CIFASIS   20631
CENTRO INTERNACIONAL FRANCO ARGENTINO DE CIENCIAS DE LA INFORMACION Y DE SISTEMAS
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
QUANTIZED STATE SIMULATION OF ADVECTION-DIFFUSION-REACTION EQUATIONS
Autor/es:
FEDERICO BERGERO; JOAQUÍN FERNÁNDEZ; ERNESTO KOFMAN; MARGARITA PORTAPILA
Lugar:
Mendoza
Reunión:
Congreso; XX Congreso sobre Métodos Numéricos y sus Aplicaciones; 2013
Institución organizadora:
Universidad Tecnológica Nacional de Mendoza
Resumen:
Time-dependent Advection-Diffusion-Reaction (ADR) equations are used in areas such as
chemistry, physics and engineering. These areas include chemical reactions, population dynamics, flame
propagation, and the evolution of concentrations in environmental and biological processes.
Each of the three phenomena (advection, diffusion, and reaction) evolves in a different time scale,
thus the model shows a stiff behavior.
This equation is usually discretized along the spatial variables using a grid, converting it into a large
sparse set of ordinary differential equations (ODEs) that can be then solved using numerical integration
methods that discretize the time variable.
An alternative way is the usage of Quantized State Systems (QSS) methods, a family of numerical
integration algorithms that replace the time discretization by the quantization of the state variables. Some
QSS algorithms can efficiently integrate sparse stiff ODEs, which makes them promising candidates for
the ADR problem.
In this article we study the use of QSS methods for ADR models semi?discretized with the Method
Of Lines. We compare the performance and the quality of the solutions obtained by these algorithms
with those of conventional methods, such as DASSL, Radau and DOPRI.
Analyzing simulation times we show that, in most situations, the second order linearly implicit QSS
method (LIQSS2) outperforms all the conventional algorithms in more than one order of magnitude.