# E pur si muove: Galilean-invariant cosmological hydrodynamical simulations on a moving mesh

@article{Springel2010EPS, title={E pur si muove: Galilean-invariant cosmological hydrodynamical simulations on a moving mesh}, author={Volker Springel}, journal={Monthly Notices of the Royal Astronomical Society}, year={2010}, volume={401}, pages={791-851} }

Hydrodynamic cosmological simulations at present usually employ either the Lagrangian smoothed particle hydrodynamics (SPH) technique or Eulerian hydrodynamics on a Cartesian mesh with (optional) adaptive mesh refinement (AMR). Both of these methods have disadvantages that negatively impact their accuracy in certain situations, for example the suppression of fluid instabilities in the case of SPH, and the lack of Galilean invariance and the presence of overmixing in the case of AMR. We here…

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## References

SHOWING 1-10 OF 122 REFERENCES

A High resolution adaptive moving mesh hydrodynamic algorithm

- Physics
- 1997

An algorithm for simulating self-gravitating cosmological astrophysical fluids is presented. The advantages include a large dynamic range, parallelizability, high resolution per grid element, and…

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

- Computer Science
- 2004

A newly developed cosmological hydrodynamics code based on weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws is presented and subjected to a number of typical tests to test the accuracy and convergence rate of the code.

BETHE-Hydro: An Arbitrary Lagrangian-Eulerian Multidimensional Hydrodynamics Code for Astrophysical Simulations

- Physics
- 2008

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…

Hydrodynamic and N-body schemes on an unstructured, adaptive mesh with applications to cosmological simulations

- Computer Science, Physics
- 1997

The numerical results show that the N-body and hydrodynamic algorithms based on unstructured meshes with mesh refinement are well-suited for hierarchical structure formation problems.

Comparing AMR and SPH Cosmological Simulations. I. Dark Matter and Adiabatic Simulations

- Physics
- 2005

We compare two cosmological hydrodynamic simulation codes in the context of hierarchical galaxy formation: the Lagrangian smoothed particle hydrodynamics (SPH) code GADGET, and the Eulerian adaptive…

A high order Godunov scheme with constrained transport and adaptive mesh refinement for astrophysical magnetohydrodynamics

- Physics
- 2006

Aims. In this paper, we present a new method to perform numerical simulations of astrophysical MHD flows using the Adaptive Mesh Refinement framework and Constrained Transport. Methods. The algorithm…

Adaptive Smoothed Particle Hydrodynamics: Methodology. II.

- Physics
- 1998

Further development and additional details and tests of adaptive smoothed particle hydrodynamics (ASPH), the new version of smoothed particle hydrodynamics (SPH) described in the first paper in this…

PLUTO: a Numerical Code for Computational Astrophysics

- Physics
- 2007

We present a new numerical code, PLUTO, for the solution of hypersonic flows in 1, 2, and 3 spatial dimensions and different systems of coordinates. The code provides a multiphysics, multialgorithm…