black hole of 8M0 and a small secondary component of 0.5M$\bigodot$ to favour spiral structures formations and possible spiral shocks via gas compression due to a strong gravitational attraction. We performed two 3D SPH simulations and two 2D SPH simulations and characterized a low compressibility model and a high compressibility model for each couple of simulations. 2D models reveal spiral structures existence. Moreover, spiral shocks are also evident in high compressibility 2D model at the outer disc edge. We believe that we could develop even well defined spiral shocks considering a more massive primary component.