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Your search keyword '"Gundlach, Carsten"' showing total 17 results
Start Over Author "Gundlach, Carsten" Publisher iop publishing
17 results on '"Gundlach, Carsten"'

17. A conservation law formulation of nonlinear elasticity in general relativity.

Author

Gundlach, Carsten, Hawke, Ian, and Erickson, Stephanie J.

Subjects
*CONSERVATION laws (Physics), *NONLINEAR systems, *BLACK holes, *ELASTICITY, *RELATIVITY (Physics), *NUMERICAL analysis
Abstract

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 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. [ABSTRACT FROM AUTHOR]

Published
2012
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