37 research outputs found
A space-time discontinuous Galerkin method for coupled poroelasticity-elasticity problems
This work is concerned with the analysis of a space-time finite element
discontinuous Galerkin method on polytopal meshes (XT-PolydG) for the numerical
discretization of wave propagation in coupled poroelastic-elastic media. The
mathematical model consists of the low-frequency Biot's equations in the
poroelastic medium and the elastodynamics equation for the elastic one. To
realize the coupling, suitable transmission conditions on the interface between
the two domains are (weakly) embedded in the formulation. The proposed PolydG
discretization in space is then coupled with a dG time integration scheme,
resulting in a full space-time dG discretization. We present the stability
analysis for both the continuous and the semidiscrete formulations, and we
derive error estimates for the semidiscrete formulation in a suitable energy
norm. The method is applied to a wide set of numerical test cases to verify the
theoretical bounds. Examples of physical interest are also presented to
investigate the capability of the proposed method in relevant geophysical
scenarios
Numerical modelling of wave propagation phenomena in thermo-poroelastic media via discontinuous Galerkin methods
We present and analyze a high-order discontinuous Galerkin method for the
space discretization of the wave propagation model in thermo-poroelastic media.
The proposed scheme supports general polytopal grids. Stability analysis and
-version error estimates in suitable energy norms are derived for the
semi-discrete problem. The fully-discrete scheme is then obtained based on
employing an implicit Newmark- time integration scheme. A wide set of
numerical simulations is reported, both for the verification of the theoretical
estimates and for examples of physical interest. A comparison with the results
of the poroelastic model is provided too, highlighting the differences between
the predictive capabilities of the two models
Anatomy of strong ground motion: near-source records and three-dimensional physics-based numerical simulations of the Mw 6.0 2012 May 29 Po Plain earthquake
Stimulated by the recent advances in computational tools for the simulation of seismic wave propagation problems in realistic geologic environments, this paper presents a 3D physicsbased numerical study on the prediction of earthquake ground motion in the Po Plain, with reference to the MW 6.0 May 29 2012 earthquake. To respond to the validation objectives aimed at reproducing with a reasonable accuracy some of the most peculiar features of the nearsource strong motion records and of the damage distribution, this study required a sequence of investigations, starting from the analysis of a nearly unprecedented set of near-source records, to the calibration of an improved kinematic seismic source model, up to the development of a 3D numerical model of the portion of the Po Plain interested by the earthquake, including the irregular buried morphology, with sediment thickness varying from few tens of m to some km. The spatial resolution of the numerical model is suitable to propagate up to about 1:5 Hz.
Numerical simulations were performed using the open-source high-performance code SPEED, based on the Discontinuous Galerkin Spectral Elements (DGSE) method. The 3D numerical model coupled with the updated slip distribution along the rupturing fault proved successful to reproduce with reasonable accuracy, measured through quantitative goodness-of-fit criteria, the most relevant features of the observed ground motion both at the near- and far-field scales.
These include: (i) the large fault normal velocity peaks at the near-source stations driven by updip directivity effects; (ii) the small-scale variability at short distance from the source, resulting in the out-of-phase motion at stations separated by only 3 km distance; (iii) the propagation of prominent trains of surface waves, especially in the Northern direction, induced by the irregular buried morphology in the near-source area; (iv) the map of earthquake-induced ground uplift with maximum values of about 10 cm, in substantial agreement with satellite measurements; and (v) the two-lobed pattern of the peak ground velocity map, well correlated with the distribution of macroseismic intensity
A high-order discontinuous Galerkin method for the poro-elasto-acoustic problem on polygonal and polyhedral grids
The aim of this work is to introduce and analyze a finite element
discontinuous Galerkin method on polygonal meshes for the numerical
discretization of acoustic waves propagation through poroelastic materials.
Wave propagation is modeled by the acoustics equations in the acoustic domain
and the low-frequency Biot's equations in the poroelastic one. The coupling is
introduced by considering (physically consistent) interface conditions, imposed
on the interface between the domains, modeling both open and sealed pores.
Existence and uniqueness is proven for the strong formulation based on
employing the semigroup theory. For the space discretization we introduce and
analyze a high-order discontinuous Galerkin method on polygonal and polyhedral
meshes, which is then coupled with Newmark- time integration schemes. A
stability analysis both for the continuous problem and the semi-discrete one is
presented and error estimates for the energy norm are derived for the
semidiscrete problem. A wide set of numerical results obtained on test cases
with manufactured solutions are presented in order to validate the error
analysis. Examples of physical interest are also presented to test the
capability of the proposed methods in practical cases.Comment: The proof of the well-posedness contains an error. This has an impact
on the whole paper. We need time to fix the issu