An adaptive multiresolution scheme with local time stepping for evolutionary PDEs

  • Authors:

  • Margarete O. Domingues;Sônia M. Gomes;Olivier Roussel;Kai Schneider

  • Affiliations:

  • Laboratório Associado de Computação e Matemática Aplicada (LAC), Coordenadoria de Laboratórios Associados, Instituto Nacional de Pesquisas Espaciais (INPE), Av. dos Astron ...;Universidade Estadual de Campinas, IMECC, Caixa Postal 6065, 13083-970 Campinas SP, Brazil;Institut für Technische Chemie und Polymerchemie (TCP), Universität Karlsruhe, Kaiserstrasse 12, 76128 Karlsruhe, Germany;Laboratoire de Modélisation et Simulation Numérique en Mécanique et Génie des Procédés (MSNM-GP), CNRS and Universités d'Aix-Marseille, 38 rue Frédéric ...

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2008

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Abstract

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.