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Tie, B.; Mouronval, A.-S.; Nguyen, V.-D.; Series, L.; Aubry, D.

A unified variational framework for the space discontinuous Galerkin method for elastic wave propagation in anisotropic and piecewise homogeneous media. (English) Zbl 1440.74167

Comput. Methods Appl. Mech. Eng. 338, 299-332 (2018).
Summary: We present a unified multidimensional variational framework for the space discontinuous Galerkin method for elastic wave propagation in anisotropic and piecewise homogeneous media. Based on an elastic wave oriented formulation and using a tensorial formalism, the proposed framework allows a better understanding of the physical meaning of the terms involved in the discontinuous Galerkin method. The unified variational framework is written for first-order velocity-stress wave equations. An uncoupled upwind numerical flux and two coupled upwind numerical fluxes using respectively the Voigt and the Reuss averages of elastic moduli are defined. Two numerical fluxes that are exact solutions of the Riemann problem on physical interfaces are also developed and analyzed in the 1D case. The implemented solvers are then applied to different elastic media, especially to polycrystalline materials that present a particular case of piecewise homogeneous media. The use of the three upwind numerical fluxes, which only solve approximately the Riemann problem at element interfaces, is investigated.

Cited in 4 Documents

MSC:

74J05 Linear waves in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
74B05 Classical linear elasticity

Keywords:

space discontinuous Galerkin method; elastic wave propagation; anisotropy; piecewise homogeneous medium; polycrystalline materials

Software:

HE-E1GODF
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Full Text: DOI HAL

References:

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