Performance of Adaptive Unstructured Mesh Modelling in Idealized Advection Cases over Steep Terrains
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-11-01
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| Series: | Atmosphere |
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| Online Access: | https://www.mdpi.com/2073-4433/9/11/444 |
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| author | Jinxi Li Jie Zheng Jiang Zhu Fangxin Fang Christopher. C. Pain Jürgen Steppeler Ionel M. Navon Hang Xiao |
| author_facet | Jinxi Li Jie Zheng Jiang Zhu Fangxin Fang Christopher. C. Pain Jürgen Steppeler Ionel M. Navon Hang Xiao |
| author_sort | Jinxi Li |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T09:01:52Z |
| format | Article |
| id | doaj.art-22a87301d9254d5bb954ad34b72a29bd |
| institution | Directory Open Access Journal |
| issn | 2073-4433 |
| language | English |
| last_indexed | 2024-04-13T09:01:52Z |
| publishDate | 2018-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Atmosphere |
| spelling | doaj.art-22a87301d9254d5bb954ad34b72a29bd2022-12-22T02:53:05ZengMDPI AGAtmosphere2073-44332018-11-0191144410.3390/atmos9110444atmos9110444Performance of Adaptive Unstructured Mesh Modelling in Idealized Advection Cases over Steep TerrainsJinxi Li0Jie Zheng1Jiang Zhu2Fangxin Fang3Christopher. C. Pain4Jürgen Steppeler5Ionel M. Navon6Hang Xiao7Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, ChinaCenter for Excellence in Regional Atmospheric Environment, Institute of Urban Environment, Chinese Academy of Sciences, Xiamen 361021, ChinaInstitute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, ChinaApplied Modelling and Computation Group, Department of Earth Science and Engineering, Imperial College London, Prince Consort Road, London SW7 2AZ, UKApplied Modelling and Computation Group, Department of Earth Science and Engineering, Imperial College London, Prince Consort Road, London SW7 2AZ, UKClimate Service Center, Fischertwiete 1, 20095 Hamburg, GermanyDepartment of Scientific Computing, Florida State University, Tallahassee, FL 32306-4120, USACenter for Excellence in Regional Atmospheric Environment, Institute of Urban Environment, Chinese Academy of Sciences, Xiamen 361021, ChinaAdvection 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.https://www.mdpi.com/2073-4433/9/11/444advection errorsadaptive meshdiscontinuous Galerkin methodterrain-following coordinatenumerical experiments |
| spellingShingle | Jinxi Li Jie Zheng Jiang Zhu Fangxin Fang Christopher. C. Pain Jürgen Steppeler Ionel M. Navon Hang Xiao Performance of Adaptive Unstructured Mesh Modelling in Idealized Advection Cases over Steep Terrains Atmosphere advection errors adaptive mesh discontinuous Galerkin method terrain-following coordinate numerical experiments |
| title | Performance of Adaptive Unstructured Mesh Modelling in Idealized Advection Cases over Steep Terrains |
| title_full | Performance of Adaptive Unstructured Mesh Modelling in Idealized Advection Cases over Steep Terrains |
| title_fullStr | Performance of Adaptive Unstructured Mesh Modelling in Idealized Advection Cases over Steep Terrains |
| title_full_unstemmed | Performance of Adaptive Unstructured Mesh Modelling in Idealized Advection Cases over Steep Terrains |
| title_short | Performance of Adaptive Unstructured Mesh Modelling in Idealized Advection Cases over Steep Terrains |
| title_sort | performance of adaptive unstructured mesh modelling in idealized advection cases over steep terrains |
| topic | advection errors adaptive mesh discontinuous Galerkin method terrain-following coordinate numerical experiments |
| url | https://www.mdpi.com/2073-4433/9/11/444 |
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