Inflow/outflow with Dirichlet boundary conditions for pressure in ISPH

In the present work we propose a new algorithm for open boundary treatment in ISPH. In the literature a few models for open boundary conditions are available, but most of them are applied to weakly compressible SPH (WCSPH) only. In our method the inflow/outflow is driven by true Dirichlet boundary conditions of the projected pressure field. We ensure the Dirichlet boundary condition by a particle mirroring technique at the open boundary to compute the pressure field. This procedure enables us to handle variable inlet velocities across the open boundary. The Dirichlet boundary conditions are introduced for the projected pressure matrix. We apply an error analysis for a Hagen-Poiseuille flow driven by a pressure gradient and demonstrate the robustness and accuracy with a flow around a cylinder and an oscillating flow, where inlet and outlet conditions periodically change. Additionally, a volume flux controller is presented in combination with variable pressure boundary conditions. Finally, the new open boundary treatment is applied to a bubble formation process during gas injection and validated with experimental results.