Is Lagrangian weight crucial in the direct forcing immersed boundary method?

Abstract

Particle resolved direct numerical simulation (PR-DNS) is one of the most powerful research tools for particle laden flows. Among a few most popular PR-DNS methods, the direct forcing immersed boundary method (DF-IBM) has obtained great success and has been adopted in various simulations of rigid particulate flows. Within DF-IBM, Eulerian and Lagrangian frameworks are used to depict the continuum and dispersed phases, respectively. Interpolation between the two frameworks is accomplished through a discrete delta function. It is generally believed that a Lagrangian weight attached to each Lagrangian marker, which is distributed on a particle’s surface, needs to be carefully chosen. To be more specific, the Lagrangian weight is supposed to match the local Eulerian cell. The matching requirement is not trivial for non-uniform Eulerian mesh or irregular shaped particles. There are various methods developed to calculate the Lagrangian weight. Here, the Lagrangian weights in a few testing cases have been calculated following two intuitively “straightforward” methods. It turns out there are substantial discrepancies in the Lagrangian weights obtained from different methods. However, further numerical examples demonstrate that such discrepancies have negligible effects on the flow dynamics. So a natural question is raised: Is Lagrangian weight crucial in the direct forcing immersed boundary method? A negative answer to this question is suggested. More detailed analysis is provided in a forthcoming paper.