Second-order spatial accuracy in Lagrangian-Eulerian spray calculations

The current work establishes the order of accuracy of existing Lagrangian - Eulerian tracking methods and requirements for second-order spatial accuracy. A simple, unconditionally stable method can be used for basic velocity integration, and linear interpolation is required for gas-to-liquid coupling. A theoretical approach is presented for calculating spatial errors in liquid-to-gas coupling, which indicates that a simple "nearest- neighbor" approach is adequate for second-order accuracy. This result is contrary to past observations in the literature, but it is confirmed with convergence tests. Numerical test results include two-phase simulations with a Monte Carlo treatment of particle injection.