Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 77, Issue 3, Pages 1832-1873Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-018-0768-9
Keywords
Elastic wave propagation; Helmholtz decomposition; Potentials; Stability of the evolution problem
Categories
Funding
- FEDER
- Spanish Ministry of Science and Innovation [MTM2013-43745-R, MTM2017-86459-R]
- Xunta de Galicia [ED431C 2017/60]
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In this work we present a method for the computation of numerical solutions of 2D homogeneous isotropic elastodynamics equations by solving scalar wave equations. These equations act on the potentials of a Helmholtz decomposition of the displacement field and are decoupled inside the propagation domain. We detail how these equations are coupled at the boundary depending on the nature of the boundary condition satisfied by the displacement field. After presenting the case of rigid boundary conditions, that presents no specific difficulty, we tackle the challenging case of free surface boundary conditions that presents severe stability issues if a straightforward approach is used. We introduce an adequate functional framework as well as a time domain mixed formulation to circumvent these issues. Numerical results confirm the stability of the proposed approach.
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