A Boundary Thickening-based Direct Forcing Immersed Boundary Method for Fully Resolved Simulation of Particle-laden Flows

TL;DR

This paper introduces a boundary thickening-based direct forcing immersed boundary method that improves boundary condition enforcement in particle-laden flow simulations, achieving high accuracy with lower computational cost.

Contribution

The proposed BTDF method enhances boundary condition accuracy in immersed boundary simulations by boundary thickening, maintaining low computational cost and robustness across various flow regimes.

Findings

Achieves accuracy comparable to advanced methods like MDF, IVC, RKPM.

Maintains low computational cost similar to conventional DF.

Demonstrates robustness in diverse flow simulations around a cylinder.

Abstract

A boundary thickening-based direct forcing (BTDF) immersed boundary (IB) method is proposed for fully resolved simulation of incompressible viscous flows laden with finite size particles. By slightly thickening the boundary thickness, the local communication between the Lagrangian points on the solid boundary and their neighboring fluid Eulerian grids is improved, based on an implicit direct forcing (IDF) approach and a partition-of-unity condition for the regularized delta function. This strategy yields a simple, yet much better imposition of the no-slip and no-penetration boundary conditions than the conventional direct forcing (DF) technique. In particular, the present BTDF method can achieve a numerical accuracy comparable with other representative improved methods, such as multi-direct forcing (MDF), implicit velocity correction (IVC) and the reproducing kernel particle method (RKPM), while its computation cost remains much lower and nearly equivalent to the conventional DF scheme. The dependence of the optimum thickness value of boundary thickening on the form of the regularized delta functions is also revealed. By coupling the lattice Boltzmann method (LBM) with BTDF-IB, the robustness of the present BTDF IB method is demonstrated using numerical simulations of creeping flow (Re=0.1), steady vortex separating flow (Re=40) and unsteady vortex shedding flow (Re=200) around a circular cylinder.