A modified higher order Godunov's scheme for stiff source conservative hydrodynamics

  • Authors:

  • Francesco Miniati;Phillip Colella

  • Affiliations:

  • Physics Department, Wolfgang-Pauli-Strasse 16, ETH Zürich, CH-8093 Zürich, Switzerland;Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

Quantified Score

Hi-index 31.47

Visualization

Abstract

We present an efficient second-order accurate scheme to treat stiff source terms within the framework of higher order Godunov's methods. We employ Duhamel's formula to devise a modified predictor step which accounts for the effects of stiff source terms on the conservative fluxes and recovers the correct isothermal behavior in the limit of an infinite cooling/reaction rate. Source term effects on the conservative quantities are fully accounted for by means of a one-step, second-order accurate semi-implicit corrector scheme based on the deferred correction method of Dutt et al. We demonstrate the accurate, stable and convergent results of the proposed method through a set of benchmark problems for a variety of stiffness conditions and source types.