2:00 PM - 2:15 PM
[MGI29-08] Development of a global atmospheric dynamical core using discontinuous Galerkin method: Introduction to a turbulent model and validation experiment
Keywords:Global atmospheric dynamical core based on high-order method, Large-eddy simulation, Idealized numerical experiment of planetary boundary layer turbulence
Introduction
Considering high-resolution atmospheric simulations with a grid spacing of O(10 m), Kawai & Tomita (2021, MWR) investigated a order of accuracy with the dynamical core necessary for atmospheric large-eddy simulations (LES) in conventional grid-point methods. Since our study suggested it is much higher than conventional second-order accuracy, we focus on the discontinuous Galerkin method (DGM), which has a simple strategy for high discretization accuracy and computational locality. To investigate the applicability to atmospheric simulations, we develop an atmospheric dynamics core based on DGM; Using it, we attempt to obtain deep understandings of its numerical properties. Kawai & Tomita (2023, MWR) (hereinafter, KT2023) discussed the issue of numerical accuracy for LES in the context of DGM, and indicated that the degree of the expansion polynomial (p) need be more than 4; The validity was confirmed by an idealized experiment of planetary boundary layer (PBL) turbulence using a regional LES model. After that, we attempted to introduce the moist process and the topography (reported in JpGU2023) in the DGM framework. Recently, for the future global moist LES, we are constructing a global dynamical core and introducing a turbulence model. In this presentation, we will show the formulation and preliminary results from validation experiments.
LES of atmospheric PBL turbulence using a global dynamical core based on DGM
[Calculation method] The governing equations of the dynamical process ar a fully compressible nonhydrostatic equations. To treat the spherical geometry, a cubed spherical coordinate based on an equiangular projection are used. The shallow-atmosphere approximation is basically applied, but calculations without this approximation are also possible in this model. The turbulent processes are represented by a Smagorinsky-Lilly type turbulence model (Brown et al., 1994). Although the derivation of eddy viscosity terms is rather complicated due to the non-orthogonal horizontal coordinates, it can be systematically done using a tensor analysis. For the spatial discretization, we apply a nodal DGM (e.g., Hesthaven and Warburton, 2007). The computational domain is divided using hexahedral elements, and (p+1)3 degrees of freedom are located within an element according to the required discretization accuracy. For the numerical fluxes, we use the Rusanov flux for the inviscid terms, while the central flux for the eddy viscous and diffusion terms. To ensure numerical stability, a 32nd-order modal filter is used to decay high-order expansion modes. As the temporal scheme, we use the fully explict Runge=Kutta method with fourth-order accuracy.
[Experimental setup] To validate our global LES model, we extend the setup of the idealized PBL turbulence experiment in Nishizawa et al. (2015) to the global domain. Due to the limitation of computational resources, the planetary radius is set to 3.4 km. Initially, we add the potential temperature disturbance to a rest and stable stratified atmosphere. We impose a heat flux of 200 W/m2 at the surface and perform the temporal integration during four hours. As in KT2023, to investigate the effect of p on the energy spectra, we consider the case of p=3, 4, 7 when the effective grid spacing is fixed to about 10 m.
[Simulation results] As shown in Fig.(a), we obtain open-cell convection cells with horizontal scales of a few km, similar to the plane regional model. Figure (b) shows the vertical structure of PBL and, for comparison, the results from KT2023 are represented using gray shade. The results with the shallow atmospheric approximation well reproduce that with the plane regional model. In Fig. (c), we show the kinetic energy spectra of three-dimensional winds at the interoir of PBL. When focusing on the wavelength range shorter than the eight grids in the terms of numerical criteria same as KT2023, we confirmed that the degree of expansion polynominal need to be more than 4 in the numerical experiments with the global domain. When the shallow atmospheric approximation is removed, the growth of PBL becomes slow and the variance of vertical wind and energy spectra tends to decrease (see green lines Figs. (b) and (c)); Such results are consistent to the effect of the volume expansion of the spherical shell with height. We consider that this experimental setting and calculation results will be useful as a benchmark test for a global dynamical core introducing a turbulence model.
Considering high-resolution atmospheric simulations with a grid spacing of O(10 m), Kawai & Tomita (2021, MWR) investigated a order of accuracy with the dynamical core necessary for atmospheric large-eddy simulations (LES) in conventional grid-point methods. Since our study suggested it is much higher than conventional second-order accuracy, we focus on the discontinuous Galerkin method (DGM), which has a simple strategy for high discretization accuracy and computational locality. To investigate the applicability to atmospheric simulations, we develop an atmospheric dynamics core based on DGM; Using it, we attempt to obtain deep understandings of its numerical properties. Kawai & Tomita (2023, MWR) (hereinafter, KT2023) discussed the issue of numerical accuracy for LES in the context of DGM, and indicated that the degree of the expansion polynomial (p) need be more than 4; The validity was confirmed by an idealized experiment of planetary boundary layer (PBL) turbulence using a regional LES model. After that, we attempted to introduce the moist process and the topography (reported in JpGU2023) in the DGM framework. Recently, for the future global moist LES, we are constructing a global dynamical core and introducing a turbulence model. In this presentation, we will show the formulation and preliminary results from validation experiments.
LES of atmospheric PBL turbulence using a global dynamical core based on DGM
[Calculation method] The governing equations of the dynamical process ar a fully compressible nonhydrostatic equations. To treat the spherical geometry, a cubed spherical coordinate based on an equiangular projection are used. The shallow-atmosphere approximation is basically applied, but calculations without this approximation are also possible in this model. The turbulent processes are represented by a Smagorinsky-Lilly type turbulence model (Brown et al., 1994). Although the derivation of eddy viscosity terms is rather complicated due to the non-orthogonal horizontal coordinates, it can be systematically done using a tensor analysis. For the spatial discretization, we apply a nodal DGM (e.g., Hesthaven and Warburton, 2007). The computational domain is divided using hexahedral elements, and (p+1)3 degrees of freedom are located within an element according to the required discretization accuracy. For the numerical fluxes, we use the Rusanov flux for the inviscid terms, while the central flux for the eddy viscous and diffusion terms. To ensure numerical stability, a 32nd-order modal filter is used to decay high-order expansion modes. As the temporal scheme, we use the fully explict Runge=Kutta method with fourth-order accuracy.
[Experimental setup] To validate our global LES model, we extend the setup of the idealized PBL turbulence experiment in Nishizawa et al. (2015) to the global domain. Due to the limitation of computational resources, the planetary radius is set to 3.4 km. Initially, we add the potential temperature disturbance to a rest and stable stratified atmosphere. We impose a heat flux of 200 W/m2 at the surface and perform the temporal integration during four hours. As in KT2023, to investigate the effect of p on the energy spectra, we consider the case of p=3, 4, 7 when the effective grid spacing is fixed to about 10 m.
[Simulation results] As shown in Fig.(a), we obtain open-cell convection cells with horizontal scales of a few km, similar to the plane regional model. Figure (b) shows the vertical structure of PBL and, for comparison, the results from KT2023 are represented using gray shade. The results with the shallow atmospheric approximation well reproduce that with the plane regional model. In Fig. (c), we show the kinetic energy spectra of three-dimensional winds at the interoir of PBL. When focusing on the wavelength range shorter than the eight grids in the terms of numerical criteria same as KT2023, we confirmed that the degree of expansion polynominal need to be more than 4 in the numerical experiments with the global domain. When the shallow atmospheric approximation is removed, the growth of PBL becomes slow and the variance of vertical wind and energy spectra tends to decrease (see green lines Figs. (b) and (c)); Such results are consistent to the effect of the volume expansion of the spherical shell with height. We consider that this experimental setting and calculation results will be useful as a benchmark test for a global dynamical core introducing a turbulence model.