In this article, we study the effects of replacing the time discretization by the quantization of the state variables on a one dimensional 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 the conventional algorithms (DOPRI, Radau and DASSL) in more than one order of magnitude.
Cellular automata are discrete dynamical systems that provide a mathematical framework for modelling, studying and predicting the behaviour and response of systems across many different disciplines and domains, ranging from physical and biological to computational and social models. Cell-DEVS is a formalism that provides a discrete event approach to define cellular models with timing delay constructions and using simple definition of complex timing. It has been shown that the application of the Cell-DEVS paradigm produces a significant reduction in the development times of cell-shaped models and a wide variety of complex models has been developed using this approach. In this work we present the definition of complex cellular automata models using the Cell-DEVS paradigm, we use the CD++ tool to obtain executable models and study their behaviour through computer simulation.
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