Energy dissipative characteristic schemes for the diffusive Oldroyd-B viscoelastic fluid

Mária Lukáčová-Medvid'ová, Hirofumi Notsu, Bangwei She

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

In this paper, we propose new energy dissipative characteristic numerical methods for the approximation of diffusive Oldroyd-B equations that are based either on the finite element or finite difference discretization. We prove energy stability of both schemes and illustrate their behavior on a series of numerical experiments. Using both the diffusive model and the logarithmic transformation of the elastic stress, we are able to obtain methods that converge as mesh parameter is refined.

Original languageEnglish
JournalInternational Journal for Numerical Methods in Fluids
DOIs
Publication statusAccepted/In press - 2015

Fingerprint

Oldroyd-B Fluid
Viscoelastic Fluid
Numerical methods
Characteristics Method
Fluids
Energy
Finite Difference
Logarithmic
Discretization
Experiments
Numerical Methods
Numerical Experiment
Mesh
Finite Element
Converge
Series
Approximation
Model

Keywords

  • Characteristic finite difference
  • Characteristic finite element
  • Energy stable
  • High Weissenberg
  • Logarithmic transformation
  • Viscoelastic fluids

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics
  • Applied Mathematics
  • Mechanical Engineering
  • Mechanics of Materials

Cite this

Energy dissipative characteristic schemes for the diffusive Oldroyd-B viscoelastic fluid. / Lukáčová-Medvid'ová, Mária; Notsu, Hirofumi; She, Bangwei.

In: International Journal for Numerical Methods in Fluids, 2015.

Research output: Contribution to journalArticle

@article{e40107a44d484c0aa3559d3f6a923265,
title = "Energy dissipative characteristic schemes for the diffusive Oldroyd-B viscoelastic fluid",
abstract = "In this paper, we propose new energy dissipative characteristic numerical methods for the approximation of diffusive Oldroyd-B equations that are based either on the finite element or finite difference discretization. We prove energy stability of both schemes and illustrate their behavior on a series of numerical experiments. Using both the diffusive model and the logarithmic transformation of the elastic stress, we are able to obtain methods that converge as mesh parameter is refined.",
keywords = "Characteristic finite difference, Characteristic finite element, Energy stable, High Weissenberg, Logarithmic transformation, Viscoelastic fluids",
author = "M{\'a}ria Luk{\'a}čov{\'a}-Medvid'ov{\'a} and Hirofumi Notsu and Bangwei She",
year = "2015",
doi = "10.1002/fld.4195",
language = "English",
journal = "International Journal for Numerical Methods in Fluids",
issn = "0271-2091",
publisher = "John Wiley and Sons Ltd",

}

TY - JOUR

T1 - Energy dissipative characteristic schemes for the diffusive Oldroyd-B viscoelastic fluid

AU - Lukáčová-Medvid'ová, Mária

AU - Notsu, Hirofumi

AU - She, Bangwei

PY - 2015

Y1 - 2015

N2 - In this paper, we propose new energy dissipative characteristic numerical methods for the approximation of diffusive Oldroyd-B equations that are based either on the finite element or finite difference discretization. We prove energy stability of both schemes and illustrate their behavior on a series of numerical experiments. Using both the diffusive model and the logarithmic transformation of the elastic stress, we are able to obtain methods that converge as mesh parameter is refined.

AB - In this paper, we propose new energy dissipative characteristic numerical methods for the approximation of diffusive Oldroyd-B equations that are based either on the finite element or finite difference discretization. We prove energy stability of both schemes and illustrate their behavior on a series of numerical experiments. Using both the diffusive model and the logarithmic transformation of the elastic stress, we are able to obtain methods that converge as mesh parameter is refined.

KW - Characteristic finite difference

KW - Characteristic finite element

KW - Energy stable

KW - High Weissenberg

KW - Logarithmic transformation

KW - Viscoelastic fluids

UR - http://www.scopus.com/inward/record.url?scp=84951806645&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84951806645&partnerID=8YFLogxK

U2 - 10.1002/fld.4195

DO - 10.1002/fld.4195

M3 - Article

AN - SCOPUS:84951806645

JO - International Journal for Numerical Methods in Fluids

JF - International Journal for Numerical Methods in Fluids

SN - 0271-2091

ER -