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

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Title: High order ADER-DG schemes for the simulation of linear seismic waves induced by nonlinear dispersive free-surface water waves.
Authors: Bassi, C.1 (AUTHOR) caterina.bassi@polimi.it, Busto, S.2 (AUTHOR) saray.busto@unitn.it, Dumbser, M.2 (AUTHOR) michael.dumbser@unitn.it
Source: Applied Numerical Mathematics. Dec2020, Vol. 158, p236-263. 28p.
Subjects: Seismic waves, Water waves, Surface waves (Seismic waves), Elastic waves, Tsunamis, Nonlinear waves, Elastic wave propagation
Abstract: 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. In particular, 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. To this end, Cartesian non-conforming meshes are defined in the solid and fluid domains 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 that contain higher order derivatives and typically require implicit solvers. Since the two systems that describe the seismic waves and the free surface water waves are written in the same form of a first order hyperbolic system they can also be efficiently solved in a unique numerical framework. In this paper we choose the family of arbitrary high order accurate discontinuous Galerkin finite element schemes, which have already shown to be suitable for the numerical simulation of wave propagation problems. The developed methodology is carefully assessed by first considering several benchmarks for each system separately, i.e. in the framework of linear elasticity and non-hydrostatic free surface flows, 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. • Simulation of seismic waves induced by free surface water waves. • Coupling of nonlinear dispersive water waves with linear elasticity. • Hyperbolic reformulation of the Serre-Green-Naghdi model. • Arbitrary high order accurate discontinuous Galerkin finite element schemes. • Comparison with exact, numerical and experimental reference solutions. [ABSTRACT FROM AUTHOR]
Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: High order ADER-DG schemes for the simulation of linear seismic waves induced by nonlinear dispersive free-surface water waves.
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  Data: <searchLink fieldCode="AR" term="%22Bassi%2C+C%2E%22">Bassi, C.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> caterina.bassi@polimi.it</i><br /><searchLink fieldCode="AR" term="%22Busto%2C+S%2E%22">Busto, S.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> saray.busto@unitn.it</i><br /><searchLink fieldCode="AR" term="%22Dumbser%2C+M%2E%22">Dumbser, M.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> michael.dumbser@unitn.it</i>
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  Data: <searchLink fieldCode="JN" term="%22Applied+Numerical+Mathematics%22">Applied Numerical Mathematics</searchLink>. Dec2020, Vol. 158, p236-263. 28p.
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  Data: <searchLink fieldCode="DE" term="%22Seismic+waves%22">Seismic waves</searchLink><br /><searchLink fieldCode="DE" term="%22Water+waves%22">Water waves</searchLink><br /><searchLink fieldCode="DE" term="%22Surface+waves+%28Seismic+waves%29%22">Surface waves (Seismic waves)</searchLink><br /><searchLink fieldCode="DE" term="%22Elastic+waves%22">Elastic waves</searchLink><br /><searchLink fieldCode="DE" term="%22Tsunamis%22">Tsunamis</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+waves%22">Nonlinear waves</searchLink><br /><searchLink fieldCode="DE" term="%22Elastic+wave+propagation%22">Elastic wave propagation</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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. In particular, 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. To this end, Cartesian non-conforming meshes are defined in the solid and fluid domains 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 that contain higher order derivatives and typically require implicit solvers. Since the two systems that describe the seismic waves and the free surface water waves are written in the same form of a first order hyperbolic system they can also be efficiently solved in a unique numerical framework. In this paper we choose the family of arbitrary high order accurate discontinuous Galerkin finite element schemes, which have already shown to be suitable for the numerical simulation of wave propagation problems. The developed methodology is carefully assessed by first considering several benchmarks for each system separately, i.e. in the framework of linear elasticity and non-hydrostatic free surface flows, 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. • Simulation of seismic waves induced by free surface water waves. • Coupling of nonlinear dispersive water waves with linear elasticity. • Hyperbolic reformulation of the Serre-Green-Naghdi model. • Arbitrary high order accurate discontinuous Galerkin finite element schemes. • Comparison with exact, numerical and experimental reference solutions. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.apnum.2020.08.005
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      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 28
        StartPage: 236
    Subjects:
      – SubjectFull: Seismic waves
        Type: general
      – SubjectFull: Water waves
        Type: general
      – SubjectFull: Surface waves (Seismic waves)
        Type: general
      – SubjectFull: Elastic waves
        Type: general
      – SubjectFull: Tsunamis
        Type: general
      – SubjectFull: Nonlinear waves
        Type: general
      – SubjectFull: Elastic wave propagation
        Type: general
    Titles:
      – TitleFull: High order ADER-DG schemes for the simulation of linear seismic waves induced by nonlinear dispersive free-surface water waves.
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            NameFull: Bassi, C.
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            NameFull: Busto, S.
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            NameFull: Dumbser, M.
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            – D: 01
              M: 12
              Text: Dec2020
              Type: published
              Y: 2020
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              Value: 158
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            – TitleFull: Applied Numerical Mathematics
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