On modeling the grain settling through viscous incompressible fluid problem using smoothed particle hydrodynamics method

I. I. Potapov, O. V. Reshetnikova

Computer Centre of Far Eastern Branch RAS, Khabarovsk

Abstract: In this paper was formulates the settling velocity determining problem for a single particle. To solve it, an original version of the smoothed particle method (SPH) is proposed where settling particle affects on surrounding fluid particles movement. Herewith the calculation of forces acting on particle (except for inertial forces which takes attached mass effect) is performed according by analytical mechanics formulas for a material point. This mathematical formulation and calculation algorithm was verificated by using open source code «SPH_Lab2d». Dependences for the particle settling velocity on its diameter are obtained for various cases of fluid volume discretization. The results demonstrate a good conformance this property to values, that determined by the experimental data and known phenomenological dependences for quartz sand.

Keywords: settling velocity, mesh-free SPH method, composite kernel, smoothing radius, open source software.

DOI: 10.15514/ISPRAS-2024-36(4)-15