Open Access

ARTICLE

RBF-Based Multiscale Control Volume Method for Second Order Elliptic Problems with Oscillatory Coefficients

D.-A. An-Vo¹, C.-D. Tran¹, N. Mai-Duy¹, T. Tran-Cong¹

1 Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia

Computer Modeling in Engineering & Sciences 2012, 89(4), 303-359. https://doi.org/10.3970/cmes.2012.089.303

Abstract

Many important engineering problems have multiple-scale solutions. Thermal conductivity of composite materials, flow in porous media, and turbulent transport in high Reynolds number flows are examples of this type. Direct numerical simulations for these problems typically require extremely large amounts of CPU time and computer memory, which may be too expensive or impossible on the present supercomputers. In this paper, we develop a high order computational method, based on multiscale basis function approach and integrated radialbasis- function (IRBF) approximant, for the solution of multiscale elliptic problems with reduced computational cost. Unlike other methods based on multiscale basis function approach, sets of basis and correction functions here are obtained through C2-continuous IRBF element formulations. High accuracy and efficiency of this method are demonstrated by several one- and two-dimensional examples.

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