Dynamical pressure boundary condition for weakly compressible smoothed particle hydrodynamics

This paper introduces a novel dynamical pressure boundary condition for the weakly compressible smoothed particle hydrodynamics simulation of channel flows. Unlike previous methods that rely on indirect approaches or ghost particles, our method integrates the boundary pressure directly into the SPH approximation of the pressure gradient on near-boundary particles. Additionally, we develop a meshfree bidirectional in-/outflow buffer by periodically relabeling buffer particles at each time step. This simple yet effective buffer enables the simulation of both unidirectional and bidirectional flows, especially those with mixed in-/outflow boundary conditions. We validate the accuracy and convergence of our method through benchmark cases involving unidirectional/bidirectional in-/outflows under constant and dynamic pressure or velocity conditions with available analytical solutions. Furthermore, we demonstrate its versatility in hemodynamic simulations by investigating generic carotid and aorta flows with the Windkessel model, paving the way for studying the cardiovascular system within a unified meshfree computational framework.