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High‐order methods for low Reynolds number flows around moving obstacles based on universal meshes
Author(s) -
Gawlik Evan S.,
Kabaria Hardik,
Lew Adrian J.
Publication year - 2015
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4891
Subject(s) - reynolds number , polygon mesh , convergence (economics) , mathematics , obstacle , finite element method , triangulation , boundary (topology) , flow (mathematics) , computer science , mathematical analysis , geometry , mathematical optimization , mechanics , physics , turbulence , political science , law , economics , thermodynamics , economic growth
Summary We propose a family of methods for simulating two‐dimensional incompressible, low Reynolds number flow around a moving obstacle whose motion is prescribed. The methods make use of a universal mesh: a fixed background mesh that adapts to the geometry of the immersed obstacle at all times by adjusting a few elements in the neighborhood of the obstacle's boundary. The resulting mesh provides a conforming triangulation of the fluid domain over which discretizations of any desired order of accuracy in space and time can be constructed using standard finite element spaces together with off‐the‐shelf time integrators. We demonstrate the approach by using Taylor‐Hood elements to approximate the fluid velocity and pressure. To integrate in time, we consider implicit Runge‐Kutta schemes as well as a fractional step scheme. We illustrate the methods and study their convergence numerically via examples that involve flow around obstacles that undergo prescribed deformations. Copyright © 2015 John Wiley & Sons, Ltd.