EulerianLagrangianModelle

EulerianLagrangianModelle, commonly referred to as Eulerian–Lagrangian models, are numerical methods for simulating dispersed multiphase flows in which the carrier fluid is described on a fixed spatial grid (Eulerian frame) while the dispersed phase particles are tracked individually in a moving reference frame (Lagrangian frame).

The fluid phase is governed by the Navier–Stokes equations on the Eulerian grid. The particle phase follows Newton’s second law, with forces including drag, buoyancy, gravity, and sometimes added mass and history effects. The two phases exchange momentum and energy through coupling terms, enabling one-way or two-way coupling depending on particle loading and physics.

Numerical implementation involves interpolating fluid velocities to particle positions, integrating particle trajectories in time, and depositing the drag forces back onto the grid. Common drag models range from Stokes’ law for small Reynolds numbers to more general correlations like Schiller–Naumann. The approach often uses the point-particle assumption for subgrid-scale particles, and may include heat and mass transfer between phases.

Applications include spray drying, combustion with droplets or soot, aerosol transport, inkjet and spray cooling, and sediment transport. Eulerian–Lagrangian models provide detailed particle histories and feedback effects but require accurate drag and transfer models and can be computationally intensive for large particle populations.

Variants and software packages exist that implement Eulerian–Lagrangian models, including discrete phase models in commercial CFD codes and open-source tools. Related approaches include Eulerian–Eulerian two-fluid models, which treat the dispersed phase as a continuous field.