A non-column based, fully unstructured implementation of Kessler's microphysics with warm rain using continuous and discontinuous spectral elements

Tissaoui, Yassine; Marras, Simone; Quaini, Annalisa; Alves, Felipe A. V. De Braganca; Giraldo, Francix X.

doi:10.1002/essoar.10511896.1

Cited by 3 publications

(2 citation statements)

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“…Future work could also include the investigation of the methods here in the presence of complex physics parameterizations, such as earth system modeling, with geophysical fluids that are generally turbulent. Physics parameterizations, such as parameterizations of moist convection and cloud microphysics, are in use in a variety of forms in both idealized and comprehensive numerical simulations (Bendall et al., 2020; Dias & Pauluis, 2009; Khouider & Majda, 2005; McIntyre et al., 2020; Tissaoui et al., 2022; Wetzel et al., 2020; Zarzycki et al., 2015). Such parameterizations were beyond the scope of the present paper, where here the focus was given to the formulation and justification of the methodology for minimizing refinement artifacts, and focus was given here to testing other aspects such as different equations in different spatial dimensions and with different classes of numerical methods.…”

Section: Discussionmentioning

confidence: 99%

A Universal Predictor‐Corrector Approach for Minimizing Artifacts Due To Mesh Refinement

Du,

Stechmann

2023

J Adv Model Earth Syst

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With nested grids or related approaches, it is known that numerical artifacts can be generated at the interface of mesh refinement. Most of the existing methods of minimizing these artifacts are either problem‐dependent or numerical methods‐dependent. In this paper, we propose a universal predictor‐corrector approach to minimize these artifacts. By its construction, the approach can be applied to a wide class of models and numerical methods without modifying the existing methods but instead incorporating an additional step. The idea is to use an additional grid setup with a refinement interface at a different location, and then to correct the predicted state near the refinement interface by using information from the other grid setup. We give some analysis for our method in the setting of a one‐dimensional advection equation, showing that the key to the success of the method depends on an optimized way of choosing the weight functions, which determine the strength of the corrector at a certain location. Furthermore, the method is also tested in more general settings by numerical experiments, including shallow water equations, multi‐dimensional problems, and a variety of underlying numerical methods including finite difference/finite volume and spectral element. Numerical tests suggest the effectiveness of the method on reducing numerical artifacts due to mesh refinement.

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Section: Discussionmentioning

confidence: 99%

A Universal Predictor‐Corrector Approach for Minimizing Artifacts Due To Mesh Refinement

Du,

Stechmann

2023

J Adv Model Earth Syst

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“…Each discretization comes with its advantages and disadvantages. We choose a FV method for the following reasons: i) it enforces conservation of quantities (e.g., mass, momentum, energy) at the discrete level, i.e., these quantities remain conserved also at a local scale; ii) it can take full advantage of arbitrary meshes to approximate complex geometries (e.g., orography [48]); iii) many fluid dynamics codes are based on FV methods, hence a FV-based code can appeal to a larger workforce.…”

Section: Introductionmentioning

confidence: 99%

A novel Large Eddy Simulation model for the Quasi-Geostrophic equations in a Finite Volume setting

Girfoglio

Quaini

Rozza

2023

Journal of Computational and Applied Mathematics

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A long short-term memory neural network-based error estimator for three-dimensional dynamically adaptive mesh generation

Wu,

Gan,

et al. 2023

Physics of Fluids

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Adaptive meshes are pivotal in numerical modeling and simulation, offering a means to efficiently, precisely, and flexibly represent intricate physical phenomena, particularly when grappling with their intricacies and varying scales. However, the transition from two dimensions (2D) to three dimensions (3D) poses a substantial challenge, as the computational demands of dynamically adaptive mesh techniques increase exponentially. Addressing this challenge effectively, we turn to the cutting-edge realm of artificial intelligence and neural networks. In our study, we harness the innovative power of a long short-term memory (LSTM) neural network as an error estimator for adapting unstructured meshes in both 2D and 3D scenarios. This LSTM network predicts the evolution of the adaptive grid based on specified variables, presenting itself as an artificial intelligence-driven architecture to optimize the adaptive criterion for the target variable. This is achieved by establishing a direct correspondence between the Riemann metric and these variables. To demonstrate the practical applicability of our approach, we seamlessly integrate the LSTM error estimator into the 3D adaptive atmospheric model Fluidity-Atmosphere (Fluidity-Atmos), thereby enabling real-time mesh adaptation during numerical simulations. We assess the effectiveness of this method in terms of simulation precision and computational efficiency through a series of experiments in both 2D and 3D settings. Our results not only reveal that the mesh patterns generated by the LSTM error estimator within Fluidity-Atmos closely resemble those produced by traditional error estimators but also underscore its superior performance in enhancing simulation accuracy. Notably, as the number of nodes increases, the LSTM mesh generator substantially reduces CPU time requirements by up to 50% in 3D cases compared to the conventional mesh generator within Fluidity-Atmos, highlighting its remarkable computational efficiency.

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A non-column based, fully unstructured implementation of Kessler's microphysics with warm rain using continuous and discontinuous spectral elements

Cited by 3 publications

References 0 publications

A Universal Predictor‐Corrector Approach for Minimizing Artifacts Due To Mesh Refinement

A Universal Predictor‐Corrector Approach for Minimizing Artifacts Due To Mesh Refinement

A novel Large Eddy Simulation model for the Quasi-Geostrophic equations in a Finite Volume setting

A long short-term memory neural network-based error estimator for three-dimensional dynamically adaptive mesh generation

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