Local time steps for a finite volume scheme

Isabelle Faille (1) , Frédéric Nataf (2) , Françoise Willien (1) , Sylvie Wolf (3)

1 IFPEN - IFP Energies nouvelles
2 LJLL - Laboratoire Jacques-Louis Lions
3 LT - Laboratoire de tectonique

We present a strategy for solving time-dependent problems on grids with local refinements in time using different time steps in different regions of space. We discuss and analyze two conservative approximations based on finite volume with piecewise constant projections and domain decomposition techniques. Next we present an iterative method for solving the composite-grid system that reduces to solution of standard problems with standard time stepping on the coarse and fine grids. At every step of the algorithm, conservativity is ensured. Finally, numerical results illustrate the accuracy of the proposed methods.

Mots clés: local time step; finite volume; domain decomposition

Domaines: Analyse numérique [math.NA]

Isabelle Faille, Frédéric Nataf, Françoise Willien, Sylvie Wolf. Local time steps for a finite volume scheme. 2008. ⟨hal-00277186⟩