An Error Analysis of Streaklines as Curves

Kazuhiro Itakura, Masahisa Tabata

Research output: Contribution to journalArticle

Abstract

A streakline is a visible curve consisting of fluid particles which emerged continuously from a fixed point in a given flow field. In many cases we do not know the exact velocity field but can get an approximate velocity field. The computation of streaklines includes the discretization error as well as the error caused by the approximate velocity field. We give an error analysis of streaklines as curves in terms of τ and h, discretization parameters of the streakline and of the velocity field. We show that, when the velocity field is approximated piecewise linearly, a computation scheme based on the Heun method is the best choice to approximate streaklines from the viewpoint of accuracy and efficiency. We present simulation results of streaklines emerging from the surface of a circular cylinder at Reynolds numbers 100 and 10000.

Original languageEnglish
Pages (from-to)1-23
Number of pages23
JournalJapan Journal of Industrial and Applied Mathematics
Volume16
Issue number1
Publication statusPublished - 1999 Feb
Externally publishedYes

Fingerprint

Error Analysis
Error analysis
Velocity Field
Curve
Discretization Error
Circular Cylinder
Circular cylinders
Flow Field
Reynolds number
Flow fields
Linearly
Discretization
Fixed point
Fluid
Fluids
Simulation

Keywords

  • Error analysis
  • Flows past a circular cylinder
  • Hausdorff distance
  • One-step methods for ordinary differential equations
  • Streaklines

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

An Error Analysis of Streaklines as Curves. / Itakura, Kazuhiro; Tabata, Masahisa.

In: Japan Journal of Industrial and Applied Mathematics, Vol. 16, No. 1, 02.1999, p. 1-23.

Research output: Contribution to journalArticle

Itakura, Kazuhiro ; Tabata, Masahisa. / An Error Analysis of Streaklines as Curves. In: Japan Journal of Industrial and Applied Mathematics. 1999 ; Vol. 16, No. 1. pp. 1-23.
@article{630124b8cb6b47eb9962b7d67bc34c21,
title = "An Error Analysis of Streaklines as Curves",
abstract = "A streakline is a visible curve consisting of fluid particles which emerged continuously from a fixed point in a given flow field. In many cases we do not know the exact velocity field but can get an approximate velocity field. The computation of streaklines includes the discretization error as well as the error caused by the approximate velocity field. We give an error analysis of streaklines as curves in terms of τ and h, discretization parameters of the streakline and of the velocity field. We show that, when the velocity field is approximated piecewise linearly, a computation scheme based on the Heun method is the best choice to approximate streaklines from the viewpoint of accuracy and efficiency. We present simulation results of streaklines emerging from the surface of a circular cylinder at Reynolds numbers 100 and 10000.",
keywords = "Error analysis, Flows past a circular cylinder, Hausdorff distance, One-step methods for ordinary differential equations, Streaklines",
author = "Kazuhiro Itakura and Masahisa Tabata",
year = "1999",
month = "2",
language = "English",
volume = "16",
pages = "1--23",
journal = "Japan Journal of Industrial and Applied Mathematics",
issn = "0916-7005",
publisher = "Springer Japan",
number = "1",

}

TY - JOUR

T1 - An Error Analysis of Streaklines as Curves

AU - Itakura, Kazuhiro

AU - Tabata, Masahisa

PY - 1999/2

Y1 - 1999/2

N2 - A streakline is a visible curve consisting of fluid particles which emerged continuously from a fixed point in a given flow field. In many cases we do not know the exact velocity field but can get an approximate velocity field. The computation of streaklines includes the discretization error as well as the error caused by the approximate velocity field. We give an error analysis of streaklines as curves in terms of τ and h, discretization parameters of the streakline and of the velocity field. We show that, when the velocity field is approximated piecewise linearly, a computation scheme based on the Heun method is the best choice to approximate streaklines from the viewpoint of accuracy and efficiency. We present simulation results of streaklines emerging from the surface of a circular cylinder at Reynolds numbers 100 and 10000.

AB - A streakline is a visible curve consisting of fluid particles which emerged continuously from a fixed point in a given flow field. In many cases we do not know the exact velocity field but can get an approximate velocity field. The computation of streaklines includes the discretization error as well as the error caused by the approximate velocity field. We give an error analysis of streaklines as curves in terms of τ and h, discretization parameters of the streakline and of the velocity field. We show that, when the velocity field is approximated piecewise linearly, a computation scheme based on the Heun method is the best choice to approximate streaklines from the viewpoint of accuracy and efficiency. We present simulation results of streaklines emerging from the surface of a circular cylinder at Reynolds numbers 100 and 10000.

KW - Error analysis

KW - Flows past a circular cylinder

KW - Hausdorff distance

KW - One-step methods for ordinary differential equations

KW - Streaklines

UR - http://www.scopus.com/inward/record.url?scp=0347156356&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347156356&partnerID=8YFLogxK

M3 - Article

VL - 16

SP - 1

EP - 23

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

IS - 1

ER -