SPH Simulation of Poiseuille Flow

This document describes the implementation of Smoothed Particle Hydrodynamics (SPH) for simulating Poiseuille flow, where fluid motion is approximated by modeling interactions between discrete fluid particles. The computational approach incorporates periodic boundary conditions to handle flow periodicity and virtual particle solid wall conditions to represent boundary interactions efficiently. These boundary treatments are implemented through neighbor list management and force calculations that reduce computational overhead while maintaining accuracy. The core SPH algorithm involves calculating density approximations using kernel functions and solving momentum equations with particle-particle interaction forces. Proper implementation of these boundary conditions is critical for obtaining physically accurate results, as they directly affect pressure distribution and velocity profiles. While the author may have employed additional techniques such as time integration schemes or smoothing length adaptation to optimize the simulation, further details would be needed to confirm specific methodological enhancements.