%0 Journal Article
%4 dpi.inpe.br/plutao@80/2009/07.22.13.26
%2 dpi.inpe.br/plutao@80/2009/07.22.13.26.42
%@doi 10.1002/nme.2501
%@issn 0029-5981
%@issn 1097-0207
%F lattes: 4693848330845067 1 DominguesRousSchn:2009:AdMuMe
%T An adaptive multiresolution method for parabolic PDEs with time-step control
%D 2009
%A Domingues, Margarete Oliveira,
%A Roussel, Olivier,
%A Schneider, Kai,
%@affiliation Instituto Nacional de Pesquisas Espaciais (INPE)
%@electronicmailaddress mo.domingues@lac.inpe.br
%B International Journal for Numerical Methods in Engineering
%V 78
%N 6
%P 652-670
%K adaptivity, multiresolution, finite volume, Runge–Kutta, partial differential equation, time-step control.
%X We present an efficient adaptive numerical scheme for parabolic partial differential equations based on a finite volume (FV) discretization with explicit time discretization using embedded RungeKutta (RK) schemes. A multiresolution strategy allows local grid refinement while controlling the approximation error in space. The costly fluxes are evaluated on the adaptive grid only. Compact RK methods of second and third order are then used to choose automatically the new time step while controlling the approximation error in time. Non-admissible choices of the time step are avoided by limiting its variation. The implementation of the multiresolution representation uses a dynamic tree data structure, which allows memory compression and CPU time reduction. This new numerical scheme is validated using different classical test problems in one, two and three space dimensions. The gain in memory and CPU time with respect to the FV scheme on a regular grid is reported, which demonstrates the efficiency of the new method.
%3 2501_ftp.pdf
%O Setores de Atividade: Transporte Aéreo.