Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A well balanced finite volume scheme for general relativity   In this work we present a novel second order accurate well balanced (WB)
finite volume (FV) scheme for the solution of the general relativistic
magnetohydrodynamics (GRMHD) equations and the first order CCZ4 formulation
(FO-CCZ4) of the Einstein field equations of general relativity, as well as the
fully coupled FO-CCZ4 + GRMHD system. These systems of first order hyperbolic
PDEs allow to study the dynamics of the matter and the dynamics of the
space-time according to the theory of general relativity.
  The new well balanced finite volume scheme presented here exploits the
knowledge of an equilibrium solution of interest when integrating the
conservative fluxes, the nonconservative products and the algebraic source
terms, and also when performing the piecewise linear data reconstruction. This
results in a rather simple modification of the underlying second order FV
scheme, which, however, being able to cancel numerical errors committed with
respect to the equilibrium component of the numerical solution, substantially
improves the accuracy and long-time stability of the numerical scheme when
simulating small perturbations of stationary equilibria. In particular, the
need for well balanced techniques appears to be more and more crucial as the
applications increase their complexity. We close the paper with a series of
numerical tests of increasing difficulty, where we study the evolution of small
perturbations of accretion problems and stable TOV neutron stars. Our results
show that the well balancing significantly improves the long-time stability of
the finite volume scheme compared to a standard one.

15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys