Accurate computation of surface stresses and forces with immersed boundary methods

Andres Goza, Sebastian Liska, Benjamin Morley, Tim Colonius

Research output: Contribution to journalArticlepeer-review

Abstract

Many immersed boundary methods solve for surface stresses that impose the velocity boundary conditions on an immersed body. These surface stresses may contain spurious oscillations that make them ill-suited for representing the physical surface stresses on the body. Moreover, these inaccurate stresses often lead to unphysical oscillations in the history of integrated surface forces such as the coefficient of lift. While the errors in the surface stresses and forces do not necessarily affect the convergence of the velocity field, it is desirable, especially in fluid-structure interaction problems, to obtain smooth and convergent stress distributions on the surface. To this end, we show that the equation for the surface stresses is an integral equation of the first kind whose ill-posedness is the source of spurious oscillations in the stresses. We also demonstrate that for sufficiently smooth delta functions, the oscillations may be filtered out to obtain physically accurate surface stresses. The filtering is applied as a post-processing procedure, so that the convergence of the velocity field is unaffected. We demonstrate the efficacy of the method by computing stresses and forces that converge to the physical stresses and forces for several test problems.

Original languageEnglish (US)
Pages (from-to)860-873
Number of pages14
JournalJournal of Computational Physics
Volume321
DOIs
StatePublished - Sep 15 2016
Externally publishedYes

Keywords

  • Fluid-structure interaction
  • Immersed boundary method
  • Integral equation of the first kind
  • Non-physical surface forces
  • Regularization

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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