Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 227, Issue 8, Pages 3758-3780Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2007.11.046
Keywords
finite volume; adaptivity; multiresolution; evolutionary partial differential equation
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We present a fully adaptive numerical scheme for evolutionary PDEs in Cartesian geometry based on a second-order finite volume discretization. A multiresolution strategy allows local grid refinement while controlling the approximation error in space. For time discretization we use an explicit Runge-Kutta scheme of second-order with a scale-dependent time step. On the finest scale the size of the time step is imposed by the stability condition of the explicit scheme. On larger scales, the time step can be increased without violating the stability requirement of the explicit scheme. The implementation uses a dynamic tree data structure. Numerical validations for test problems in one space dimension demonstrate the efficiency and accuracy of the local time-stepping scheme with respect to both multiresolution scheme with global time stepping and finite volume scheme on a regular grid. Fully adaptive three-dimensional computations for reaction-diffusion equations illustrate the additional speed-up of the local time stepping for a thermo-diffusive flame instability. (C) 2007 Elsevier Inc. All rights reserved.
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