Time discretization versus state quantization in the simulation of a one-dimensional advection–diffusion–reaction equation

In this article, we study the effects of replacing the time discretization by the quantization of the state variables on a one-dimensional (1D) advection–diffusion–reaction (ADR) problem. For that purpose the 1D ADR equation is first discretized in space using a regular grid, to obtain a set of time...

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Bibliographic Details
Published in:Simulation (San Diego, Calif.) Calif.), 2016-01, Vol.92 (1), p.47-61
Main Authors: Bergero, Federico, Fernández, Joaquín, Kofman, Ernesto, Portapila, Margarita
Format: Article
Language:English
Subjects:
Algorithms
Computer simulation
Differential equations
Diffusion
Discretization
Mathematical analysis
Quantization
Time dependence
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Summary:In this article, we study the effects of replacing the time discretization by the quantization of the state variables on a one-dimensional (1D) advection–diffusion–reaction (ADR) problem. For that purpose the 1D ADR equation is first discretized in space using a regular grid, to obtain a set of time-dependent ordinary differential equations (ODEs). Then we compare the simulation performance using classic discrete time algorithms and using quantized state systems (QSS) methods. The performance analysis is done for different sets of diffusion and reaction parameters and also changing the space discretization refinement. This analysis shows that, in advection–reaction-dominated situations, the second-order linearly implicit QSS method outperforms all of the conventional algorithms (DOPRI, Radau and DASSL) by more than one order of magnitude.
ISSN:0037-5497
1741-3133
DOI:10.1177/0037549715616683