Implicit integrations for SPH in Semi-Lagrangian approach: application to the accretion disc modelling in a microquasar

TL;DR

This paper introduces an implicit integration scheme for SPH in a Semi-Lagrangian framework, enabling stable and efficient accretion disc simulations around black holes, overcoming explicit method limitations.

Contribution

The paper presents a novel implicit SPH integration method in a Semi-Lagrangian approach that avoids Jacobian matrix inversion, improving stability and efficiency in viscous flow simulations.

Findings

Successful application to accretion disc modeling around a black hole.

Comparison shows improved stability over explicit methods.

Validated with 1D and 2D critical tests.

Abstract

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.