A globally Eulerian locally Lagrangian particle concentration scheme

For gas flows, a Lagrangian Concentration Differential Equation (LCDE) was solved along a particle path using Eulerian derivatives for the particle velocity divergence field. This equation is solved by a Globally Eulerian Locally Lagrangian (GELL) discretization technique which avoids the computationally intensive Jacobian calculations of the Full Lagrangian method, the steady-state assumption of the area method, and the computational inefficiency of the box-counting methods. The LCDE–GELL method was compared to such methods using a high-order temporal integration technique and evaluated for two fundamental flowfields: flow past a corner and past a cylinder. In the dilute limit, the particle concentration fields were predicted for various particle inertias (characterized by a range of Stokes numbers) including the zero-mass (tracer) limit for which an exact particle concentration solution exists. Both the weighted-average and ensemble-average methods required far more parcels to achieve the same accuracy demonstrated by the LCDE–GELL method. It is recommended that future work investigates the LCDE approach for three-dimensional, complex flows with particle–particle interaction to investigate its robustness.