An Immersed Boundary Method with Direct Forcing for the Simulation of Particulate Flows

TL;DR

This paper introduces an improved immersed boundary method with direct forcing for simulating viscous flows around particles, enhancing accuracy and efficiency in complex particulate flow scenarios.

Contribution

It integrates Peskin's regularized delta function into a direct fluid-solid interaction formulation within a finite-difference framework, enabling smoother transfer and larger time steps.

Findings

Accurate simulation of flow around a single cylinder.

Efficient sedimentation of 1000 spherical particles.

Demonstrated improved accuracy and computational efficiency.

Abstract

We present an improved method for computing incompressible viscous flow around suspended rigid particles using a fixed and uniform computational grid. The main idea is to incorporate Peskin's regularized delta function approach [Acta Numerica 11 (2002) 1] into a direct formulation of the fluid-solid interaction force in order to allow for a smooth transfer between Eulerian and Lagrangian representations while at the same time avoiding strong restrictions of the time step. This technique was implemented in a finite-difference and fractional-step context. A variety of two- and three-dimensional simulations are presented, ranging from the flow around a single cylinder to the sedimentation of 1000 spherical particles. The accuracy and efficiency of the current method are clearly demonstrated.