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On the application of SUPG/θ-method in 2D advection–diffusion-reaction simulation

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Abstract

The SUPG/θ-method for applications in 2D advection–diffusion transport simulation is reviewed and it is presented in details. Spatial discretization is done with finite elements method with stabilized streamline upwind Petrov–Galerkin method, and time discretization was done with θ-stable finite difference operator. Numerical tests showed that this algorithm is general and robust and it can be applied to simulate simple problems of mass transport; for example, pure advection phenomenon in structured mesh, as well as reactive advection–diffusion transport with an unstructured mesh, and not well-behaved velocity field. The method was applied in a simulation of the transport of total phosphorus in the Lake Água Preta, and the results were validated by comparison with experimental data. The computational cost is directly associated with the value of the safety factor, introduced to assure the stability of the method.

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Abbreviations

\(\varvec{C}\) :

Damping matrix

\(C\) :

Mass concentration, mg/L

D :

Diffusion coefficient or diffusivity, m2/s

h :

Local size mesh

k :

Reaction coefficient

\(\varvec{N}\) :

Basis function vector

n :

Normal vector

n :

Time step

\(P\) :

Perturbation term to the weighting function

s :

Safety factor

S :

Source term

t :

Time, s

u :

Velocity vector, m/s

\(w\) :

Weight function

x :

Spatial vector, m

\(\Upgamma\) :

Contour of the model

\(\theta\) :

Method for time discretization

\(\tau\) :

Stabilization parameter

\({\varvec{\Upomega}}\) :

Domain of the model

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Acknowledgments

The first author would like to thanks to FAPESPA for financial support.

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Authors and Affiliations

  1. Faculty of Exact Sciences and Technology, Federal University of Pará, Abaetetuba, Pará, Brazil

    Rômulo Correa Lima

  2. Faculty of Mechanical Engineering, Federal University of Pará, Belém, Pará, Brazil

    André Luis Amarante Mesquita & Erb Ferreira Lins

  3. Faculty of Sanitary and Environmental Engineering, Federal University of Pará, Belém, Pará, Brazil

    Claudio José Cavalcante Blanco

  4. Graduate Program in Civil Engineering, Federal University of Pará, Belém, Pará, Brazil

    Maria de Lourdes Souza Santos

  5. INRS-ETE Institut National de la Recherche Scientifique, Québec, QC, Canada

    Yves Secretan

Authors
  1. Rômulo Correa Lima
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  2. André Luis Amarante Mesquita
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  3. Claudio José Cavalcante Blanco
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  4. Erb Ferreira Lins
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  5. Maria de Lourdes Souza Santos
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  6. Yves Secretan
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Correspondence to Rômulo Correa Lima.

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Technical Editor: Francisco Cunha.

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Lima, R.C., Mesquita, A.L.A., Blanco, C.J.C. et al. On the application of SUPG/θ-method in 2D advection–diffusion-reaction simulation. J Braz. Soc. Mech. Sci. Eng. 36, 591–603 (2014). https://doi.org/10.1007/s40430-013-0099-6

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  • DOI: https://doi.org/10.1007/s40430-013-0099-6

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