A semi-implicit compressible model for atmospheric flows with seamless access to soundproof and hydrostatic dynamics

We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in conservation form while relying on Exner pressure for the pressure gradient term. It discretises the rotating compressible equations by evolving full variables rather than perturbations around a background state, and operates with time steps constrained by the advection speed only. Perturbation variables are only used as auxiliary quantities in the formulation of the elliptic problem. Borrowing ideas on forward-in-time differencing, the algorithm reframes the authors' previously proposed schemes into a sequence of implicit midpoint, advection, and implicit trapezoidal steps that allows for a time integration unconstrained by the internal gravity wave speed. Compared with existing approaches, results on a range of benchmarks of nonhydrostatic- and hydrostatic-scale dynamics are competitive. The test suite includes a new planetary-scale inertia-gravity wave test highlighting the properties of the scheme and its large time step capabilities. In the hydrostatic-scale cases the model is run in pseudo-incompressible and hydrostatic mode with simple switching within a uniform discretization framework. The differences with the compressible runs return expected relative magnitudes. By providing seamless access to soundproof and hydrostatic dynamics, the developments represent a necessary step towards an all-scale blended multimodel solver

A blended soundproof-to-compressible numerical model for small- to mesoscale atmospheric dynamic

A blended model for atmospheric flow simulations is introduced that enables seamless transition from semi-implicit fully compressible to pseudo-incompressible dynamics. The model equations are written in non-perturbational form and integrated using a wellbalanced second-order finite volume discretization. The scheme combines an explicit predictor for advection with elliptic corrections for the pressure field. Compressibility is implemented through a diagonal term in the elliptic equation. The compressible/soundproof transition is realized by weighting this term appropriately and it provides a mechanism for removing unwanted acoustic imbalances in compressible runs, with potential ramifications for data assimilation. As the thermodynamic pressure gradient is used in the momentum equation, the influence of perturbation pressure on buoyancy is included for thermodynamic consistency. This model is equivalent to Durran's original pseudo- incompressible model, which uses the Exner pressure. Numerical experiments demonstrate quadratic convergence and competitive solution quality for several benchmarks. With the thermodynamically consistent buoyancy correction the "p-\rho-formulation" of the sound-proof model closely reproduces the compressible results. The proposed approach offers a framework for model comparison largely free of biases due to different discretizations. With data assimilation applications in mind, the seamless compressible-sound-proof transition mechanism is also shown to enable the removal of acoustic imbalances in initial data for which balanced pressure distributions are unknown

GPUs Based Material Point Method for Compressible Flows

Particle-In-Cell (PIC) methods such as the Material Point Method (MPM) can be cast in formulations suitable to the requirements of data locality and fine-grained parallelism of modern hardware accelerators such as Graphics Processing Units (GPUs). While continuum mechanics simulations have already shown the capabilities of MPM on a wide range of phenomena, the use of the method in compressible gas dynamics is less frequent. This contribution aims to show the potential of a GPU-based MPM parallel implementation for compressible fluid dynamics, as well as to assess the reliability of this approach in reproducing supersonic gas flows against solid obstacles. The results in the paper represent a stepping stone towards a highly parallel, Multi-GPU, MPM-base solver for M ach > 1 Fluid-Structure Interaction problems

A mixed finite-element, finite-volume, semi-implicit discretisation for atmospheric dynamics: Cartesian geometry

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this recordTo meet the challenges posed by future generations of massively parallel supercomputers a reformulation of the dynamical core for the Met Office’s weather and climate model is presented. This new dynamical core uses explicit finite-volume type discretisations for the transport of scalar fields coupled with an iterated-implicit, mixed finite-element discretisation for all other terms. The target model aims to maintain the accuracy, stability and mimetic properties of the existing Met Office model independent of the chosen mesh while improving the conservation properties of the model. This paper details that proposed formulation and, as a first step towards complete testing, demonstrates its performance for a number of test cases in (the context of) a Cartesian domain. The new model is shown to produce similar results to both the existing semi-implicit semi-Lagrangian model used at the Met Office and other models in the literature on a range of bubble tests and orographically forced flows in two and three dimensions.Natural Environment Research Council (NERC

A mixed finite-element, finite-volume, semi-implicit discretisation for atmospheric dynamics: Spherical geometry

This is the author accepted manuscriptThe reformulation of the Met Office’s dynamical core for weather and climate prediction previously described by the authors is extended to spherical domains using a cubed- sphere mesh. This paper updates the semi-implicit mixed finite-element formulation to be suitable for spherical do- mains. In particular the finite-volume transport scheme is extended to take account of non-uniform, non-orthogonal meshes and uses an advective-then-flux formulation so that increment from the transport scheme is linear in the diver- gence. The resulting model is then applied to a standard set of dry dynamical core tests and compared to the exist- ing semi-implicit semi-Lagrangian dynamical core currently used in the Met Office’s operational model.Natural Environment Research Council (NERC)Natural Environment Research Council (NERC)Engineering and Physical Sciences Research Council (EPSRC)Engineering and Physical Sciences Research Council (EPSRC

The intrinsic shape of galaxy bulges

The knowledge of the intrinsic three-dimensional (3D) structure of galaxy components provides crucial information about the physical processes driving their formation and evolution. In this paper I discuss the main developments and results in the quest to better understand the 3D shape of galaxy bulges. I start by establishing the basic geometrical description of the problem. Our understanding of the intrinsic shape of elliptical galaxies and galaxy discs is then presented in a historical context, in order to place the role that the 3D structure of bulges play in the broader picture of galaxy evolution. Our current view on the 3D shape of the Milky Way bulge and future prospects in the field are also depicted.Comment: Invited Review to appear in "Galactic Bulges" Editors: Laurikainen E., Peletier R., Gadotti D. Springer Publishing. 24 pages, 7 figure

Intrinsic Shapes of Elliptical Galaxies

Tests for the intrinsic shape of the luminosity distribution in elliptical galaxies are discussed, with an emphasis on the uncertainties. Recent determinations of the ellipticity frequency function imply a paucity of nearly spherical galaxies, and may be inconsistent with the oblate hypothesis. Statistical tests based on the correlation of surface brightness, isophotal twisting, and minor axis rotation with ellipticity have so far not provided strong evidence in favor of the nearly oblate or nearly prolate hypothesis, but are at least qualitatively consistent with triaxiality. The possibility that the observed deviations of elliptical galaxy isophotes form ellipses are due to projection effects is evaluated. Dynamical instabilities may explain the absence of elliptical galaxies flatter than about E6, and my also play a role in the lack of nearly-spherical galaxies

A semi-implicit compressible model for atmospheric flows with seamless access to soundproof and hydrostatic dynamics

When written in conservation form for mass, momentum, and density-weighted potential temperature, and with Exner pressure in the momentum equation, the pseudoincompressible model and the hydrostatic model only differ from the full compressible equations by some additive terms. This structural proximity is transferred here to a numerical discretization providing seamless access to all three analytical models. The semi-implicit second-order scheme discretizes the rotating compressible equations by evolving full variables, and, optionally, with two auxiliary fields that facilitate the construction of an implicit pressure equation. Time steps are constrained by the advection speed only as a result. Borrowing ideas on forward-in-time differencing, the algorithm reframes the authors’ previously proposed schemes into a sequence of implicit midpoint step, advection step, and implicit trapezoidal step. Compared with existing approaches, results on benchmarks of nonhydrostatic- and hydrostatic-scale dynamics are competitive. The tests include a new planetary-scale gravity wave test that highlights the scheme’s ability to run with large time steps and to access multiple models. The advancement represents a sizeable step toward generalizing the authors’ acoustics-balanced initialization strategy to also cover the hydrostatic case in the framework of an all-scale blended multimodel solver