Accelerated non-linear finite volume method for diffusion

Authors:
D. Vidović;M. Dimkić;M. Pušić
Affiliations:
Jaroslav erni Institute, Jaroslava ernog 80, 11226 Pinosava, Belgrade, Serbia;Jaroslav erni Institute, Jaroslava ernog 80, 11226 Pinosava, Belgrade, Serbia;University of Belgrade, Faculty of Mining and Geology, íušina 7, 11000 Belgrade, Serbia
Venue:
Journal of Computational Physics
Year:
2011

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Abstract

A non-linear finite volume method with monotone matrix for the diffusion equation is presented. It does not extrapolate the primary variable to Neumann boundaries, as this was previously done in similar methods. This change results in faster convergence. Computation time is significantly shortened further using the reduced rank extrapolation method (RRE), and imposing an upper limit on the number of linear iterations per non-linear step. Second-order accuracy and performance improvement are demonstrated by numerical examples.