A class of finite-volume models for atmospheric flows across scales

The paper examines recent advancements in the class of Nonoscillatory Forward-in-Time (NFT) schemes that exploit the implicit LES (ILES) properties of Multidimensional Positive Definite Advection Transport Algorithm (MPDATA). The reported developments address both global and limited area models spanning a range of atmospheric flows, from the hydrostatic regime at planetary scale, down to mesoscale and microscale where flows are inherently nonhydrostatic. All models operate on fully unstructured (and hybrid) meshes and utilize a median dual mesh finite volume discretisation. High performance computations for global flows employ a bespoke hybrid MPI-OpenMP approach and utilise the ATLAS library. Simulations across scales—from a global baroclinic instability epitomising evolution of weather systems down to stratified orographic flows rich in turbulent phenomena due to gravity-wave breaking in dispersive media, verify the computational advancements and demonstrate the efficacy of ILES both in regularizing large scale flows at the scale of the mesh resolution and taking a role of a subgrid-scale turbulence model in simulation of turbulent flows in the LES regime

Non-oscillatory forward-in-time integrators for viscous incompressible flows past a sphere

A non-oscillatory forward-in-time (NFT) integrator is developed to provide solutions of the Navier-Stokes equations for incompressible flows. Simulations of flows past a sphere are chosen as a benchmark representative of a class of engineering flows past obstacles. The methodology is further extended to moderate Reynolds number, stably stratified flows under gravity, for Froude numbers that typify the characteristic regimes of natural flows past distinct isolated features of topography in weather and climate models. The key elements of the proposed method consist of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) and a robust non-symmetric Krylov-subspace elliptic solver. The solutions employ a finite volume spatial discretisation on unstructured and hybrid meshes and benefit from a collocated arrangement of all flow variables while being inherently stable. The development includes the implementation of viscous terms with the detachededdy simulation (DES) approach employed for turbulent flows. Results demonstrate that the proposed methodology enables direct comparisons of the numerical solutions with corresponding laboratory studies of viscous and stratified flows while illustrating accuracy, robustness and flexibility of the NFT schemes. The presented simulations also offer a better insight into stably stratified flows past a sphere

DCMIP2016: a review of non-hydrostatic dynamical core design and intercomparison of participating models

Atmospheric dynamical cores are a fundamental component of global atmospheric modeling systems and are responsible for capturing the dynamical behavior of the Earth's atmosphere via numerical integration of the Navier-Stokes equations. These systems have existed in one form or another for over half of a century, with the earliest discretizations having now evolved into a complex ecosystem of algorithms and computational strategies. In essence, no two dynamical cores are alike, and their individual successes suggest that no perfect model exists. To better understand modern dynamical cores, this paper aims to provide a comprehensive review of 11 non-hydrostatic dynamical cores, drawn from modeling centers and groups that participated in the 2016 Dynamical Core Model Intercomparison Project (DCMIP) workshop and summer school. This review includes a choice of model grid, variable placement, vertical coordinate, prognostic equations, temporal discretization, and the diffusion, stabilization, filters, and fixers employed by each syste

FVM 1.0: a nonhydrostatic finite-volume dynamical core for the IFS

We present a nonhydrostatic finite-volume global atmospheric model formulation for numerical weather prediction with the Integrated Forecasting System (IFS) at ECMWF and compare it to the established operational spectral-transform formulation. The novel Finite-Volume Module of the IFS (henceforth IFS-FVM) integrates the fully compressible equations using semi-implicit time stepping and non-oscillatory forward-in-time (NFT) Eulerian advection, whereas the spectral-transform IFS solves the hydrostatic primitive equations (optionally the fully compressible equations) using a semi-implicit semi-Lagrangian scheme. The IFS-FVM complements the spectral-transform counterpart by means of the finite-volume discretization with a local low-volume communication footprint, fully conservative and monotone advective transport, all-scale deep-atmosphere fully compressible equations in a generalized height-based vertical coordinate, and flexible horizontal meshes. Nevertheless, both the finite-volume and spectral-transform formulations can share the same quasi-uniform horizontal grid with co-located arrangement of variables, geospherical longitude–latitude coordinates, and physics parameterizations, thereby facilitating their comparison, coexistence, and combination in the IFS. We highlight the advanced semi-implicit NFT finite-volume integration of the fully compressible equations of IFS-FVM considering comprehensive moist-precipitating dynamics with coupling to the IFS cloud parameterization by means of a generic interface. These developments – including a new horizontal–vertical split NFT MPDATA advective transport scheme, variable time stepping, effective preconditioning of the elliptic Helmholtz solver in the semi-implicit scheme, and a computationally efficient implementation of the median-dual finite-volume approach – provide a basis for the efficacy of IFS-FVM and its application in global numerical weather prediction. Here, numerical experiments focus on relevant dry and moist-precipitating baroclinic instability at various resolutions. We show that the presented semi-implicit NFT finite-volume integration scheme on co-located meshes of IFS-FVM can provide highly competitive solution quality and computational performance to the proven semi-implicit semi-Lagrangian integration scheme of the spectral-transform IFS.</p