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Convection-Diffusion Models

The diffusion equation is very similar to the heat transfer equation. As a result, model reduction should work exactly the same way as for thermal problems.

Diffusion Model in Electrochemistry

Provided that electrochemical reactions at the electrode are modeled by the Buttler-Volmer equation, we have a pure diffusion problem with mixed boundary conditions at the electrode. However, there are additional problems to solve during model reduction.

L. H. Feng, D. Koziol, E. B. Rudnyi, J. G. Korvink.
Model Order Reduction for Scanning Electrochemical Microscope: The treatment of nonzero initial conditions.
IEEE Sensors 2004, The Third IEEE conference on sensors, Vienna, Austria, Oct. 24-27, 2004, Technical Program & Abstracts, Special Session W1Le, Scanning Probe Tip Integrated Sensors, p. 257.
Proceedings of IEEE Sensors 2004, v. 3, p. 1236-1239.
Final paper at IEEE

At present time, model order reduction is a well-established technique for fast simulation of large-scale models based on ordinary differential equations, especially those in the field of integrated circuits and micro-electro-mechanical systems. We describe the application of model reduction to electrochemical simulation related to scanning electrochemical microscope. Model reduction allows us to reduce the simulation time significantly and, at the same time, it maintains the high accuracy.

L. H. Feng, D. Koziol, E. B. Rudnyi, J. G. Korvink.
Parametric Model Order Reduction for Scanning Electrochemical Microscopy: Fast Simulation of Cyclic Voltammogram.
In: Thermal, Mechanical and Multi-Physics Simulation and Experiments in Micro-Electronics and Micro-Systems. Proceedings of EuroSimE 2005, Berlin, Germany, April 18-20, 2005, p. 55-59.
Final paper at IEEE

We propose the use of parametric model reduction for fast simulation of cyclic voltammograms. The model for a cyclic voltammogram is treated as a system with a parameter (applied voltage) to be preserved during model reduction. The voltage is preserved in the symbolic form during model reduction and we can accurately simulate the cyclic voltammograms with a reduced system by spending much less time and memory as compared with direct simulation based on the original large-scale model.

L. Feng, D. Koziol, E. B. Rudnyi, and J. G. Korvink.
Parametric Model Reduction for Fast Simulation of Cyclic Voltammograms .
Sensors Letters, v. 4, N 2, p. 165-173, 2006.
Final Paper at IngentaConnect.

Model order reduction is a well-established technique for fast simulation of large-scale models based on ordinary differential equations, especially those in the field of integrated circuits and micro-electro-mechanical systems. In this paper, we propose the use of parametric model reduction for fast simulation of a cyclic voltammogram. Instead of being considered as a time varying system, the model for a cyclic voltammogram is treated as a system with a parameter (applied voltage) which is to be preserved during model reduction. Because voltage is preserved in the symbolic form during model reduction, we can simulate the cyclic voltammogram with a reduced system and therefore invest much less time and memory as compared with direct simulation based on the original large-scale model. We present our approach for a case study based on scanning electrochemical microscopy.

Convection-Diffusion Model

The next work has been made as a part of the joint work in the framework of GOSPEL under the jointly executed research Biomimetic Measurement Systems.

E. B. Rudnyi.
Odorant Transport Modeling.
IMTEK, Report for GOSPEL, 2006.

The document describes results of simple 2D simulation for the convection-diffusion transport within a sensor array. Geometry and numerical values of the parameters are chosen rather arbitrary. The goal is rather to demonstrate what typical simulation results look like and how one can speed simulation up considerably by means of modern model reduction. We will start with the description of a case study, then we will present model reduction and discuss what computational advantages it brings forward and after that we will show how the concentration profile depends on the consumption rate at sensors and flow velocity.

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Allan D. Woodbury


Evgenii B. Rudnyi, CADFEM
My e-mail is erudnyi at cadfem point de. Phone is +49 8092 7005 82.

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Masha Rudnaya