%0 Journal Article
%4 sid.inpe.br/mtc-m17@80/2008/06.06.15.16
%2 sid.inpe.br/mtc-m17@80/2008/06.06.15.16.12
%@doi 10.1016/j.jcp.2007.11.046
%@issn 0021-9991
%T An adaptive multiresolution scheme with local time stepping for evolutionary PDEs
%D 2008
%8 Apr.
%A Domingues, Margarte Oliveira,
%A Gomes, Sonia M.,
%A Roussel, Olivier,
%A Schneider, Kai,
%@affiliation Instituto Nacional de Pesquisas Espaciais (INPE)
%@affiliation Universidade Estadual de Campinas (UNICAMP)
%@affiliation Institut für Technische Chemie und Polymerchemie (TCP)
%@affiliation Laboratoire de Modélisation et Simulation Numérique en Mécanique et Génie des Procédés (MSNM-GP)
%B Journal of Computational Physics
%V 227
%N 8
%P 3758-3780
%K finite volume, adaptivity, multiresolution, evolutionary partial differential equation.
%X 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.
%@language en
%3 an adaptive.pdf