Application of diagonally implicit Runge-Kutta method for solving time-dependent convection-diffusion equation

Zhihong Deng, Yuliang Sun, Fu Li, Rizwan-Uddin

Research output: Research - peer-reviewArticle

Abstract

An efficient scheme for solving transient convection-diffusion equation was developed. Modified nodal expansion method (MNEM) was utilized for spatial discretization, while two kinds of diagonally implicit Runge-Kutta (DIRK) schemes-second-order DIRK and fourth-order DIRK were adopted for time discretization. The numerical results show that the numerical results of TDMNEM code agree with analytical solutions very well. MNEM has good ability in capturing sharp temperature variation. The efficiency of two time discretization methods depend on problem and the error criteria which been selected.

LanguageEnglish (US)
Pages5-9
Number of pages5
JournalHedongli Gongcheng/Nuclear Power Engineering
Volume35
Issue number1
StatePublished - 2014

Fingerprint

Runge Kutta methods
Convection

Keywords

  • Convection-diffusion equation
  • Diagonally implicit Runge-Kutta schemes
  • Modified nodal expansion method

ASJC Scopus subject areas

  • Nuclear Energy and Engineering

Cite this

Application of diagonally implicit Runge-Kutta method for solving time-dependent convection-diffusion equation. / Deng, Zhihong; Sun, Yuliang; Li, Fu; Rizwan-Uddin.

In: Hedongli Gongcheng/Nuclear Power Engineering, Vol. 35, No. 1, 2014, p. 5-9.

Research output: Research - peer-reviewArticle

@article{c1cd578a759f410ca7c7b2354f82e960,
title = "Application of diagonally implicit Runge-Kutta method for solving time-dependent convection-diffusion equation",
abstract = "An efficient scheme for solving transient convection-diffusion equation was developed. Modified nodal expansion method (MNEM) was utilized for spatial discretization, while two kinds of diagonally implicit Runge-Kutta (DIRK) schemes-second-order DIRK and fourth-order DIRK were adopted for time discretization. The numerical results show that the numerical results of TDMNEM code agree with analytical solutions very well. MNEM has good ability in capturing sharp temperature variation. The efficiency of two time discretization methods depend on problem and the error criteria which been selected.",
keywords = "Convection-diffusion equation, Diagonally implicit Runge-Kutta schemes, Modified nodal expansion method",
author = "Zhihong Deng and Yuliang Sun and Fu Li and Rizwan-Uddin",
year = "2014",
volume = "35",
pages = "5--9",
journal = "Hedongli Gongcheng/Nuclear Power Engineering",
issn = "0258-0926",
publisher = "Yuan Zi Neng Chuban She",
number = "1",

}

TY - JOUR

T1 - Application of diagonally implicit Runge-Kutta method for solving time-dependent convection-diffusion equation

AU - Deng,Zhihong

AU - Sun,Yuliang

AU - Li,Fu

AU - Rizwan-Uddin,

PY - 2014

Y1 - 2014

N2 - An efficient scheme for solving transient convection-diffusion equation was developed. Modified nodal expansion method (MNEM) was utilized for spatial discretization, while two kinds of diagonally implicit Runge-Kutta (DIRK) schemes-second-order DIRK and fourth-order DIRK were adopted for time discretization. The numerical results show that the numerical results of TDMNEM code agree with analytical solutions very well. MNEM has good ability in capturing sharp temperature variation. The efficiency of two time discretization methods depend on problem and the error criteria which been selected.

AB - An efficient scheme for solving transient convection-diffusion equation was developed. Modified nodal expansion method (MNEM) was utilized for spatial discretization, while two kinds of diagonally implicit Runge-Kutta (DIRK) schemes-second-order DIRK and fourth-order DIRK were adopted for time discretization. The numerical results show that the numerical results of TDMNEM code agree with analytical solutions very well. MNEM has good ability in capturing sharp temperature variation. The efficiency of two time discretization methods depend on problem and the error criteria which been selected.

KW - Convection-diffusion equation

KW - Diagonally implicit Runge-Kutta schemes

KW - Modified nodal expansion method

UR - http://www.scopus.com/inward/record.url?scp=84896944191&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84896944191&partnerID=8YFLogxK

M3 - Article

VL - 35

SP - 5

EP - 9

JO - Hedongli Gongcheng/Nuclear Power Engineering

T2 - Hedongli Gongcheng/Nuclear Power Engineering

JF - Hedongli Gongcheng/Nuclear Power Engineering

SN - 0258-0926

IS - 1

ER -