Simulations of moist convection by a variational multiscale stabilized finite element method

Marras, Simone; Moragues, Margarida; Vázquez, Mariano; Jorba, Oriol; Houzeaux, Guillaume

doi:10.1016/j.jcp.2013.06.006

Cited by 22 publications

(18 citation statements)

References 43 publications

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“…In the last two decades, Finite element methods have become a popular discretisation approach for numerical weather prediction (NWP). The main focus has been on spectral elements or discontinuous Galerkin (DG) methods (Fournier et al, 2004;Thomas and Loft, 2005;Dennis et al, 2012;Kelly and Giraldo, 2012;Giraldo et al, 2013;Marras et al, 2013;Brdar et al, 2013;Bao et al, 2015;Marras et al, 2015). Another track of research, which we continue here, has been on compatible finite element methods (e.g.…”

Section: Introductionmentioning

confidence: 99%

Vertical slice modelling of nonlinear Eady waves using a compatible finite element method

Yamazaki

Shipton

Cullen

et al. 2017

Journal of Computational Physics

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A vertical slice model is developed for the Euler–Boussinesq equations with a constant temperature gradient in the direction normal to the slice (the Eady–Boussinesq model). The model is a solution of the full three-dimensional equations with no variation normal to the slice, which is an idealised problem used to study the formation and subsequent evolution of weather fronts. A compatible finite element method is used to discretise the governing equations. To extend the Charney–Phillips grid staggering in the compatible finite element framework, we use the same node locations for buoyancy as the vertical part of velocity and apply a transport scheme for a partially continuous finite element space. For the time discretisation, we solve the semi-implicit equations together with an explicit strong-stability-preserving Runge–Kutta scheme to all of the advection terms. The model reproduces several quasi-periodic lifecycles of fronts despite the presence of strong discontinuities. An asymptotic limit analysis based on the semi-geostrophic theory shows that the model solutions are converging to a solution in cross-front geostrophic balance. The results are consistent with the previous results using finite difference methods, indicating that the compatible finite element method is performing as well as finite difference methods for this test problem. We observe dissipation of kinetic energy of the cross-front velocity in the model due to the lack of resolution at the fronts, even though the energy loss is not likely to account for the large gap on the strength of the fronts between the model result and the semi-geostrophic limit solution

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Section: Introductionmentioning

confidence: 99%

Vertical slice modelling of nonlinear Eady waves using a compatible finite element method

Yamazaki

Shipton

Cullen

et al. 2017

Journal of Computational Physics

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“…In recent years, finite‐element methods have been developed and considered for numerical weather prediction and climate modelling (Fournier et al , 2004; Thomas and Loft, 2005; Dennis et al , 2011; Kelly and Giraldo, 2012; Brdar et al , 2013; Giraldo et al , 2013; Bao et al , 2015; Marras et al , 2015). The use of stabilized finite‐element methods in atmospheric simulations has been investigated by Marras et al (2013). Compatible finite‐element methods have been developed in order to extend conservation and stability properties from C‐grid staggered finite‐difference methods to the finite‐element setting (Cotter and Shipton, 2012; McRae and Cotter, 2014; Natale et al , 2016); these methods provide the context for this article.…”

Section: Introductionmentioning

confidence: 99%

Scale‐selective dissipation in energy‐conserving finite‐element schemes for two‐dimensional turbulence

Natale

Cotter

2017

Quart J Royal Meteoro Soc

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We analyze the multiscale properties of energy‐conserving upwind‐stabilized finite‐element discretizations of the two‐dimensional incompressible Euler equations. We focus our attention on two particular methods: the Lie derivative discretization introduced by Natale and Cotter and the Streamline Upwind/Petrov–Galerkin (SUPG) discretization of the vorticity advection equation. Such discretizations provide control on enstrophy by modelling different types of scale interactions. We quantify the performance of the schemes in reproducing the non‐local energy backscatter that characterizes two‐dimensional turbulent flows.

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“…Although the use of residual-based stabilizing schemes has been largely assessed for the finite element method during the past thirty years (e.g. Streamline-Upwind/Petrov-Galerkin (SUPG) [3], Galerkin/Least-Squares (GLS) [10], Variational Multiscale (VMS) [9,8,2,14]), hyper viscosity is still today the most classical approach in spite of its important drawbacks and mathematical inconsistency.…”

Section: Introductionmentioning

confidence: 99%

Physics-Based Stabilization of Spectral Elements for the 3D Euler Equations of Moist Atmospheric Convection

Marras

Müller

Giraldo

2015

Lecture Notes in Computational Science and Engineering

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In the context of stabilization of high order spectral elements, we introduce a dissipative scheme based on the solution of the compressible Euler equations that are regularized through the addition of a residual-based stress tensor. Because this stress tensor is proportional to the residual of the unperturbed equations, its e↵ect is close to none where the solution is su ciently smooth, whereas it increases elsewhere. This paper represents a first extension of the work by Nazarov and Ho↵man [Nazarov M. and Ho↵man J. (2013), Int. J. Numer. Methods Fluids, 71:339-357.] to high-order spectral elements in the context of low Mach number atmospheric dynamics. The simulations show that the method is reliable and robust for problems with important stratification and thermal processes such as the case of moist convection. The results are partially compared against a Smagorinsky solution. With this work we mean to make a step forward in the implementation of a stabilized, high order, spectral element large eddy simulation (LES) model within the Nonhydrostatic Unified Model of the Atmosphere, NUMA.

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Simulations of moist convection by a variational multiscale stabilized finite element method

Cited by 22 publications

References 43 publications

Vertical slice modelling of nonlinear Eady waves using a compatible finite element method

Vertical slice modelling of nonlinear Eady waves using a compatible finite element method

Scale‐selective dissipation in energy‐conserving finite‐element schemes for two‐dimensional turbulence

Physics-Based Stabilization of Spectral Elements for the 3D Euler Equations of Moist Atmospheric Convection

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