A hyperbolic reformulation of the Serre-Green-Naghdi model for general bottom topographies

We present a novel hyperbolic reformulation of the Serre-Green-Naghdi (SGN) model for the description of dispersive water waves. Contrarily to the classical Boussinesq-type models, it contains only first order derivatives, thus allowing to overcome the numerical difficulties and the severe time step restrictions arising from higher order terms. The proposed model reduces to the original SGN model when an artificial sound speed tends to infinity. Moreover, it is endowed with an energy conservation law from which the energy conservation law associated with the original SGN model is retrieved when the artificial sound speed goes to infinity. The governing partial differential equations are then solved at the aid of high order ADER discontinuous Galerkin finite element schemes. The new model has been successfully validated against numerical and experimental results, for both flat and non-flat bottom. For bottom topographies with large variations, the new model proposed in this paper provides more accurate results with respect to the hyperbolic reformulation of the SGN model with the mild bottom approximation recently proposed in "C. Escalante, M. Dumbser and M.J. Castro. An efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution with high order discontinuous Galerkin schemes, Journal of Computational Physics 2018"

High order ADER-DG schemes for the simulation of linear seismic waves induced by nonlinear dispersive free-surface water waves

In this paper, we propose a unified and high order accurate fully-discrete one-step ADER Discontinuous Galerkin method for the simulation of linear seismic waves in the sea bottom that are generated by the propagation of free surface water waves. A hyperbolic reformulation of the Serre-Green-Naghdi model for nonlinear dispersive free surface flows is coupled with a first order velocity-stress formulation for linear elastic wave propagation in the sea bottom. Cartesian non-conforming meshes are defined and the coupling is achieved by an appropriate time-dependent pressure boundary condition in the three-dimensional domain for the elastic wave propagation, where the pressure is a combination of hydrostatic and non-hydrostatic pressure in the water column above the sea bottom. The use of a first order hyperbolic reformulation of the nonlinear dispersive free surface flow model leads to a straightforward coupling with the linear seismic wave equations, which are also written in first order hyperbolic form. It furthermore allows the use of explicit time integrators with a rather generous CFL-type time step restriction associated with the dispersive water waves, compared to numerical schemes applied to classical dispersive models. Since the two systems employed are written in the same form of a first order hyperbolic system they can also be efficiently solved in a unique numerical framework. We choose the family of arbitrary high order accurate discontinuous Galerkin finite element schemes. The developed methodology is carefully assessed by first considering several benchmarks for each system separately showing a good agreement with exact and numerical reference solutions. Finally, also coupled test cases are addressed. Throughout this paper we assume the elastic deformations in the solid to be sufficiently small so that their influence on the free surface water waves can be neglected

Inelastic material response in multi-physics earthquake rupture simulations

Dynamic rupture models are able to shed light on earthquake source dynamics where direct observations are rare or non-existent. These multi-physics simulations incorporate earthquake rupture along a fault governed by frictional constitutive laws, which is coupled to seismic wave propagation described by the linear elastic wave equation. To accurately model the earthquake process, numerical models need to include realistic material properties such as the ability of rocks to deform plastically. This dissertation extends the Arbitrary High Order Derivative Discontinuous Galerkin (ADER-DG) framework of the dynamic rupture software SeisSol to account for non-linear off-fault plasticity. The impact of plasticity on rupture dynamics and the emitted seismic wave field is investigated in realistic simulations motivated by past earthquakes on geometrically complex faults. We first present the implementation of off-fault plasticity, which is verified in community benchmark problems and by three-dimensional numerical refinement studies. Motivated by the high efficiency of the implementation, we present a large-scale simulation of earthquake rupture along the segmented fault system of the 1992 Landers earthquake including plasticity. The results indicate that spatio-temporal rupture transfers are altered by plastic energy absorption, correlating with locations of geometrical fault complexity. In a next step, the model of the 1992 Landers earthquake is further extended to account for a new degree of realism among dynamic rupture models by incorporating high-resolution topography, 3D velocity structure, and viscoelastic attenuation in addition to off-fault plasticity. The simulation reproduces a broad range of observations including moment release rate, seismic waveform characteristics, mapped off-fault deformation patterns, and peak ground motions. We find that plasticity reduces the directivity effect and the spatial variability of peak ground velocities in comparison to the purely elastic simulation. In addition to this continental strike-slip earthquake, we investigate the effect of off-fault plasticity on source dynamics and seafloor deformation in a 3D subduction zone model of the 2004 Sumatra-Andaman earthquake. Simulated seafloor displacements are drastically altered by inelastic processes within the entire accretionary wedge, depending on fault- strike and the applied regional stress field, which potentially affects the tsunamigenesis. Finally, since these application scenarios show that rupture dynamics and the occurrence of off-fault plasticity are highly influenced by the assumed initial stresses and fault geometry, we propose a workflow to constrain dynamic rupture initial conditions with plasticity by long-term seismic cycling modelling. The exploited seismo-thermo-mechanical model provides a self-consistent slab geometry as well as initial stress and strength conditions that evolve according to the tectonic stress build-up and the temperature-dependent strength of the rocks. The geomechanically constrained subduction zone model suggests that the accretionary wedge is very close to plastic failure such that the occurrence of plastic strain hampers rupture to the trench, but locally increases the vertical seafloor uplift