A conservation law formulation of nonlinear elasticity in general relativity
arXiv:1107.2551 · doi:10.1088/0264-9381/29/1/015005
Abstract
We present a practical framework for ideal hyperelasticity in numerical relativity. For this purpose, we recast the formalism of Carter and Quintana as a set of Eulerian conservation laws in an arbitrary 3+1 split of spacetime. The resulting equations are presented as an extension of the standard Valencia formalism for a perfect fluid, with additional terms in the stress-energy tensor, plus a set of kinematic conservation laws that evolve a configuration gradient. We prove that the equations can be made symmetric hyperbolic by suitable constraint additions, at least in a neighbourhood of the unsheared state. We discuss the Newtonian limit of our formalism and its relation to a second formalism also used in Newtonian elasticity. We validate our framework by numerically solving a set of Riemann problems in Minkowski spacetime, as well as Newtonian ones from the literature.
31 pages, 21 pdf figures
References in corpus (4)
- Accurate evolutions of inspiralling neutron-star binaries: prompt and delayed collapse to black hole
- The Breaking Strain of Neutron Star Crust and Gravitational Waves
- Neutron Star Asteroseismology. Axial Crust Oscillations in the Cowling Approximation
- Magneto-elastic oscillations and the damping of crustal shear modes in magnetars
Cited by in corpus (12)
- High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: viscous heat-conducting fluids and elastic solids
- Relativistic fluid dynamics: physics for many different scales
- Beyond ideal magnetohydrodynamics: From fibration to 3+1 foliation
- A covariant action principle for dissipative fluid dynamics: From formalism to fundamental physics
- A new continuum model for general relativistic viscous heat-conducting media
- Elasticity Theory in General Relativity
- Dynamical compact elastic bodies in general relativity
- Quantised vortices and mutual friction in relativistic superfluids
- The nonlinear development of the relativistic two-stream instability
- Higher-level large-eddy filtering strategy for general relativistic fluid simulations
- Extended body dynamics in general relativity: hyperelastic models
- Souriau's Relativistic general covariant formulation of hyperelasticity revisited