ADER-DG with a-posteriori finite-volume limiting to simulate tsunamis in a parallel adaptive mesh refinement framework. In this paper, we present the application of the ADER discontinuous Galerkin method with an -posteriori finite-volume limiter on the simulation of tsunamis. The goal is to obtain a method of high-order convergence in deep water areas while being able to handle wetting & drying at coast lines. Several adjustments of the original ADER-DG method are presented to preserve characteristics like the well-balanced property. We evaluate and confirm developed concepts by a series of numerical tests and present them in the context of reconstructed tsunamis.

References in zbMATH (referenced in 12 articles , 1 standard article )

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  1. Gaburro, Elena; Dumbser, Michael: A posteriori subcell finite volume limiter for general (P_NP_M) schemes: applications from gasdynamics to relativistic magnetohydrodynamics (2021)
  2. Li, Gang; Li, Jiaojiao; Qian, Shouguo; Gao, Jinmei: A well-balanced ADER discontinuous Galerkin method based on differential transformation procedure for shallow water equations (2021)
  3. Reyes, Adam; Lee, Dongwook; Graziani, Carlo; Tzeferacos, Petros: A variable high-order shock-capturing finite difference method with GP-WENO (2019)
  4. Dumbser, Michael; Fambri, Francesco; Tavelli, Maurizio; Bader, Michael; Weinzierl, Tobias: Efficient implementation of ADER discontinuous Galerkin schemes for a scalable hyperbolic PDE engine (2018)
  5. Rannabauer, Leonhard; Dumbser, Michael; Bader, Michael: ADER-DG with a-posteriori finite-volume limiting to simulate tsunamis in a parallel adaptive mesh refinement framework (2018)
  6. Montecinos, G. I.; López-Rios, J. C.; Lecaros, R.; Ortega, J. H.; Toro, E. F.: An ADER-type scheme for a class of equations arising from the water-wave theory (2016)
  7. Montecinos, Gino I.: A strategy to implement Dirichlet boundary conditions in the context of ADER finite volume schemes. One-dimensional conservation laws (2016)
  8. Toro, Eleuterio F.: Brain venous haemodynamics, neurological diseases and mathematical modelling. A review (2016)
  9. Toro, Eleuterio F.; Castro, Cristóbal E.; Lee, Bok Jik: A novel numerical flux for the 3D Euler equations with general equation of state (2015)
  10. Toro, Eleuterio F.; Montecinos, Gino I.: Implicit, semi-analytical solution of the generalized Riemann problem for stiff hyperbolic balance laws (2015)
  11. Montecinos, Gino I.; Müller, Lucas O.; Toro, Eleuterio F.: Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemes (2014)
  12. Montecinos, Gino I.; Toro, Eleuterio F.: Reformulations for general advection-diffusion-reaction equations and locally implicit ADER schemes (2014)