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A Space-Time Adaptive Algorithm to Illustrate the Lack of Collision of a Rigid Disk Falling in an Incompressible Fluid

Authors
  • Dubuis, Samuel1
  • Picasso, Marco1
  • Wittwer, Peter1
  • 1 Institute of Mathematics, EPFL, 1015 , (Switzerland)
Type
Published Article
Journal
Computational Methods in Applied Mathematics
Publisher
De Gruyter
Publication Date
Nov 07, 2020
Volume
21
Issue
2
Pages
317–334
Identifiers
DOI: 10.1515/cmam-2020-0046
Source
De Gruyter
Keywords
License
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Abstract

A space-time adaptive algorithm to solve the motion of a rigid disk in an incompressible Newtonian fluid is presented, which allows collision or quasi-collision processes to be computed with high accuracy. In particular, we recover the theoretical result proven in [M. Hillairet, Lack of collision between solid bodies in a 2D incompressible viscous flow, Comm. Partial Differential Equations 32 2007, 7–9, 1345–1371], that the disk will never touch the boundary of the domain in finite time. Anisotropic, continuous piecewise linear finite elements are used for the space discretization, the Euler scheme for the time discretization. The adaptive criteria are based on a posteriori error estimates for simpler problems.

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