A high-order WENO-limited finite-volume algorithm for atmospheric flow using the ADER-differential transform time discretization

Norman, Matthew R.

doi:10.1002/qj.3989

Title: A high-order WENO-limited finite-volume algorithm for atmospheric flow using the ADER-differential transform time discretization

Journal Article · Mon Feb 01 00:00:00 EST 2021 · Quarterly Journal of the Royal Meteorological Society

DOI:https://doi.org/10.1002/qj.3989· OSTI ID:1817609

^[1]

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

A high-order-accurate weighted essentially non-oscillatory (WENO) limited upwind finite-volume scheme is detailed for the compressible, nonhydrostatic, inviscid Euler equations using an arbitrary derivatives (ADER) time-stepping scheme based on differential transforms (DTs). A second-order-accurate alternating Strang dimensional splitting is compared against multidimensional simulation with 2D transport using solid body rotation of various data. The two were found to give nearly identical accuracy in orthogonal, Cartesian coordinates. Orders of convergence are demonstrated at up to ninth-order accuracy with 2D transport. 1D transport is used to confirm that error decreases monotonically with increasing order of accuracy with WENO limiting even for discontinuous data. Further, WENO limiting always decreased the error compared with simulation without limiting in the L₁ norm. A series of standard 2D compressible nonhydrostatic Euler equation test cases were validated against previous results from literature. Finally, it was demonstrated that increasing the order of accuracy led to better resolved features and increased power for kinetic energy at small wavelengths.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

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

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1817609

Journal Information:: Quarterly Journal of the Royal Meteorological Society, Vol. 147, Issue 736; ISSN 0035-9009

Publisher:: Royal Meteorological SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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