Gowdy waves as a test-bed for constraint-preserving boundary conditions

Abstract

Gowdy waves, one of the standard 'apples with apples' tests, is proposed as a test-bed for constraint-preserving boundary conditions in the non-linear regime. As an illustration, energy-constraint preservation is separately tested in the Z4 framework. Both algebraic conditions, derived from energy estimates, and derivative conditions, deduced from the constraint-propagation system, are considered. The numerical errors at the boundary are of the same order than those at the interior points.

5 pages, 1 figure. Contribution to the Spanish Relativity Meeting 2009

References in corpus (5)

• Implementation of standard testbeds for numerical relativity
• Implementation of higher-order absorbing boundary conditions for the Einstein equations
• Well-posed initial-boundary value problem for the harmonic Einstein equations using energy estimates
• Constraint-preserving Sommerfeld conditions for the harmonic Einstein equations
• Geometrization of metric boundary data for Einstein's equations

Cited by in corpus (5)

• Continuum and Discrete Initial-Boundary-Value Problems and Einstein's Field Equations
• Constraint damping for the Z4c formulation of general relativity
• Boundary Conditions for the Gravitational Field
• Constraint-preserving boundary conditions in the 3+1 first-order approach
• Aliasing Instabilities in the Numerical Evolution of the Einstein Field Equations