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arXiv · 1604.00355

High order implicit time integration schemes on multiresolution adaptive grids for stiff PDEs

Max Duarte·Richard Dobbins·Mitchell Smooke
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Abstract

We consider high order, implicit Runge-Kutta schemes to solve time-dependent stiff PDEs on dynamically adapted grids generated by multiresolution analysis for unsteady problems disclosing localized fronts. The multiresolution finite volume scheme yields highly compressed representations within a user-defined accuracy tolerance, hence strong reductions of computational requirements to solve large, coupled nonlinear systems of equations. SDIRK and RadauIIA Runge-Kutta schemes are implemented with particular interest in those with L-stability properties and accuracy-based time-stepping capabilities. Numerical evidence is provided of the computational efficiency of the numerical strategy to cope with highly unsteady problems modeling various physical scenarios with a broad spectrum of time and space scales.

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Max Duarte, Richard Dobbins, Mitchell Smooke. 2016-04-01. High order implicit time integration schemes on multiresolution adaptive grids for stiff PDEs. https://arxiv.org/abs/1604.00355

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