A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains

Mark N. Linnick, Hermann F Fasel

Research output: Contribution to journalArticle

211 Citations (Scopus)

Abstract

Immersed boundary methods and immersed interface methods are becoming increasingly popular for the computation of unsteady flows around complex geometries using a Cartesian grid. While good results, both qualitative and quantitative, have been obtained, most of the methods rely on low-order corrections to account for the immersed boundary. The objective of the present work is to present, as an alternative, a high-order modified immersed interface method for the 2D, unsteady, incompressible Navier-Stokes equations in stream function-vorticity formulation. The method employs an explicit fourth-order Runge-Kutta time integration scheme, fourth-order compact finite-differences for computation of spatial derivatives, and a nine-point, fourth-order compact discretization of the Poisson equation for computation of the stream function. Corrections to the finite difference schemes are used to maintain high formal accuracy at the immersed boundary, as confirmed by analytical tests. To validate the method in its application to incompressible flows, several physically relevant test cases are computed, including uniform flow past a circular cylinder and Tollmien - Schlichting waves in a boundary layer.

Original languageEnglish (US)
Pages (from-to)157-192
Number of pages36
JournalJournal of Computational Physics
Volume204
Issue number1
DOIs
StatePublished - Mar 20 2005

Fingerprint

incompressible flow
Incompressible flow
Tollmien-Schlichting waves
uniform flow
unsteady flow
Poisson equation
circular cylinders
Unsteady flow
Circular cylinders
Vorticity
Navier-Stokes equation
vorticity
Navier Stokes equations
boundary layers
Boundary layers
grids
Derivatives
formulations
Geometry
geometry

Keywords

  • Cartesian grid method
  • Finite difference methods
  • Immersed boundary
  • Immersed interface
  • Incompressible viscous fluids

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains. / Linnick, Mark N.; Fasel, Hermann F.

In: Journal of Computational Physics, Vol. 204, No. 1, 20.03.2005, p. 157-192.

Research output: Contribution to journalArticle

@article{86ecdeb7f5a5463a8493edfcc078d206,
title = "A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains",
abstract = "Immersed boundary methods and immersed interface methods are becoming increasingly popular for the computation of unsteady flows around complex geometries using a Cartesian grid. While good results, both qualitative and quantitative, have been obtained, most of the methods rely on low-order corrections to account for the immersed boundary. The objective of the present work is to present, as an alternative, a high-order modified immersed interface method for the 2D, unsteady, incompressible Navier-Stokes equations in stream function-vorticity formulation. The method employs an explicit fourth-order Runge-Kutta time integration scheme, fourth-order compact finite-differences for computation of spatial derivatives, and a nine-point, fourth-order compact discretization of the Poisson equation for computation of the stream function. Corrections to the finite difference schemes are used to maintain high formal accuracy at the immersed boundary, as confirmed by analytical tests. To validate the method in its application to incompressible flows, several physically relevant test cases are computed, including uniform flow past a circular cylinder and Tollmien - Schlichting waves in a boundary layer.",
keywords = "Cartesian grid method, Finite difference methods, Immersed boundary, Immersed interface, Incompressible viscous fluids",
author = "Linnick, {Mark N.} and Fasel, {Hermann F}",
year = "2005",
month = "3",
day = "20",
doi = "10.1016/j.jcp.2004.09.017",
language = "English (US)",
volume = "204",
pages = "157--192",
journal = "Journal of Computational Physics",
issn = "0021-9991",
publisher = "Academic Press Inc.",
number = "1",

}

TY - JOUR

T1 - A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains

AU - Linnick, Mark N.

AU - Fasel, Hermann F

PY - 2005/3/20

Y1 - 2005/3/20

N2 - Immersed boundary methods and immersed interface methods are becoming increasingly popular for the computation of unsteady flows around complex geometries using a Cartesian grid. While good results, both qualitative and quantitative, have been obtained, most of the methods rely on low-order corrections to account for the immersed boundary. The objective of the present work is to present, as an alternative, a high-order modified immersed interface method for the 2D, unsteady, incompressible Navier-Stokes equations in stream function-vorticity formulation. The method employs an explicit fourth-order Runge-Kutta time integration scheme, fourth-order compact finite-differences for computation of spatial derivatives, and a nine-point, fourth-order compact discretization of the Poisson equation for computation of the stream function. Corrections to the finite difference schemes are used to maintain high formal accuracy at the immersed boundary, as confirmed by analytical tests. To validate the method in its application to incompressible flows, several physically relevant test cases are computed, including uniform flow past a circular cylinder and Tollmien - Schlichting waves in a boundary layer.

AB - Immersed boundary methods and immersed interface methods are becoming increasingly popular for the computation of unsteady flows around complex geometries using a Cartesian grid. While good results, both qualitative and quantitative, have been obtained, most of the methods rely on low-order corrections to account for the immersed boundary. The objective of the present work is to present, as an alternative, a high-order modified immersed interface method for the 2D, unsteady, incompressible Navier-Stokes equations in stream function-vorticity formulation. The method employs an explicit fourth-order Runge-Kutta time integration scheme, fourth-order compact finite-differences for computation of spatial derivatives, and a nine-point, fourth-order compact discretization of the Poisson equation for computation of the stream function. Corrections to the finite difference schemes are used to maintain high formal accuracy at the immersed boundary, as confirmed by analytical tests. To validate the method in its application to incompressible flows, several physically relevant test cases are computed, including uniform flow past a circular cylinder and Tollmien - Schlichting waves in a boundary layer.

KW - Cartesian grid method

KW - Finite difference methods

KW - Immersed boundary

KW - Immersed interface

KW - Incompressible viscous fluids

UR - http://www.scopus.com/inward/record.url?scp=14544280218&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=14544280218&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2004.09.017

DO - 10.1016/j.jcp.2004.09.017

M3 - Article

AN - SCOPUS:14544280218

VL - 204

SP - 157

EP - 192

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 1

ER -