A conservative fully adaptive multiresolution algorithm for parabolic PDEs

  • Authors:

  • Olivier Roussel;Kai Schneider;Alexei Tsigulin;Henning Bockhorn

  • Affiliations:

  • Lab. de Modé/lisation et Simulation Numé/rique en Mé/canique, CNRS et Univ. d' Aix-Marseille, Marseille, France and Institut fü/r Chemische Technik, Universitä/t Karlsruhe (TH) ...;Lab. de Modé/lisation et Simulation Numé/rique en Mé/canique, CNRS et Univ d' Aix-Marseille, Marseille, France and Centre de Mathé/matiques et d'Informatique, Univ./ d'Aix-Marseill ...;Institute of Computational Mathematics and Mathematical Geophysics (RAS), Novosibirsk State Technical University, Lavrentiev pr. 6, 630090 Novosibirsk, Russia;Institut fü/r Chemische Technik, Universitä/t Karlsruhe (TH), Kaiserstr. 12, 76128 Karlsruhe, Germany

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2003

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Abstract

We present a new adaptive numerical scheme for solving parabolic PDEs in Cartesian geometry. Applying a finite volume discretization with explicit time integration, both of second order, we employ a fully adaptive multiresolution scheme to represent the solution on locally refined nested grids. The fluxes are evaluated on the adaptive grid. A dynamical adaption strategy to advance the grid in time and to follow the time evolution of the solution directly exploits the multiresolution representation. Applying this new method to several test problems in one, two and three space dimensions, like convection-diffusion, viscous Burgers and reaction-diffusion equations, we show its second-order accuracy and demonstrate its computational efficiency.