Modeling Incompressible Fluid Flow Using SPH

Smoothed Particle Hydrodynamics, SPH, is a pure Lagrangian method. SPH has certain advantages over other numerical methods especially for problems encounter deformable boundaries, multiphase fluid and free surfaces. However, like all methods using discrete particles to integral governing equations, SPH sufferers from severe numerical errors in implementing boundary conditions. In this study, a SPH method is extended to model two dimensional incompressible steady state flows between two parallel plates. Solid wall boundary condition is modeled by using three types of particles. It will be shown that by utilizing these types of particles, fluid particles are not allowed to penetrate into the solid boundary and also the no slip condition is satisfied. The accuracy of proposed methods is assessed by comparing the obtained results to the analytical result. In this issue periodic and nonperiodic boundary condition at inlet/outlet are also described. For the nonperiodic case, the velocity profile of two dimensional flow between two parallel plates in Re=20 is exactly similar to the analytical solution.

Keywords:

SPH method , Incompressible Flow , Boundary Condition