BETHE-hydro: An arbitrary Lagrangian-Eulerian multidimensional hydrodynamics code for astrophysical simulations

Jeremiah W. Murphy, Adam S. Burrows

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


In this paper, we describe a new hydrodynamics code for one- and two-dimensional (1D and 2D) astrophysical simulations, BETHE-hydro, that uses time-dependent, arbitrary, unstructured grids. The core of the hydrodynamics algorithm is an arbitrary Lagrangian-Eulerian (ALE) approach, in which the gradient and divergence operators are made compatible using the support-operator method. We present 1D and 2D gravity solvers that are finite differenced using the support-operator technique, and the resulting system of linear equations are solved using the tridiagonal method for 1D simulations and an iterative multigrid-preconditioned conjugate-gradient method for 2D simulations. Rotational terms are included for 2D calculations using cylindrical coordinates. We document an incompatibility between a subcell pressure algorithm to suppress hourglass motions, and the subcell remapping algorithm and present a modified subcell pressure scheme that avoids this problem. Strengths of this code include a straightforward structure, enabling simple inclusion of additional physics packages, the ability to use a general equation of state, and most importantly, the ability to solve self-gravitating hydrodynamic flows on time-dependent, arbitrary grids. In what follows, we describe in detail the numerical techniques employed and,with a large suite of tests, demonstrate that BETHE-hydro finds accurate solutions with second-order convergence.

Original languageEnglish (US)
Pages (from-to)209-241
Number of pages33
JournalAstrophysical Journal, Supplement Series
Issue number1
StatePublished - Nov 2008

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Hydrodynamics
  • Instabilities
  • Methods: numerical
  • Shock waves
  • Supernovae: general


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