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Demonstration of a three-dimensional dynamically adaptive atmospheric dynamic framework for the simulation of mountain waves

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Abstract

In this paper, Fluidity-Atmosphere, representative of a three-dimensional (3D) non-hydrostatic Galerkin compressible atmospheric dynamic framework, is generated to resolve large-scale and small-scale phenomena simultaneously. This achievement is facilitated by the use of non-hydrostatic equations and the adoption of a flexible 3D dynamically adaptive mesh where the mesh is denser in areas with higher gradients of variable solutions and relatively sparser in the rest of the domain while maintaining promising accuracy and reducing computational resource requirements. The dynamic core is formulated based on anisotropic tetrahedral meshes in both the horizontal and vertical directions. The performance of the adaptive mesh techniques in Fluidity-Atmosphere is evaluated by simulating the formation and propagation of a non-hydrostatic mountain wave. The 2D anisotropic adaptive mesh shows that the numerical solution is in good agreement with the analytic solution. The variation in the horizontal and vertical resolutions has a strong impact on the smoothness of the results and maintains convergence even at high resolutions. When the simulation is extended to 3D, Fluidity-Atmosphere shows stable and symmetric results in the benchmark test cases. The flows over a bell-shaped mountain are resolved quite smoothly. For steep mountains, Fluidity-Atmosphere performs very well, which shows the potential of using 3D adaptive meshes in atmospheric modeling. Finally, as an alternative cut-cell mesh in Fluidity-Atmosphere, the anisotropic adaptive mesh coupled with the Galerkin method provides an alternative accurate representation of terrain-induced flow.

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Fig. 1
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reproduced from Gallus and Klemp (2000); b and c: the solutions of the CV1 method; d and e: the solutions of the CV2 method; f and g: the solutions of the CG method. b, d and f are for a fixed mesh, while c, e and g are for an adaptive mesh

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Data availability

The datasets generated during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

No author reported any potential conflicts of interest. This work is jointly supported by the National Natural Science Foundation of China (Grant No. 41905093), the China Scholarship Council (No. 201904910136) and Special Research Assistant Project of Chinese Academy of Sciences. Drs. Fang and Wu acknowledge the support of UK EPSRC grant: Managing Air for Green Inner Cities (MAGIC: Grant No. EP/N010221/1).

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Authors and Affiliations

  1. International Center for Climate and Environment Sciences, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100029, China

    J. Li & J. Zhu

  2. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WA, UK

    J. Li

  3. Applied Modelling and Computation Group, Department of Earth Science and Engineering, Imperial College London, London, SW7 2AZ, UK

    F. Fang & X. Wu

  4. Climate Service Center Germany (GERICS), Helmholtz-Zentrum Hereon, Fischertwiete 1, 20095, Hamburg, Germany

    J. Steppeler

  5. Department of Atmospheric Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    J. Zhu

  6. Key Laboratory of Atmospheric Sounding, Chengdu University of Information Technology, Chengdu, 610225, China

    Y. Cheng

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  1. J. Li
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Correspondence to J. Li.

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Li, J., Fang, F., Steppeler, J. et al. Demonstration of a three-dimensional dynamically adaptive atmospheric dynamic framework for the simulation of mountain waves. Meteorol Atmos Phys 133, 1627–1645 (2021). https://doi.org/10.1007/s00703-021-00828-8

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