The two roles of the SPH Kernel and dissipation on accretion disc modelling in semi-detached Low-Mass Close Binaries

Abstract

This study addresses two aspects of the SPH technique. The first aspect regards the 3D (2D) numerical integration. The second aspect deals with the necessary damping for handling inviscid flow discontinuities. Accretion discs in Low-Mass Close Binaries (LMCBs) are a context pushing the limit of SPH codes since turbulence, shocks, and shear flows coexist. Thus, an LMCB with high mass-transfer from the inner Lagrangian point is considered. This choice is made for an in-depth understanding of the numerical and physical aspects related to pressure forces computed through SPH Kernel spatial gradients in high-speed collisional flows. In this regard, gas compressibility also plays a role. Firstly, we pay attention to the algebraic term 4πr2 coming from the cubic differential d3r and affecting any 3D SPH integration. This is made through a comparison of physically inviscid SPH structures referring to the same LMCB and mass-transfer conditions. Then, a reformulation of the non-viscous damping is also considered by adopting a Lagrangian-free physical formulation. Inviscid accretion discs should develop a steady toroidal structure because radial transport mechanisms should be excluded by missing any radial shear flow damping. Therefore, thinner discs, also including a steady toroidal ring, identify that SPH inviscid modelling free of any incorrect pressure gradient excess among thick disc structures. This task is simplified since initial conditions deliberately favour thick discs. The physically viscous hydrodynamics of the disc is also addressed by adopting a Prandtl-like turbulent kinematic viscosity coefficient in the Navier–Stokes equations, distinguishing the roles of the bulk and shear viscosities.