Constraint-preserving boundary conditions in the Z4 Numerical Relativity formalism
arXiv:gr-qc/0411110 · doi:10.1088/0264-9381/22/13/007
Abstract
The constraint-preserving approach, which aim is to provide consistent boundary conditions for Numerical Relativity simulations, is discussed in parallel with other recent developments. The case of the Z4 system is considered, and constraint-preserving boundary conditions of the Sommerfeld type are provided. A necessary condition for the stability of the proposed boundary conditions is obtained, which amounts to the requirement of a symmetric ordering of space derivatives. This requirement is numerically seen to be also sufficient in the absence of corners and edges. Maximally dissipative boundary conditions are also implemented. In this case, a less restrictive stability condition is obtained, which is shown numerically to be also sufficient even in the presence of corners and edges.
arXiv commentEnhanced version, including a new Appendix on maximally dissipative boundary conditions (12 pages, 5 figures)
References in corpus (24)
- On the Numerical Integration of Einstein's Field Equations
- New Formalism for Numerical Relativity
- General-covariant evolution formalism for Numerical Relativity
- Extending the lifetime of 3D black hole computations with a new hyperbolic system of evolution equations
- On the Newtonian Limit of General Relativity
- Well-Posed Initial-Boundary Evolution in General Relativity
- Toward standard testbeds for numerical relativity
- First-order symmetric-hyperbolic Einstein equations with arbitrary fixed gauge
- Well posed constraint-preserving boundary conditions for the linearized Einstein equations
- A symmetry-breaking mechanism for the Z4 general-covariant evolution system
- Boundary conditions in linearized harmonic gravity
- Constraint-preserving boundary conditions in numerical relativity
- Summation by parts and dissipation for domains with excised regions
- Black Hole Excision with Multiple Grid Patches
- Cauchy boundaries in linearized gravitational theory
- Exploiting gauge and constraint freedom in hyperbolic formulations of Einstein's equations
- Dynamical shift conditions for the Z4 and BSSN hyperbolic formalisms
- Spherical excision for moving black holes and summation by parts for axisymmetric systems
- Boundary conditions for hyperbolic formulations of the Einstein equations
- Einstein boundary conditions for the 3+1 Einstein equations
- Detecting ill posed boundary conditions in General Relativity
- Einstein boundary conditions in relation to constraint propagation for the initial-boundary value problem of the Einstein equations
- A remedy for constraint growth in Numerical Relativity
- Einstein boundary conditions for the Einstein equations in the conformal-traceless decomposition
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- Constraint damping for the Z4c formulation of general relativity
- An explicit harmonic code for black-hole evolution using excision
- Exploring New Physics Frontiers Through Numerical Relativity
- Numerical Relativity of Compact Binaries in the 21st Century
- Constraint preserving boundary conditions for the Z4c formulation of general relativity
- Harmonic Initial-Boundary Evolution in General Relativity
- From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
- Numerical stability of the Z4c formulation of general relativity
- Efficient implementation of finite volume methods in Numerical Relativity
- Absorbing boundary conditions for Einstein's field equations
- A minimization problem for the lapse and the initial-boundary value problem for Einstein's field equations
- Cosmology using numerical relativity
- Boundary Conditions for the Gravitational Field
- Constraint-preserving boundary conditions in the 3+1 first-order approach
- The initial boundary value problem for free-evolution formulations of General Relativity
- Gowdy waves as a test-bed for constraint-preserving boundary conditions
- On constraint preservation and strong hyperbolicity