Algorithmic improvements for schemes using the ADER time discretization

M. R. Norman

doi:10.1016/j.jcp.2013.03.003

Algorithmic improvements for schemes using the ADER time discretization

M. R. Norman

Advanced Computing for Life Sciences and

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We detail several algorithmic changes to the ADER Multi-Moment Finite-Volume Methods (ADER. +. MMFV) of Norman and Finkel (2012) [2]. The DT recurrence relations are improved, flux and source term differential transforms are saved, each are expanded as polynomials, quadrature is removed from the algorithm, integration is performed analytically, and a different Riemann solver admitting direct use of time-averaged fluxes is used. These algorithmic changes were implemented and tested, and smooth 1-D shallow water experiments confirm the same or slightly better accuracy as well as 2-3× lower runtimes compared to Norman and Finkel (2012) [2].

Original language	English
Pages (from-to)	176-1178
Number of pages	1003
Journal	Journal of Computational Physics
Volume	243
DOIs	https://doi.org/10.1016/j.jcp.2013.03.003
State	Published - Jun 5 2013

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
F-waves
Finite-Volume
Multi-Moment

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10.1016/j.jcp.2013.03.003

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AB - We detail several algorithmic changes to the ADER Multi-Moment Finite-Volume Methods (ADER. +. MMFV) of Norman and Finkel (2012) [2]. The DT recurrence relations are improved, flux and source term differential transforms are saved, each are expanded as polynomials, quadrature is removed from the algorithm, integration is performed analytically, and a different Riemann solver admitting direct use of time-averaged fluxes is used. These algorithmic changes were implemented and tested, and smooth 1-D shallow water experiments confirm the same or slightly better accuracy as well as 2-3× lower runtimes compared to Norman and Finkel (2012) [2].

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JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -

Algorithmic improvements for schemes using the ADER time discretization

Abstract

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Keywords

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