Kyle T. Mandli

The GeoClaw software for depth-averaged flows with adaptive refinement

Many geophysical flow or wave propagation problems can be modeled with two-dimensional depth-averaged equations, of which the shallow water equations are the simplest example. We describe the GeoClaw software that has been designed to solve problems of this nature, consisting of open source Fortran programs together with Python tools for the user interface and flow visualization. This software uses high-resolution shock-capturing finite volume methods on logically rectangular grids, including latitude–longitude grids on the sphere. Dry states are handled automatically to model inundation. The code incorporates adaptive mesh refinement to allow the efficient solution of large-scale geophysical problems. Examples are given illustrating its use for modeling tsunamis and dam-break flooding problems. Documentation and download information is available at www.clawpack.org/geoclaw.

PYCLAW: ACCESSIBLE, EXTENSIBLE, SCALABLE TOOLS FOR WAVE PROPAGATION PROBLEMS "

Development of scientific software involves tradeoffs between ease of use, generality, and performance. We describe the design of a general hyperbolic PDE solver that can be operated with the convenience of MATLAB yet achieves efficiency near that of hand-coded Fortran and scales to the largest supercomputers. This is achieved by using Python for most of the code while employing automatically wrapped Fortran kernels for computationally intensive routines, and using Python bindings to interface with a parallel computing library and other numerical packages. The software described here is PyClaw, a Python-based structured grid solver for general systems of hyperbolic PDEs [K. T. Mandli et al., PyClaw Software, Version 1.0, http://numerics.kaust.edu.sa/pyclaw/ (2011)]. PyClaw provides a powerful and intuitive interface to the algorithms of the existing Fortran codes Clawpack and SharpClaw, simplifying code development and use while providing massive parallelism and scalable solvers via the PETSc library. The...

A numerical method for the two layer shallow water equations with dry states

Abstract A numerical method is proposed for solving the two layer shallow water equations with variable bathymetry in one dimension based on high-resolution f-wave-propagation finite volume methods. The method splits the jump in the fluxes and source terms into waves propagating away from each grid cell interface. It addresses the required determination of the system’s eigenstructure and a scheme for evaluating the flux and source terms. It also handles dry states in the system where the bottom layer depth becomes zero, utilizing existing methods for the single layer solution and handling single layer dry states that can exist independently. Sample results are shown illustrating the method and its handling of dry states including an idealized ocean setting.

Adaptive mesh refinement for storm surge

Abstract An approach to utilizing adaptive mesh refinement algorithms for storm surge modeling is proposed. Currently numerical models exist that can resolve the details of coastal regions but are often too costly to be run in an ensemble forecasting framework without significant computing resources. The application of adaptive mesh refinement algorithms substantially lowers the computational cost of a storm surge model run while retaining much of the desired coastal resolution. The approach presented is implemented in the GeoClaw framework and compared to ADCIRC for Hurricane Ike along with observed tide gauge data and the computational cost of each model run.

ForestClaw: Hybrid forest-of-octrees AMR for hyperbolic conservation laws

We present a new hybrid paradigm for parallel adaptive mesh refinement (AMR) that combines the scalability and lightweight architecture of tree-based AMR with the computational efficiency of patch-based solvers for hyperbolic conservation laws. The key idea is to interpret each leaf of the AMR hierarchy as one uniform compute patch in

Visualizing uncertainties in a storm surge ensemble data assimilation and forecasting system

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Bayesian inference of earthquake parameters from buoy data using a polynomial chaos-based surrogate

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Quantifying uncertainties in fault slip distribution during the Tōhoku tsunami using polynomial chaos

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Evolution and Controls of Large Glacial Lakes in the Nepal Himalaya

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Surrogate-based parameter inference in debris flow model

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