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2020 | OriginalPaper | Chapter

1. Immersed Boundary Projection Methods

Authors : Benedikt Dorschner, Tim Colonius

Published in: Immersed Boundary Method

Publisher: Springer Singapore

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Abstract

Immersed boundary methods are an attractive alternative to body-fitted grids for complex geometries and fluid–structure interaction problems. The simplicity of the underlying Cartesian mesh allows for a number of useful conservation and stability properties to be embedded in the numerics, and for the resulting discrete equations to be solved efficiently and scalably. We review the immersed boundary projection method for incompressible flows, which implicitly satisfies the no-slip condition at immersed surfaces by solving a system of algebraic equations for surface traction. We discuss issues related to the smoothness of the surface stresses and solution strategies for strongly coupled fluid–structure interaction. For three-dimensional flows on unbounded domains, we discuss a fast lattice Green’s function method that provides for an adaptive domain comprising the vortical flow region and at the same time can be solved efficiently using extensions of the fast multipole method. To illustrate the methods, we present a series of benchmark simulations in two and three dimensions, ranging from inverted flag flutter, flow past spinning and inclined disks, and turbulent flow past a sphere.

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next chapter Direct Lagrangian Forcing Methods Based on Moving Least Squares

Typically, the first-order errors that are associated with the regularization of the delta functions are limited to a finite region near the surface, and this results in better than first-order accuracy in the \(L_2\) norm.

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Title: Immersed Boundary Projection Methods
Authors: Benedikt Dorschner
Tim Colonius
Publisher: Springer Singapore
Book: Immersed Boundary Method
Print ISBN: 978-981-15-3939-8

Electronic ISBN: 978-981-15-3940-4

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-981-15-3940-4_1

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