A Posteriori Error Analysis of Fluid-Stucture Interactions: Time Dependent Error
For researchers using MRS in biological applications, this work offers a novel approach to monitor regularization error and derive adjoint equations, but the results are incremental as they only illustrate error evolution without quantitative improvements.
This paper develops a posteriori error analysis for the Method of Regularized Stokelets (MRS) in fluid-structure interactions, providing numerical results that show how error components evolve over time in quasi-steady state simulations.
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.