Stability and error analysis of nodal expansion method for convection-diffusion equation

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The development, and stability and error analyses of nodal expansion method (NEM) for one dimensional steady-state convection diffusion equation is presented. Following the traditional procedure to develop NEM, the discrete formulation of the convection-diffusion equation, which is similar to the standard finite difference scheme, is derived. The method of discrete perturbation analysis is applied to this discrete form to study the stability of the NEM. The scheme based on the NEM is found to be stable for local Peclet number less than 4.644. A maximum principle is proved for the NEM scheme, followed by an error analysis carried out by applying the Maximum principle together with a carefully constructed comparison function. The scheme for the convection diffusion equation is of second-order. Numerical experiments are carried and the results agree with the conclusions of the stability and error analyses.

Original languageEnglish (US)
Title of host publicationInternational Congress on Advances in Nuclear Power Plants 2012, ICAPP 2012
Pages2248-2257
Number of pages10
StatePublished - Nov 19 2012
EventInternational Congress on Advances in Nuclear Power Plants 2012, ICAPP 2012 - Chicago, IL, United States
Duration: Jun 24 2012Jun 28 2012

Publication series

NameInternational Congress on Advances in Nuclear Power Plants 2012, ICAPP 2012
Volume4

Other

OtherInternational Congress on Advances in Nuclear Power Plants 2012, ICAPP 2012
CountryUnited States
CityChicago, IL
Period6/24/126/28/12

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Nuclear Energy and Engineering

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  • Cite this

    Deng, Z., Rizwan-uddin, Li, F., & Sun, Y. (2012). Stability and error analysis of nodal expansion method for convection-diffusion equation. In International Congress on Advances in Nuclear Power Plants 2012, ICAPP 2012 (pp. 2248-2257). (International Congress on Advances in Nuclear Power Plants 2012, ICAPP 2012; Vol. 4).