Convergence Analysis of Numerical Solutions of Advection-Diffusion-Reaction Equations Using a Finite Difference Method an Application to Air Pollution Problems

Surattana Sungnul; Kanokwarun Para; Elvin James Moore; Sekson Sirisubtawee; Sutthisak Phongthanapanich

doi:10.20944/preprints202309.1123.v1

How to cite: Sungnul, S.; Para, K.; Moore, E.J.; Sirisubtawee, S.; Phongthanapanich, S. Convergence Analysis of Numerical Solutions of Advection-Diffusion-Reaction Equations Using a Finite Difference Method an Application to Air Pollution Problems. Preprints 2023, 2023091123. https://doi.org/10.20944/preprints202309.1123.v1 Sungnul, S.; Para, K.; Moore, E.J.; Sirisubtawee, S.; Phongthanapanich, S. Convergence Analysis of Numerical Solutions of Advection-Diffusion-Reaction Equations Using a Finite Difference Method an Application to Air Pollution Problems. Preprints 2023, 2023091123. https://doi.org/10.20944/preprints202309.1123.v1

Abstract

In this paper, we analyze the convergence of a finite difference method with the implicit forward time central space (FTCS) scheme for solving the three-dimensional advection-diffusion-reaction equation (ADRE). It is proved that the method is unconditionally convergent. We apply the scheme to obtain numerical solutions for the transport of pollutants in street tunnel problems with various reaction coefficients and various rates of change of concentrations of sources or sinks of pollution.

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Convergence Analysis of Numerical Solutions of Advection-Diffusion-Reaction Equations Using a Finite Difference Method an Application to Air Pollution Problems

Abstract

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