16,745 research outputs found
Relativistic MHD with Adaptive Mesh Refinement
This paper presents a new computer code to solve the general relativistic
magnetohydrodynamics (GRMHD) equations using distributed parallel adaptive mesh
refinement (AMR). The fluid equations are solved using a finite difference
Convex ENO method (CENO) in 3+1 dimensions, and the AMR is Berger-Oliger.
Hyperbolic divergence cleaning is used to control the
constraint. We present results from three flat space tests, and examine the
accretion of a fluid onto a Schwarzschild black hole, reproducing the Michel
solution. The AMR simulations substantially improve performance while
reproducing the resolution equivalent unigrid simulation results. Finally, we
discuss strong scaling results for parallel unigrid and AMR runs.Comment: 24 pages, 14 figures, 3 table
Error and symmetry analysis of Misner's algorithm for spherical harmonic decomposition on a cubic grid
Computing spherical harmonic decompositions is a ubiquitous technique that
arises in a wide variety of disciplines and a large number of scientific codes.
Because spherical harmonics are defined by integrals over spheres, however, one
must perform some sort of interpolation in order to compute them when data is
stored on a cubic lattice. Misner (2004, Class. Quant. Grav., 21, S243)
presented a novel algorithm for computing the spherical harmonic components of
data represented on a cubic grid, which has been found in real applications to
be both efficient and robust to the presence of mesh refinement boundaries. At
the same time, however, practical applications of the algorithm require
knowledge of how the truncation errors of the algorithm depend on the various
parameters in the algorithm. Based on analytic arguments and experience using
the algorithm in real numerical simulations, I explore these dependencies and
provide a rule of thumb for choosing the parameters based on the truncation
errors of the underlying data. I also demonstrate that symmetries in the
spherical harmonics themselves allow for an even more efficient implementation
of the algorithm than was suggested by Misner in his original paper.Comment: 10 pages, 3 tables, 1 figure. Version 2 has a broader introduction,
and includes additional information on choosing parameter
Improvements to the construction of binary black hole initial data
Construction of binary black hole initial data is a prerequisite for
numerical evolutions of binary black holes. This paper reports improvements to
the binary black hole initial data solver in the Spectral Einstein Code, to
allow robust construction of initial data for mass-ratio above 10:1, and for
dimensionless black hole spins above 0.9, while improving efficiency for lower
mass-ratios and spins. We implement a more flexible domain decomposition,
adaptive mesh refinement and an updated method for choosing free parameters. We
also introduce a new method to control and eliminate residual linear momentum
in initial data for precessing systems, and demonstrate that it eliminates
gravitational mode mixing during the evolution. Finally, the new code is
applied to construct initial data for hyperbolic scattering and for binaries
with very small separation.Comment: 28 pages, 13 figures, 1 tabl
Adaptive mesh and geodesically sliced Schwarzschild spacetime in 3+1 dimensions
We present first results obtained with a 3+1 dimensional adaptive mesh code
in numerical general relativity. The adaptive mesh is used in conjunction with
a standard ADM code for the evolution of a dynamically sliced Schwarzschild
spacetime (geodesic slicing). We argue that adaptive mesh is particularly
natural in the context of general relativity, where apart from adaptive mesh
refinement for numerical efficiency one may want to use the built in
flexibility to do numerical relativity on coordinate patches.Comment: 21 pages, LaTeX, 7 figures included with eps
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