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arXiv · 1111.2269

A New Mode Reduction Strategy for the Generalized Kuramoto-Sivashinsky Equation

M. Schmuck·M. Pradas·G. A. Pavliotis·S. Kalliadasis
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Abstract

Consider the generalized Kuramoto-Sivashinsky (gKS) equation. It is a model prototype for a wide variety of physical systems, from flame-front propagation, and more general front propagation in reaction-diffusion systems, to interface motion of viscous film flows. Our aim is to develop a systematic and rigorous low-dimensional representation of the gKS equation. For this purpose, we approximate it by a renormalization group (RG) equation which is qualitatively characterized by rigorous error bounds. This formulation allows for a new stochastic mode reduction guaranteeing optimality in the sense of maximal information entropy. Herewith, noise is systematically added to the reduced gKS equation and gives a rigorous and analytical explanation for its origin. These new results would allow to reliably perform low-dimensional numerical computations by accounting for the neglected degrees of freedom in a systematic way. Moreover, the presented reduction strategy might also be useful in other applications where classical mode reduction approaches fail or are too complicated to be implemented.

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M. Schmuck, M. Pradas, G. A. Pavliotis, S. Kalliadasis. 2011-11-08. A New Mode Reduction Strategy for the Generalized Kuramoto-Sivashinsky Equation. https://arxiv.org/abs/1111.2269

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