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Atmosphere 2018, 9(11), 444; https://doi.org/10.3390/atmos9110444

Performance of Adaptive Unstructured Mesh Modelling in Idealized Advection Cases over Steep Terrains

1
Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
2
Center for Excellence in Regional Atmospheric Environment, Institute of Urban Environment, Chinese Academy of Sciences, Xiamen 361021, China
3
Department of Atmospheric Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
4
Applied Modelling and Computation Group, Department of Earth Science and Engineering, Imperial College London, Prince Consort Road, London SW7 2AZ, UK
5
Climate Service Center, Fischertwiete 1, 20095 Hamburg, Germany
6
Department of Scientific Computing, Florida State University, Tallahassee, FL 32306-4120, USA
*
Author to whom correspondence should be addressed.
Received: 31 August 2018 / Revised: 20 October 2018 / Accepted: 22 October 2018 / Published: 13 November 2018
(This article belongs to the Section Climatology and Meteorology)
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Abstract

Advection errors are common in basic terrain-following (TF) coordinates. Numerous methods, including the hybrid TF coordinate and smoothing vertical layers, have been proposed to reduce the advection errors. Advection errors are affected by the directions of velocity fields and the complexity of the terrain. In this study, an unstructured adaptive mesh together with the discontinuous Galerkin finite element method is employed to reduce advection errors over steep terrains. To test the capability of adaptive meshes, five two-dimensional (2D) idealized tests are conducted. Then, the results of adaptive meshes are compared with those of cut-cell and TF meshes. The results show that using adaptive meshes reduces the advection errors by one to two orders of magnitude compared to the cut-cell and TF meshes regardless of variations in velocity directions or terrain complexity. Furthermore, adaptive meshes can reduce the advection errors when the tracer moves tangentially along the terrain surface and allows the terrain to be represented without incurring in severe dispersion. Finally, the computational cost is analyzed. To achieve a given tagging criterion level, the adaptive mesh requires fewer nodes, smaller minimum mesh sizes, less runtime and lower proportion between the node numbers used for resolving the tracer and each wavelength than cut-cell and TF meshes, thus reducing the computational costs. View Full-Text
Keywords: advection errors; adaptive mesh; discontinuous Galerkin method; terrain-following coordinate; numerical experiments advection errors; adaptive mesh; discontinuous Galerkin method; terrain-following coordinate; numerical experiments
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Li, J.; Zheng, J.; Zhu, J.; Fang, F.; Pain, C.C.; Steppeler, J.; Navon, I.M.; Xiao, H. Performance of Adaptive Unstructured Mesh Modelling in Idealized Advection Cases over Steep Terrains. Atmosphere 2018, 9, 444.

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