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

FEDERICO BERGERO; JOAQUIN FERNANDEZ; MARGARITA PORTAPÌLA; ERNESTO KOFMAN

SIMULATION-TRANSACTIONS OF THE SOCIETY FOR MODELING AND SIMULATION INTERNATIONAL

SAGE PUBLICATIONS LTD

Lugar: London; Año: 2016 vol. 92 p. 47 - 61

0037-5497

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 perfor-mance 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.