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

TL;DR

This paper proposes using Gowdy waves as a test-bed for evaluating constraint-preserving boundary conditions in the non-linear regime, focusing on energy-constraint preservation within the Z4 framework.

Contribution

It introduces Gowdy waves as a standard test-bed for boundary conditions and analyzes energy-constraint preservation using algebraic and derivative conditions.

Findings

Boundary errors are comparable at boundary and interior points.

Both algebraic and derivative conditions effectively preserve constraints.

Gowdy waves serve as a reliable test-bed for non-linear boundary condition evaluation.

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.