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Unconditionally Stable Pressure-Correction Schemes for a Nonlinear Fluid-Structure Interaction Model

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Abstract

We consider in this paper numerical approximation of a nonlinear fluid-structure interaction (FSI) model with a fixed interface. We construct a new class of pressure-correction schemes for the FSI problem, and prove rigorously that they are unconditionally stable. These schemes are computationally very efficient, as they lead to, at each time step, a coupled linear elliptic system for the velocity and displacement in the whole region and a discrete Poisson equation in the fluid region.

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Ying He & Jie Shen

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  1. Ying He
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  2. Jie Shen
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Correspondence to Jie Shen.

Additional information

This work is partially supported by NSF DMS-1620262, DMS-1720442 and AFOSR FA9550-16-1-0102.

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He, Y., Shen, J. Unconditionally Stable Pressure-Correction Schemes for a Nonlinear Fluid-Structure Interaction Model. Commun. Appl. Math. Comput. 1, 61–80 (2019). https://doi.org/10.1007/s42967-019-0004-0

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  • DOI: https://doi.org/10.1007/s42967-019-0004-0

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