Journal of Scientific Computing

, Volume 63, Issue 1, pp 23–48 | Cite as

Efficient GPU-Implementation of Adaptive Mesh Refinement for the Shallow-Water Equations

  • Martin L. Sætra
  • André R. Brodtkorb
  • Knut-Andreas Lie
Article

Abstract

The shallow-water equations model hydrostatic flow below a free surface for cases in which the ratio between the vertical and horizontal length scales is small and are used to describe waves in lakes, rivers, oceans, and the atmosphere. The equations admit discontinuous solutions, and numerical solutions are typically computed using high-resolution schemes. For many practical problems, there is a need to increase the grid resolution locally to capture complicated structures or steep gradients in the solution. An efficient method to this end is adaptive mesh refinement (AMR), which recursively refines the grid in parts of the domain and adaptively updates the refinement as the simulation progresses. Several authors have demonstrated that the explicit stencil computations of high-resolution schemes map particularly well to many-core architectures seen in hardware accelerators such as graphics processing units (GPUs). Herein, we present the first full GPU-implementation of a block-based AMR method for the second-order Kurganov–Petrova central scheme. We discuss implementation details, potential pitfalls, and key insights, and present a series of performance and accuracy tests. Although it is only presented for a particular case herein, we believe our approach to GPU-implementation of AMR is transferable to other hyperbolic conservation laws, numerical schemes, and architectures similar to the GPU.

Keywords

Adaptive mesh refinement (AMR) GPU computing Shallow-water simulation Conservation law Domain decomposition 

Mathematics Subject Classification

35L65 65M08 65M50 76B15 68N19 

Notes

Acknowledgments

This work is supported in part by the Research Council of Norway through Grant No. 180023 (Parallel3D), and in part by the Centre of Mathematics for Applications at the University of Oslo (Sætra and Lie).

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Martin L. Sætra
    • 1
    • 2
  • André R. Brodtkorb
    • 3
  • Knut-Andreas Lie
    • 1
    • 3
  1. 1.Centre of Mathematics for ApplicationsUniversity of OsloOsloNorway
  2. 2.Norwegian Meteorological InstituteOsloNorway
  3. 3.Department of Applied MathematicsSINTEF ICTOsloNorway

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