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CAM Seminar

Speaker: Martina Bukac
Affiliation: Department of Applied and Computational Mathematics and Statistics, University of Notre Dame

Title: Adaptive time-stepping methods for fluid-structure interaction problems

Abstract:  In realistic flow problems described by partial differential equations (PDEs), where the dynamics are not known, or in which the variables are changing rapidly, the robust, adaptive time-stepping is central to accurately and efficiently predict the long-term behavior of the solution. This is especially important in the coupled flow problems, such as the fluid-structure interaction (FSI), which often exhibit complex dynamic behavior. While the adaptive spatial mesh refinement techniques are well established and widely used, less attention has been given to the adaptive time-stepping methods for PDEs. We will discuss novel, adaptive, partitioned numerical methods for FSI problems with thick and thin structures. The time integration in the proposed methods is based on the refactorized Cauchy's one-legged 'theta-like' method, which consists of a backward Euler method, where the fluid and structure sub-problems are sub-iterated until convergence, followed by a forward Euler method.The bulk of the computation is done by the backward Euler method, as the forward Euler step is equivalent to (and implemented as) a linear extrapolation. We will present the numerical analysis of the proposed methods showing linear convergence of the sub-iterative process and unconditional stability. The time adaptation strategies will be discussed. The properties of the methods, as well as the selection of the parameters used in the adaptive process, will be explored in numerical examples.

Wednesday, October 27, 2021 at 3:35pm to 4:35pm

AYR, 112

Event Type

Lectures & Presentations




Current Students, Faculty & Staff



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Abner J. Salgado

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