An efficient parallel immersed boundary algorithm using a pseudo-compressible fluid solver

TL;DR

This paper introduces a highly efficient parallel immersed boundary algorithm that leverages a pseudo-compressibility approach, enabling explicit computation, excellent scalability, and accurate fluid-structure interaction simulations in multiple dimensions.

Contribution

It presents a novel parallel algorithm using pseudo-compressibility for immersed boundary methods, improving efficiency and scalability over existing projection-based solvers.

Findings

Achieves linear computational complexity with explicit methods

Demonstrates excellent parallel scaling in simulations

Provides accurate results comparable to second-order projection methods

Abstract

We propose an efficient algorithm for the immersed boundary method on distributed-memory architectures, with the computational complexity of a completely explicit method and excellent parallel scaling. The algorithm utilizes the pseudo-compressibility method recently proposed by Guermond and Minev [Comptes Rendus Mathematique, 348:581-585, 2010] that uses a directional splitting strategy to discretize the incompressible Navier-Stokes equations, thereby reducing the linear systems to a series of one-dimensional tridiagonal systems. We perform numerical simulations of several fluid-structure interaction problems in two and three dimensions and study the accuracy and convergence rates of the proposed algorithm. For these problems, we compare the proposed algorithm against other second-order projection-based fluid solvers. Lastly, the strong and weak scaling properties of the proposed algorithm are investigated.