Monge–Ampére based moving mesh methods for numerical weather prediction, with applications to the Eady problem

Budd, C. J.; Cullen, Michael J.; Walsh, Emily J.

doi:10.1016/j.jcp.2012.11.014

Cited by 48 publications

(63 citation statements)

References 27 publications

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“…Because unstructured-meshes are essentially free of topological constraints, they offer flexibility unmatched by the established techniques operating on regular Cartesian grids. Admittedly, such grids enable computationally efficient static and dynamic mesh adaptivity via continuous mappings [109,171,66,13,14], yet their rigid connectivity imposes stringent constraints on the adapted grids. The unavailability of regular equidistant discretisation on a spherical surface is an apparent evidence of these constraints and a venerable force for advancement of flexible meshing in atmospheric models.…”

Section: Historical Backgroundmentioning

confidence: 99%

Simulation of all-scale atmospheric dynamics on unstructured meshes

Smolarkiewicz

Szmelter

Xiao

2016

Journal of Computational Physics

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The advance of massively parallel computing in the nineteen nineties and beyond encouraged finer grid intervals in numerical weather-prediction models. This has improved resolution of weather systems and enhanced the accuracy of forecasts, while setting the trend for development of unified all-scale atmospheric models. This paper first outlines the historical background to a wide range of numerical methods advanced in the process. Next, the trend is illustrated with a technical review of a versatile nonoscillatory forward-in-time finite-volume (NFTFV) approach, proven effective in simulations of atmospheric flows from small-scale dynamics to global circulations and climate. The outlined approach exploits the synergy of two specific ingredients: the MPDATA methods for the simulation of fluid flows based on the sign-preserving properties of upstream differencing; and the flexible finite-volume median-dual unstructured-mesh discretisation of the spatial differential operators comprising PDEs of atmospheric dynamics. The paper consolidates the concepts leading to a family of generalised nonhydrostatic NFTFV flow solvers that include soundproof PDEs of incompressible Boussinesq, anelastic and pseudoincompressible systems, common in large-eddy simulation of small-and meso-scale dynamics, as well as all-scale compressible Euler equations. Such a framework naturally extends predictive skills of large-eddy simulation to the global atmosphere, providing a bottom-up alternative to the reverse approach pursued in the weatherprediction models. Theoretical considerations are substantiated by calculations attesting to the versatility and efficacy of the NFTFV approach. Some prospective developments are also discussed.

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Section: Historical Backgroundmentioning

confidence: 99%

Simulation of all-scale atmospheric dynamics on unstructured meshes

Smolarkiewicz

Szmelter

Xiao

2016

Journal of Computational Physics

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“…In this implementation K = 2 and the second order solution for auxiliary variable ψ is taken from the MPDATA procedure (12). 3 The corresponding truncation error fluxes are used to construct an error indicator as…”

Section: Mpdata Based Error Indicatorsmentioning

confidence: 99%

“…Even though the latter enable computationally efficient static and dynamic mesh adaptivity via continuous mappings [31,56,21,3,4], their rigid connectivity imposes stringent constraints on adapted grids. Flexible unstructured meshes relax the constraints and offer alternative means for optimising variable resolution required for improved representation of complex physical processes in atmospheric flows.…”

Section: Introductionmentioning

confidence: 99%

An unstructured-mesh atmospheric model for nonhydrostatic dynamics: Towards optimal mesh resolution

Szmelter

Zhang

Smolarkiewicz

2015

Journal of Computational Physics

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The paper advances the limited-area anelastic model [Smolarkiewicz et al., J. Comput. Phys., 254 (2013) 184] for investigation of nonhydrostatic dynamics in mesoscale atmospheric flows. New developments include the extension to a tetrahedral-based median-dual option for unstructured meshes and a static mesh adaptivity technique using an error indicator based on inherent properties of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA). The model employs semi-implicit nonoscillatory forward-in-time integrators for soundproof PDEs, built on MPDATA and a robust non-symmetric Krylov-subspace elliptic solver. Finitevolume spatial discretisation adopts an edge-based data structure. Simulations of stratified orographic flows and the associated gravity-wave phenomena in media with uniform and variable dispersive properties, verify the advancement and demonstrate the potential of heterogeneous anisotropic discretisation with large variation in spatial resolution for study of complex stratified flows that can be computationally unattainable with regular grids.

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“…h-adaptive schemes, on the other hand, are usually implemented using the finite element method. Although r-adaptive methods are a recent development and have not been used as frequently as h or hp-refinements, they have been successfully applied in various applications, such as computational fluid mechanics [39], convective heat transfer [40] and meteorological [41,42] problems. The r-refinement techniques also form the basis of general purpose publicly available solvers for one dimensional parabolic PDE systems, for example, MOVCOL [43] and TOMS731 [32].…”

Section: Introductionmentioning

confidence: 99%