Immersed Boundary Simulations of Flows Driven by Moving Thin Membranes

TL;DR

This paper introduces a minimal thickness modification to the Boundary Data Immersion Method (BDIM-{ extsigma}) to improve the accuracy of immersed boundary simulations involving thin membranes, especially at high Reynolds numbers.

Contribution

A new minimal thickness modification for BDIM-{ extsigma} is proposed to address boundary condition violations in thin membrane simulations, enhancing accuracy in high-speed flows.

Findings

Adjustment of the Poisson matrix reduces errors in velocity, pressure, and force predictions.

Errors increase with Reynolds number without modification.

The new method enables efficient high-speed immersed surface simulations.

Abstract

Immersed boundary methods are extensively used for simulations of dynamic solid objects interacting with fluids due to their computational efficiency and modelling flexibility compared to body-fitted grid methods. However, thin geometries, such as shells and membranes, cause a violation of the boundary conditions across the surface for many immersed boundary projection algorithms. Using a one-dimensional analytical derivation and multi-dimensional numerical simulations, this manuscript shows that adjustment of the Poisson matrix itself is require to avoid large velocity, pressure, and force prediction errors when the pressure jump across the interface is substantial and that these errors increase with Reynolds number. A new minimal thickness modification is developed for the Boundary Data Immersion Method (BDIM-{\sigma}),which avoids these issues while still enabling the use of efficient projection algorithms for high-speed immersed surface simulations.