On the role of tracking on Eulerian-Lagragian solutions of the transport equation

Abstract

We investigate the effect of tracking errors on the accuracy and stability of Eulerian-Lagrangian methods (ELMs) for the solution of the transport equation. A combination of formal analysis and numerical experimentation demonstrates that the effect is severe. Even moderate tracking errors substantially affect the preservation of the zeroth, first and second moments of concentration ( mass, phase and diffusion) and may lead to the instability of otherwise stable and very accurate ELMs. The use of accurate tracking algorithms is strongly recommended for Eulerian-Lagrangian simulations involving complex flows.

Key Words: Transport equation. Eulerian-Lagrangian methods. Tracking methods. Mass conservation. Numerical experimentation. Accuracy