Robust discontinuous Galerkin-based scheme for the fully-coupled nonlinear thermo-hydro-mechanical problem

Author:

Bonetti Stefano1,Botti Michele1,Antonietti Paola F1

Affiliation:

1. MOX , Department of Mathematics, Politecnico di Milano, P.zza Leonardo da Vinci 32, 20133 , Italy

Abstract

Abstract We present and analyze a discontinuous Galerkin method for the numerical modeling of the nonlinear fully-coupled thermo-hydro-mechanic problem. We propose an arbitrary-order weighted symmetric interior penalty scheme that supports general polytopal grids and is robust with respect to strong heterogeneities in the model coefficients. We focus on the treatment of the nonlinear convective transport term in the energy conservation equation and we propose suitable stabilization techniques that make the scheme robust for advection-dominated regimes. The stability analysis of the problem and the convergence of the fixed-point linearization strategy are addressed theoretically under mild requirements on the problem data. A complete set of numerical simulations is presented in order to assess the convergence and robustness properties of the proposed method.

Funder

European Union

Italian Ministry of Universities and Research

Italian Research Center on High Performance Computing

Big Data and Quantum Computing

NextGenerationEU

INdAM-GNCS

Publisher

Oxford University Press (OUP)

Reference49 articles.

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5. Hp-version composite discontinuous Galerkin methods for elliptic problems on complicated domains;Antonietti;SIAM J. Sci. Comput.,2013

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