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Finite volume element method for analysis of unsteady reaction–diffusion problems

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Abstract

A finite volume element method is developed for analyzing unsteady scalar reaction–diffusion problems in two dimensions. The method combines the concepts that are employed in the finite volume and the finite element method together. The finite volume method is used to discretize the unsteady reaction–diffusion equation, while the finite element method is applied to estimate the gradient quantities at cell faces. Robustness and efficiency of the combined method have been evaluated on uniform rectangular grids by using available numerical solutions of the two-dimensional reaction–diffusion problems. The numerical solutions demonstrate that the combined method is stable and can provide accurate solution without spurious oscillation along the high-gradient boundary layers.

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Authors and Affiliations

  1. Department of Mechanical Engineering Technology, College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand

    Sutthisak Phongthanapanich

  2. Mechanical Engineering Department, Chulalongkorn University, Bangkok, 10330, Thailand

    Pramote Dechaumphai

Authors
  1. Sutthisak Phongthanapanich
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  2. Pramote Dechaumphai
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Correspondence to Pramote Dechaumphai.

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Phongthanapanich, S., Dechaumphai, P. Finite volume element method for analysis of unsteady reaction–diffusion problems. Acta Mech Sin 25, 481–489 (2009). https://doi.org/10.1007/s10409-009-0237-7

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  • DOI: https://doi.org/10.1007/s10409-009-0237-7

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