A Hybrid Cosmological Hydrodynamic/N-Body Code Based on a Weighted Essentially Nonoscillatory Scheme

We present a newly developed cosmological hydrodynamics code based on weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws. WENO is a higher order accurate finite difference scheme designed for problems with piecewise smooth solutions containing discontinuities and has been successfully applied for problems involving both shocks and complicated smooth solution structures. We couple hydrodynamics based on the WENO scheme with the standard Poisson solver-particle-mesh (PM) algorithm for evolving the self-gravitating system. The third-order low-storage total variation diminishing (TVD) Runge-Kutta scheme has been used for the time integration of the system. To test the accuracy and convergence rate of the code, we subject it to a number of typical tests, including the Sod shock tube in multiple dimensions, the Sedov blast wave, and formation of the Zel'dovich pancake. These tests validate the WENO hydrodynamics with a fast convergence rate and high accuracy. We also evolve a low-density flat cosmological model (LambdaCDM) to explore the validity of the code in practical simulations.

[1]  Philippe Montarnal,et al.  Real Gas Computation Using an Energy Relaxation Method and High-Order WENO Schemes , 1999 .

[2]  Richard Liska,et al.  Two-dimensional shallow water equations by composite schemes , 1999 .

[3]  S. Noelle.  The MoT-ICE: a new high-resolution wave-propagation algorithm for multidimensional systems of conservation laws based on Fey's method of transport , 2000 .

[4]  Sergio Pirozzoli,et al.  Shock wave–thermal inhomogeneity interactions: Analysis and numerical simulations of sound generation , 2000 .

[5]  Richard Liska Burton Wendroff.  Composite Schemes For Conservation Laws , 1998 .

[6]  R. Giacconi,et al.  Evidence for x Rays From Sources Outside the Solar System , 1962 .

[7]  Matthias Steinmetz,et al.  Grapesph: cosmological smoothed particle hydrodynamics simulations with the special-purpose hardware GRAPE , 1996 .

[8]  COSMOS: A Hybrid N-Body/Hydrodynamics Code for Cosmological Problems , 1999, astro-ph/9912339.

[9]  Wayne Hu,et al.  Power Spectra for Cold Dark Matter and Its Variants , 1997, astro-ph/9710252.

[10]  Timothy J. Barth,et al.  High-order methods for computational physics , 1999 .

[11]  V. Springel,et al.  GADGET: a code for collisionless and gasdynamical cosmological simulations , 2000, astro-ph/0003162.

[12]  Jeremiah P. Ostriker,et al.  A piecewise parabolic method for cosmological hydrodynamics , 1995 .

[13]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

[14]  Jeremiah P. Ostriker,et al.  Generation of microwave background fluctuations from nonlinear perturbations at the era of galaxy formation , 1986 .

[15]  G. Efstathiou,et al.  Numerical techniques for large cosmological N-body simulations , 1985 .

[16]  Guang-Shan Jiang,et al.  A High-Order WENO Finite Difference Scheme for the Equations of Ideal Magnetohydrodynamics , 1999 .

[17]  T. N. Stevenson,et al.  Fluid Mechanics , 2021, Nature.

[18]  S. White,et al.  Simulations of dissipative galaxy formation in hierarchically clustering universes – I: Tests of the code , 1993 .

[19]  Chi-Wang Shu.  Total-variation-diminishing time discretizations , 1988 .

[20]  Chi-Wang Shu,et al.  Strong Stability-Preserving High-Order Time Discretization Methods , 2001, SIAM Rev..

[21]  S. Liang,et al.  Numerical simulation of underwater blast-wave focusing using a high-order scheme , 1999 .

[22]  Danping Peng,et al.  Weighted ENO Schemes for Hamilton-Jacobi Equations , 1999, SIAM J. Sci. Comput..

[23]  Yong-Tao Zhang,et al.  Resolution of high order WENO schemes for complicated flow structures , 2003 .

[24]  K. Olive,et al.  Primordial nucleosynthesis redux , 1991 .

[25]  Chi-Wang Shu,et al.  High Order ENO and WENO Schemes for Computational Fluid Dynamics , 1999 .

[26]  Centro internazionale matematico estivo. Session,et al.  Advanced Numerical Approximation of Nonlinear Hyperbolic Equations , 1998 .

[27]  L. Hernquist,et al.  TREESPH: A Unification of SPH with the Hierarchical Tree Method , 1989 .

[28]  Chi-Wang Shu,et al.  Total variation diminishing Runge-Kutta schemes , 1998, Math. Comput..

[29]  L. Sedov.  Similarity and Dimensional Methods in Mechanics , 1960 .

[30]  Y. Zeldovich,et al.  The interaction of matter and radiation in a hot-model universe , 1969 .

[31]  G. Bryan,et al.  Cosmological Adaptive Mesh Refinement , 1998, astro-ph/9807121.

[32]  J. Owen,et al.  Adaptive Smoothed Particle Hydrodynamics: Methodology. II. , 1995, astro-ph/9512078.

[33]  X-RAY PROPERTIES OF GROUPS OF GALAXIES , 2000, astro-ph/0009379.

[34]  A. Evrard.  Beyond N-body: 3D cosmological gas dynamics , 1988 .

[35]  Nickolay Y. Gnedin,et al.  Softened Lagrangian Hydrodynamics for Cosmology , 1995 .

[36]  Chi-Wang Shu,et al.  High order finite difference and finite volume WENO schemes and discontinuous Galerkin methods for CFD , 2001 .

[37]  L. Lucy.  A numerical approach to the testing of the fission hypothesis. , 1977 .

[38]  Chi-Wang Shu.  Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws , 1998 .

[39]  Ue-Li Pen,et al.  A High-Resolution Adaptive Moving Mesh Hydrodynamic Algorithm , 1997, astro-ph/9704258.

[40]  R. Cen.  A hydrodynamic approach to cosmology - Methodology , 1992 .

[41]  P. Woodward,et al.  The Piecewise Parabolic Method (PPM) for Gas Dynamical Simulations , 1984 .

[42]  Jeremiah P. Ostriker,et al.  A Cosmological Hydrodynamic Code Based on the Total Variation Diminishing Scheme , 1993 .

[43]  R. Teyssier.  Cosmological hydrodynamics with adaptive mesh refinement - A new high resolution code called RAMSES , 2001, astro-ph/0111367.

[44]  Jaw-Yen Yang,et al.  Implicit Weighted ENO Schemes for the Three-Dimensional Incompressible Navier-Stokes Equations , 1998 .

[45]  G. Sod.  A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws , 1978 .

[46]  M. Norman,et al.  ZEUS-2D: A radiation magnetohydrodynamics code for astrophysical flows in two space dimensions. I - The hydrodynamic algorithms and tests. II - The magnetohydrodynamic algorithms and tests , 1992 .

[47]  R W Hockney,et al.  Computer Simulation Using Particles , 1966 .

[48]  Chi-Wang Shu,et al.  Monotonicity Preserving Weighted Essentially Non-oscillatory Schemes with Increasingly High Order of Accuracy , 2000 .

[49]  F. Pearce,et al.  Hydra: An Adaptive--Mesh Implementation of PPPM--SPH , 1994 .

[50]  J. Monaghan,et al.  Smoothed particle hydrodynamics: Theory and application to non-spherical stars , 1977 .

[51]  S. Osher,et al.  Uniformly high order accurate essentially non-oscillatory schemes, 111 , 1987 .

[52]  E. Bertschinger.  SIMULATIONS OF STRUCTURE FORMATION IN THE UNIVERSE , 1998 .

[53]  Sergio Pirozzoli,et al.  Shock-Wave–Vortex Interactions: Shock and Vortex Deformations, and Sound Production , 2000 .

[54]  S. Osher,et al.  Weighted essentially non-oscillatory schemes , 1994 .