A second-order space and time nodal method for the one-dimensional convection-diffusion equation

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We present a nodal integral method for the one-dimensional convection-diffusion equation. The development is carried out in the nodal spirit, and results in a method that is second order both in space and time variables. Extension of this method, which is characterized by inherent upwinding, to multi-dimensional problems is straightforward. The nodal method's ability to yield accurate results on rather coarse mesh sizes when coupled with node interior reconstruction of the solution results in a rather powerful scheme that can accurately resolve the solution - even in regions with sharp gradients - with relatively large node sizes. Three widely used problems are solved numerically to demonstrate the properties of the nodal method developed here.

Original languageEnglish (US)
Pages (from-to)233-247
Number of pages15
JournalComputers and Fluids
Issue number3
StatePublished - Mar 1997

ASJC Scopus subject areas

  • General Computer Science
  • General Engineering

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