A conservation law formulation of nonlinear elasticity in general relativity

Monday, January 16, 2012, 10am US central time

The Einstein Toolkit weekly EVO meeting was be used for audio and slides. The slides are available as pdf, and the recordings are available in Theora or compressed, native EVO format. The talk was based on this paper.

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.

Presenter: Ian Hawke

Lecturer in the Applied Mathematics department of the School of Mathematics at the University of Southampton.

Research interests: My primary interests are numerical simulations of Einstein's equations coupled to hydrodynamic matter. I am one of the authors of the Whisky code which is used within the EU Network. I also contribute to the binary black hole simulations of the AEI Numerical Relativity group. I am also interested in mesh refinement codes such as Carpet.