A Positive-Definite, WENO-Limited, High-Order Finite Volume Solver for 2-D Transport on the Cubed Sphere Using an ADER Time Discretization

Norman, Matthew R.; Nair, R. D.

doi:10.1029/2017MS001247

Title: A Positive-Definite, WENO-Limited, High-Order Finite Volume Solver for 2-D Transport on the Cubed Sphere Using an ADER Time Discretization

Journal Article · Fri Jun 15 00:00:00 EDT 2018 · Journal of Advances in Modeling Earth Systems

DOI:https://doi.org/10.1029/2017MS001247· OSTI ID:1461937

^[1];

^[2]

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
National Center for Atmospheric Research, Boulder, CO (United States)

Modern computer architectures reward added computation if it reduces algorithmic dependence, reduces data movement, increases accuracy/robustness, and improves memory accesses. The driving motive for this study is to develop a numerical algorithm that respects these constraints while improving accuracy and robustness. This study introduces the ADER-DT (Arbitrary DERivatives in time and space-differential transform) time discretization to positive-definite, weighted essentially nonoscillatory (WENO)-limited, finite volume transport on the cubed sphere in lieu of semidiscrete integrators. The cost of the ADER-DT algorithm is significantly improved from previous implementations without affecting accuracy. A new function-based WENO implementation is also detailed for use with the ADER-DT time discretization. While ADER-DT costs about 1.5 times more than a fourth-order, five-stage strong stability preserving Runge-Kutta (SSPRK4) method, it is far more computationally dense (which is advantageous on accelerators such as graphics processing units), and it has a larger effective maximum stable time step. ADER-DT errors converge more quickly with grid refinement than SSPRK4, giving 6.5 times less error in the L_∞ norm than SSPRK4 at the highest refinement level for smooth data. For nonsmooth data, ADER-DT resolves C⁰ discontinuities more sharply. For a complex flow field, ADER exhibits less phase error than SSPRK4. In conclusion, improving both accuracy and robustness as well as better respecting modern computational efficiency requirements, we believe the method presented herein is competitive for efficiently transporting tracers over the sphere for applications targeting modern computing architectures.

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Research Organization:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1461937

Journal Information:: Journal of Advances in Modeling Earth Systems, Vol. 10, Issue 7; ISSN 1942-2466

Publisher:: American Geophysical Union (AGU)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 4 works

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Title: A Positive-Definite, WENO-Limited, High-Order Finite Volume Solver for 2-D Transport on the Cubed Sphere Using an ADER Time Discretization

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