A Posteriori Error Analysis of Fluid-Stucture Interactions: Time Dependent Error

TL;DR

This paper applies a novel a posteriori error analysis to fluid-structure interaction simulations using the Method of Regularized Stokelets, revealing how errors propagate over time in moving boundary problems.

Contribution

It introduces a new approach to monitor regularization error and derives linearized adjoint equations for MRS in elastic boundary problems.

Findings

Error propagation over time is characterized in MRS simulations.

The regularization error monitoring method is novel.

Numerical results illustrate error evolution in biological fluid-structure interactions.

Abstract

A posteriori error analysis is a technique to quantify the error in particular simulations of a numerical approximation method. In this article, we use such an approach to analyze how various error components propagate in certain moving boundary problems. We study quasi-steady state simulations where slowly moving boundaries remain in mechanical equilibrium with a surrounding fluid. Such problems can be numerically approximated with the Method of Regularized Stokelets(MRS), a popular method used for studying viscous fluid-structure interactions, especially in biological applications. Our approach to monitoring the regularization error of the MRS is novel, along with the derivation of linearized adjoint equations to the governing equations of the MRS with a elastic elements. Our main numerical results provide a clear illustration of how the error evolves over time in several MRS simulations.