Core Concepts
Implicit adaptive mesh refinement enhances accuracy in modeling dispersive tsunami propagation.
Abstract
The content introduces an algorithm for solving the dispersive depth-averaged Serre-Green-Naghdi equations using patch-based adaptive mesh refinement. The method is implicit, allowing different time steps on various refinement levels. Computational examples demonstrate stability and accuracy in realistic tsunami modeling scenarios, including a hypothetical asteroid impact generating a short-wavelength tsunami. The implementation is part of the GeoClaw software widely used for hazard modeling.
Introduction:
- Algorithm to solve dispersive SGN equations with adaptive mesh refinement.
- Implicit method requiring elliptic system solution at each time step.
- Widely used GeoClaw software enhanced for shorter wavelength phenomena.
Equations:
- Nonlinear shallow water equations (SWE) vs. Boussinesq-type equations.
- Depth-averaged system crucial for trans-oceanic propagation.
- Comparison between SWE and dispersive models based on length scales.
Solution Algorithm:
- Splitting method with elliptic equation solution and shallow water step.
- Patch-based AMR strategy with subcycling in time.
- Composite solve without subcycling for comparison.
Computational Examples:
- Radially symmetric ocean, shelf, and beach scenario tested for accuracy and stability.
- Results show dispersion effects, soliton fission, wave breaking near shore.
- Comparison of coupled vs uncoupled algorithms and uniform grid solutions.
- Convergence analysis with 4, 5, and 6 level adaptive runs.
Stats
この方程式は、水深が水平長さスケールよりもはるかに小さいことを前提とした長波近似である。
これらの方程式は、非分散であり、線形化された方程式の分散関係は一定の波速を示す。
SGNシステムの方程式は、追加の源項を持つSWE(2.1)の形をしている。
Quotes
"Several figures in this paper show outlines of the refined patches."
"Our implementation... can still solve large-scale realistic tsunami modeling problems on a laptop."