Implicit Adaptive Mesh Refinement for Dispersive Tsunami Propagation
by M. J. Berger and R. J. LeVeque SIAM J. Sci. Comput. 46 (2024) pp. B554 - B578.

Abstract. We present an algorithm to solve the dispersive depth-averaged Serre-Green-Naghdi (SGN) equations using patch-based adaptive mesh refinement. These equations require adding additional higher derivative terms to the nonlinear shallow water equations. This has been implemented as a new component of the open source GeoClaw software that is widely used for modeling tsunamis, storm surge, and related hazards, improving its accuracy on shorter wavelength phenomena. The equations require the solution of an elliptic system at each time step. The adaptive algorithm allows different time steps on different refinement levels, and solves the implicit equations level by level. Computational examples are presented to illustrate the stability and accuracy on a radially symmetric test case and two realistic tsunami modeling problems, including a hypothetical asteroid impact creating a short wavelength tsunami for which dispersive terms are necessary.

Journal: DOI 10.1137/23M1585210

Preprint: arxiv:2307.05816 [v2] is revised version from resubmission March, 2024.

Code archive:

• Github (git tag publication goes with publication)
• DOI 10.5281/zenodo.12709453 (zip file, also in Supplementary Materials)

bibtex entry:

@misc{berger2023implicit,
      title={Implicit Adaptive Mesh Refinement for Dispersive Tsunami Propagation}, 
      author={Marsha J. Berger and Randall J. LeVeque},
      year={2023},
      eprint={2307.05816},
      archivePrefix={arXiv},
      primaryClass={math.NA}
}