DG SOLVER FOR THE SIMULATION OF SIMPLIFIED ELASTIC WAVES IN TWO-DIMENSIONAL PIECEWISE HOMOGENEOUS MEDIA

Jiří Hozman, Josef Bradáč, Jan Kovanda

Abstract


The theory of elasticity is a very important discipline which has a lot
of applications in science and engineering. In this paper we are interested in elastic
materials with different properties between interfaces implicated the discontinu-
ous coefficients in the governing elasticity equations. The main aim is to develop
a practical numerical scheme for modeling the behaviour of a simplified piecewise
homogeneous medium subjected to an external action in 2D domains. Therefore,
the discontinuous Galerkin method is used for the simulation of elastic waves in
such elastic materials. The special attention is also paid to treatment of boundary
and interface conditions. For the treatment of the time dependency the implicit
Euler method is employed. Moreover, the limiting procedure is incorporated in the
resulting numerical scheme in order to overcome nonphysical spurious overshoots
and undershoots in the vicinity of discontinuities in discrete solutions. Finally, we
present computational results for two-component material, representing a planar
elastic body subjected to a mechanical hit or mechanical loading.

Keywords


elastic wave equation; piecewise homogeneous medium; discontinuous Galerkin method; interface conditions; implicit Euler method; limiting

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DOI: http://dx.doi.org/10.14311/NNW.1901.%25x

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