Nonreflecting Outlet Boundary Conditions for Smoothed Particle Hydrodynamics Simulation of Small-Scale Open-Channel Flow

Abstract

In this paper, we propose a nonreflecting outlet boundary condition (NROBC) for particle-based fluid simulation as a combination of inflow/outflow algorithm and periodic boundary condition. We assume to use δ-SPH scheme for weakly compressible flows. In the inflow/outflow algorithm, the domain is divided into four zones: fluid, wall, inflow and outflow zones. The NROBC proposed in this paper inherits the advantage of the periodic boundary condition in the sense that the number of particles is constant. This property contributes to conservation of total mass and insertion of inflow particles without rearranging process. The physical quantities such as density and velocity at the inflow zone are unknown depending on the situation. Our boundary condition supports both cases, prescribed and non-prescribed, and the loss of the accuracy is small even if the quantities are non-prescribed at the inflow zone. In addition, tensile instability is effectively reduced by particle shifting technique. Several simulations are presented to validate and demonstrate the applicability and versatility of the proposed technique. Comparisons between numerical results and analytical solutions are provided with very low Mean Square Error Percent (MSEP) in both test cases.