The velocity decomposition method for second-order accuracy in stochastic parcel simulations

In Lagrangian Monte Carlo simulations of liquid disperse flows, the prediction of inter-droplet momentum transfer and kinetic energy dissipation strongly depends on the spatial resolution of the collision algorithm. These dependencies are caused by systematic errors induced into the relative velocity between the colliding droplets. In this study, a velocity decomposition method is proposed, which eliminates the erroneous component of relative velocity. The velocity decomposition method significantly reduces numerical dependencies in the prediction of the collision outcome, leading to second order convergence of relative velocities, and of direct momentum transfer and kinetic energy dissipation. This is proven in synthetic validation cases and demonstrated by an engine-spray simulation exemplarily.