A WENO-limited, ADER-DT, finite-volume scheme for efficient, robust, and communication-avoiding multi-dimensional transport

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Abstract

The novel ADER-DT time discretization is applied to two-dimensional transport in a quadrature-free, WENO- and FCT-limited, Finite-Volume context. Emphasis is placed on (1) the serial and parallel computational properties of ADER-DT and this framework and (2) the flexibility of ADER-DT and this framework in efficiently balancing accuracy with other constraints important to transport applications. This study demonstrates a range of choices for the user when approaching their specific application while maintaining good parallel properties. In this method, genuine multi-dimensionality, single-step and single-stage time stepping, strict positivity, and a flexible range of limiting are all achieved with only one parallel synchronization and data exchange per time step. In terms of parallel data transfers per simulated time interval, this improves upon multi-stage time stepping and post-hoc filtering techniques such as hyperdiffusion. This method is evaluated with standard transport test cases over a range of limiting options to demonstrate quantitatively and qualitatively what a user should expect when employing this method in their application.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalJournal of Computational Physics
Volume274
DOIs
StatePublished - Oct 1 2014

Funding

This research used resources of the National Center for Computational Sciences at Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725 .

Keywords

  • ADER
  • Differential transform
  • FCT
  • Finite-volume
  • WENO

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