Extending Incompressible SPH framework for simulation of axisymmetric free-surface flows

Dynamics of a Newtonian fluid in a cylindrical symmetric domain can be conceptualized as axisymmetric flow. Full-scale 3D simulation of such problems requires large computational overhead. A new divergence-free Axisymmetric Incompressible Smoothed Particle Hydrodynamics (AxISPH) framework is proposed for modeling of Newtonian fluid flow with free-surface. The formulation employs the concept of variable axisymmetric volume based on current particle position to incorporate symmetry around the central axis. The framework utilizes a semi-implicit two-step approach to obtain hydrodynamic variables and minimizes errors in particle position. Laplace and gradient operators are modified to incorporate axisymmetric nature. A radial dam-break flow has been simulated with the proposed model and compared with three-dimensional ISPH result.