Evolutions in 3D numerical relativity using fixed mesh refinement

By Erik Schnetter, Scott H. Hawley, Ian Hawke. 2003

548 citations recorded by the source corpus.

We present results of 3D numerical simulations using a finite difference code featuring fixed mesh refinement (FMR), in which a subset of the computational domain is refined in space and time. We apply this code to a series of test cases including a robust stability test, a nonlinear gauge wave and an excised Schwarzschild black hole in an evolving gauge. We find that the mesh refinement results are comparable in accuracy, stability and convergence to unigrid simulations with the same effective resolution. At the same time, the use of FMR reduces the computational resources needed to obtain a given accuracy. Particular care must be taken at the interfaces between coarse and fine grids to avoid a loss of convergence at higher resolutions, and we introduce the use of 'buffer zones' as one resolution of this issue. We also introduce a new method for initial data generation, which enables higher order interpolation in time even from the initial time slice. This FMR system, 'Carpet', is a driver module in the freely available Cactus computational infrastructure, and is able to endow generic existing Cactus simulation modules ('thorns') with FMR with little or no extra effort.

Subfields: Astronomy and Astrophysics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/925bb12c5658082f82efe70b249e656d776e4081

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In Computational Mechanics

Citations in the corpus

GENERAL-RELATIVISTIC SIMULATIONS OF THREE-DIMENSIONAL CORE-COLLAPSE SUPERNOVAE (2012, methodology): “The adaptively refined central Cartesian block is based on cell-centered and flux-conservative mesh-refinement techniques, provided by the open-source AMR driver Carpet (Schnetter et al. 2004; Reisswig et al. 2013).”
Modeling ringdown: Beyond the fundamental quasinormal modes (2014, methodology): “[11] Maya makes use of the openly available Einstein Toolkit [12], which is based on the CACTUS [13] code structure and CARPET [14] mesh refinement.”
Unequal mass binary black hole plunges and gravitational recoil (2006, methodology): “Mesh refinement in the code is provided by Carpet [28], and tracking of AHs is handled by AHFinderDirect [29].”
Dynamical Mass Ejection from Binary Neutron Star Mergers (2016, methodology): “For the evolution we make use of the adaptive mesh refinement (AMR) capabilities provided by the Carpet MNRAS 000, 000–000 (0000) (Schnetter et al. 2004) mesh refinement driver for Cactus (Goodale et al. 2003).”
Binary Neutron Star Mergers: Mass Ejection, Electromagnetic Counterparts, and Nucleosynthesis (2018, methodology): “Our code uses Berger–Oliger conservative adaptive mesh refinement (AMR; Berger & Oliger 1984) with sub-cycling in time and refluxing (Berger & Colella 1989; Reisswig et al. 2013a) as provided by the Carpet module of the Einstein Toolkit (Schnetter et al. 2004).”
Large Merger Recoils and Spin Flips from Generic Black Hole Binaries (2007, methodology): “We thank Erik Schnetter for valuable discussions and providing Carpet.”
Turduckening black holes: An Analytical and computational study (2008, methodology): “We use fifth order spatial interpolation at mesh refinement boundaries, using buffer zones as described in [37] to ensure stability and convergence at mesh refinement boundaries, and using tapered grids as described in [39] to avoid the Berger–Oliger time interpolation.”
Beyond second-order convergence in simulations of binary neutron stars in full general-relativity (2013, methodology): “…formulation of the Einstein equations (Nakamura et al. 1987; Shibata & Nakamura 1995; Baumgarte & Shapiro 1998) and it is performed using theMclachlan code of theEinstein Toolkit (Löffler et al. 2012; Brown et al. 2009; Schnetter et al. 2004) using a fourth-order accurate finite-difference scheme.”