Hybrid Eulerian–Lagrangian approach for direct numerical simulations of elastic turbulence

Direct Numerical Simulation (DNS) is a fundamental tool for studying elastic turbulence (ET), as the polymer stresses that trigger ET are not directly accessible experimentally. We discuss a hybrid Eulerian–Lagrangian approach for DNS, and we show that the main ET features can be consistently observed in a wide range of concentrations and Weissenberg numbers. The hybrid approach does not require a larger resolution compared to fully Eulerian simulations, with the advantage of more accurate predictions of the polymer stress, and a clear link between model parameters and real polymer properties. Furthermore, a Lagrangian description of the polymer phase allows to explore the limiting, but realistic, conditions of small concentration and large Weissenberg number.