A fast moving least squares approximation with adaptive Lagrangian mesh refinement for large scale immersed boundary simulations

TL;DR

This paper introduces a fast moving least squares approximation and adaptive mesh refinement techniques to enhance large-scale immersed boundary simulations involving deformable bodies in turbulent flows, reducing computational costs.

Contribution

It presents a novel fast-MLS method and an adaptive Lagrangian mesh refinement procedure that improve efficiency and accuracy in large-scale immersed boundary simulations.

Findings

Fast-MLS significantly reduces computational time compared to exact MLS.

Adaptive mesh refinement decreases the number of Lagrangian nodes needed.

Collision detection algorithm efficiently identifies interactions with minimal overhead.

Abstract

In this paper we propose and test the validity of simple and easy-to-implement algorithms within the immersed boundary framework geared towards large scale simulations involving thousands of deformable bodies in highly turbulent flows. First, we introduce a fast moving least squares (fast-MLS) approximation technique with which we speed up the process of building transfer functions during the simulations which leads to considerable reductions in computational time. We compare the accuracy of the fast-MLS against the exact moving least squares (MLS) for the standard problem of uniform flow over a sphere. In order to overcome the restrictions set by the resolution coupling of the Lagrangian and Eulerian meshes in this particular immersed boundary method, we present an adaptive Lagrangian mesh refinement procedure that is capable of drastically reducing the number of required nodes of the basic Lagrangian mesh when the immersed boundaries can move and deform. Finally, a coarse-grained collision detection algorithm is presented which can detect collision events between several Lagrangian markers residing on separate complex geometries with minimal computational overhead.