A conservation law formulation of nonlinear elasticity in general relativity
Gundlach, Carsten, Hawke, Ian and Erickson, Stephanie E. (2011) A conservation law formulation of nonlinear elasticity in general relativity. Classical and Quantum Gravity, 29, (1), 015005-[53pp]. (doi:10.1088/0264-9381/29/1/015005).
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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 ψAi. 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.
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Social and Human Sciences > Mathematical Sciences > Applied Mathematics
|Date Deposited:||08 Nov 2011 14:11|
|Last Modified:||22 May 2012 09:25|
|Contributors:||Gundlach, Carsten (Author)
Hawke, Ian (Author)
Erickson, Stephanie E. (Author)
|Date:||12 December 2011|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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