Semi-Lagrangian multistep exponential integrators for index 2 differential-algebraic systems

  • Authors:

  • Elena Celledoni;Bawfeh Kingsley Kometa

  • Affiliations:

  • Norwegian University of Science and Technology, Sentralbygg 2, Alfred Getz vei 1, 7491 Trondheim, Norway;Norwegian University of Science and Technology, Sentralbygg 2, Alfred Getz vei 1, 7491 Trondheim, Norway

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2011

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Abstract

Implicit-explicit (IMEX) multistep methods are very useful for the time discretization of convection diffusion PDE problems such as the Burgers equations and the incompressible Navier-Stokes equations. In the latter as well as in PDE models of plasma physics and of electromechanical systems, semi-discretization in space gives rise to differential-algebraic (DAE) system of equations often of index higher than 1. In this paper we propose a new class of exponential integrators for index 2 DAEs arising from the semi-discretization of PDEs with a dominating and typically nonlinear convection term. This class of problems includes the incompressible Navier-Stokes equations. The integration methods are based on the backward differentiation formulae (BDF) and they can be applied without modifications in the semi-Lagrangian integration of convection diffusion problems. The approach gives improved performance at low viscosity regimes.