A hybrid immersed boundary method for dense particle-laden flows

TL;DR

This paper introduces a hybrid immersed boundary method (HyBM) for simulating dense particle-laden flows, combining symmetrical and non-symmetrical interpolation to improve accuracy especially near boundaries and other particles.

Contribution

The paper presents a novel hybrid immersed boundary method that adaptively switches between interpolation schemes to enhance accuracy in dense particle flows.

Findings

HyBM outperforms classical IBM in accuracy at coarser meshes.

HyBM effectively handles complex boundary interactions.

Validated with multiple literature test-cases.

Abstract

A novel smooth immersed boundary method (IBM) based on a direct-forcing formulation is proposed to simulate incompressible dense particle-laden flows. This IBM relies on a regularization of the transfer function between the Eulerian grid points (to discretise the fluid governing equations) and Lagrangian markers (to represent the particle surface) to fulfill the no-slip condition at the surfaces of the particles, allowing both symmetrical and non-symmetrical interpolation and spreading supports to be used. This enables that local source term contributions to the Eulerian grid, accounting for the boundary condition enforced at a Lagrangian marker on the surface of a particle, can be present on the inside of the particle only when this is beneficial, for instance when the Lagrangian marker is near another particle surface or near a domain boundary. However, when the Lagrangian marker is not near another particle surface or a domain boundary, the interpolation and spreading operators are locally symmetrical, meaning a ``classic'' IBM scheme is adopted. This approach, named hybrid IBM (HyBM), is validated with a number of test-cases from the literature. These results show that the HyBM achieves more accurate results compared to a classical IBM framework, especially at coarser mesh resolutions, when there are Lagrangian markers close to a particle surface or a domain wall.