Implementation of Hybridizable Discontinuous Galerkin method for time-harmonic anisotropic poroelasticity in two dimensions.

Hélène Barucq (1) , Julien Diaz (1) , Rose-Cloé Meyer (1, 2) , Ha Pham (1)

1 MAKUTU - Modélisation et simulation de la propagation des ondes fondées sur des mesures expérimentales pour caractériser des milieux géophysiques et héliophysiques et concevoir des objets complexes
2 UPPA - Université de Pau et des Pays de l'Adour

We apply a Hybridizable Discontinuous Galerkin (HDG) method to numerically solve two-dimensional anisotropic poroelastic wave equations in the frequency domain given by Biot theory. The motivation for choosing HDG method comes from the complexity of the considered equations and the high number of unknowns. The HDG method possesses all the advantages of Discontinuous Galerkin method (hpadaptivity, accuracy, ability to model complex tectonics,...) without a drastic increase in the number of degrees of freedom. After a description of its implementation, we illustrate the accuracy of the proposed method by comparisons with analytical solutions. We then perform a sensitivity analysis of the method as a function of stabilization parameters and frequency, and show in particular that there exists optimal values of these parameters in order to obtain a very good level of accuracy. We also show the ability of the method to reproduce the different types of poroelastic waves including the slow Biot wave.

Mots clés: anisotropic poroelasticity; harmonic domain; Hybridizable Discontinuous Galerkin method

Domaines: Equations aux dérivées partielles [math.AP]

Hélène Barucq, Julien Diaz, Rose-Cloé Meyer, Ha Pham. Implementation of Hybridizable Discontinuous Galerkin method for time-harmonic anisotropic poroelasticity in two dimensions.. International Journal for Numerical Methods in Engineering, 2021, ⟨10.1002/nme.6651⟩. ⟨hal-03464413⟩