Some conservation issues for the dynamical cores of NWP and climate models

Thuburn, John

doi:10.1016/j.jcp.2006.08.016

Cited by 95 publications

(72 citation statements)

References 74 publications

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“…The mixed Eulerian semi-implicit and SISL discretization of equations (1),(2) respectively, based on the TR-BDF2 scheme, is obtained by performing the two stages in TR-BDF2, after semi-Lagrangian reinterpretation of the intermediate values in equation (2): this is achieved through the introduction of proper discrete semi-Lagrangian evolution operators, [16,17], in the following called E. If G = G(x, t) denotes a generic function of space and time, then the expression [E(t n , ∆t)G](x) refers to a numerical approximation of G(x D , t n ) where x D is the position at time t n of the fluid parcel reaching location x at time t n+1 and, according to standard terminology, it is called the departure point associated with the arrival point x. For a detailed review of the definition of such operators on vector fields on the sphere, see section 4 of [1].…”

Section: A Tr-bdf2 Time Integration Approach For the Shallow Water Eqmentioning

confidence: 99%

A mass conservative TR-BDF2 semi-implicit semi-Lagrangian DG discretization of the shallow water equations on general structured meshes of quadrilaterals

Tumolo

2016

Communications in Applied and Industrial Mathematics

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As an extension of a previous work considering a fully advective formulation on Cartesian meshes, a mass conservative discretization approach is presented here for the shallow water equations, based on discontinuous finite elements on general structured meshes of quadrilaterals. A semi-implicit time integration is performed by employing the TR-BDF2 scheme and is combined with the semi-Lagrangian technique for the momentum equation only. Indeed, in order to simplify the derivation of the discrete linear Helmoltz equation to be solved at each time-step, a non-conservative formulation of the momentum equation is employed. The Eulerian flux form is considered instead for the continuity equation in order to ensure mass conservation. Numerical results show that on distorted meshes and for relatively high polynomial degrees, the proposed numerical method fully conserves mass and presents a higher level of accuracy than a standard off-centered Crank Nicolson approach. This is achieved without any significant imprinting of the mesh distortion on the solution.

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Section: A Tr-bdf2 Time Integration Approach For the Shallow Water Eqmentioning

confidence: 99%

A mass conservative TR-BDF2 semi-implicit semi-Lagrangian DG discretization of the shallow water equations on general structured meshes of quadrilaterals

Tumolo

2016

Communications in Applied and Industrial Mathematics

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“…multiphysics simulations or fluid-structure interaction (FSI) problems, where specific meshes are considered for each sub-problem, see [1,2]. The preservation of the conservation property during the interpolation stage is also crucial for the accuracy in long time scale simulations, see [3,4]. It is an essential component of Arbitrary Lagrangian-Eulerian (ALE) methods as well.…”

Section: Introductionmentioning

confidence: 99%

A parallel matrix-free conservative solution interpolation on unstructured tetrahedral meshes

Alauzet

2016

Computer Methods in Applied Mechanics and Engineering

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This document presents an interpolation operator on unstructured tetrahedral meshes that satisfies the properties of mass conservation, P 1 -exactness (order 2) and maximum principle. Interpolation operators are important for many applications in scientific computing. For instance, in the context of anisotropic mesh adaptation for time-dependent problems, the interpolation stage becomes crucial as the error due to solution transfer accumulates throughout the simulation. This error can eventually spoil the overall solution accuracy. When dealing with conservation laws in CFD, solution accuracy requires enforcement of mass preservation throughout the computation, in particular in long time scale computations. In the proposed approach, the conservation property is achieved by local mesh intersection and quadrature formulae. Derivatives reconstruction is used to obtain a second order method. Algorithmically, our goal is to design a method which is robust and efficient. The robustness is mandatory to obtain a reliable method on real-life applications and to apply the operator to highly anisotropic meshes. The efficiency is achieved by designing a matrix-free operator which is highly parallel. A multi-thread parallelization is given in this work. Several numerical examples are presented to illustrate the efficiency of the proposed approach.Key-words: Solution interpolation, matrix-free conservative interpolation, parallel interpolation, unstructured mesh, mesh adaptation, conservation laws * INRIA, Équipe-projet Gamma3, Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France. email: frederic.alauzet@inria.fr A parallel matrix-free conservative solution interpolation on unstructured tetrahedral meshes Résumé : Ce document présente un opérateur d'interpolation sur des maillages tétraé-driques non-structurés qui satisfait les propriétés de conservation de la masse, P 1 -exactitude (ordre 2) et principe du maximum.Mots-clés : Interpolation de solution, interpolation conservative sans matrice, interpolation parallèle, maillage non-structuré, adaptation de maillage, adaptation de maillage, loi de conservation A parallel matrix-free conservative solution interpolation on tetrahedral meshes 3

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“…A lot of research has been spent in designing dynamical cores that conserve mass and energy (Thuburn, 2008). Common strategies include a careful selection of the prognostic variables (Ooyama, 1990(Ooyama, , 2001Klemp et al, 2007), the formulation of the equations in flux form (Satoh, 2003), or taking advantage of properties of the Hamiltonian character of the atmospheric equations (Salmon, 2004;Gassmann and Herzog, 2008;Zängl et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

Generalization and application of the flux-conservative thermodynamic equations in the AROME model of the ALADIN system

Degrauwe¹,

Seity²,

Bouyssel³

et al. 2016

Geosci. Model Dev.

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Abstract. General yet compact equations are presented to express the thermodynamic impact of physical parameterizations in a NWP or climate model. By expressing the equations in a flux-conservative formulation, the conservation of mass and energy by the physics parameterizations is a builtin feature of the system. Moreover, the centralization of all thermodynamic calculations guarantees a consistent thermodynamical treatment of the different processes. The generality of this physics-dynamics interface is illustrated by applying it in the AROME NWP model. The physics-dynamics interface of this model currently makes some approximations, which typically consist of neglecting some terms in the total energy budget, such as the transport of heat by falling precipitation, or the effect of diffusive moisture transport. Although these terms are usually quite small, omitting them from the energy budget breaks the constraint of energy conservation. The presented set of equations provides the opportunity to get rid of these approximations, in order to arrive at a consistent and energy-conservative model. A verification in an operational setting shows that the impact on monthlyaveraged, domain-wide meteorological scores is quite neutral. However, under specific circumstances, the supposedly small terms may turn out not to be entirely negligible. A detailed study of a case with heavy precipitation shows that the heat transport by precipitation contributes to the formation of a region of relatively cold air near the surface, the so-called cold pool. Given the importance of this cold pool mechanism in the life cycle of convective events, it is advisable not to neglect phenomena that may enhance it.

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Some conservation issues for the dynamical cores of NWP and climate models

Cited by 95 publications

References 74 publications

A mass conservative TR-BDF2 semi-implicit semi-Lagrangian DG discretization of the shallow water equations on general structured meshes of quadrilaterals

A mass conservative TR-BDF2 semi-implicit semi-Lagrangian DG discretization of the shallow water equations on general structured meshes of quadrilaterals

A parallel matrix-free conservative solution interpolation on unstructured tetrahedral meshes

Generalization and application of the flux-conservative thermodynamic equations in the AROME model of the ALADIN system

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