Numerical characterisation of stably stratified flows past spheres

A numerical study of stably stratified flows past spheres at moderate Reynolds numbers is presented. The resolved flows can adequately describe a wide class of geophysical, environmental, and engineering flows characterised by the density stratification of the terrestrial atmosphere and oceanic thermocline. The range of physical phenomena developing when stratified flows impact single and multiple spheres constitute a convenient benchmark for complex geometry applications, e.g. mountains, islands, wind turbines, and buildings. Solutions of Navier-Stokes equations, in the incompressible Boussinesq limit, are obtained by applying a semi-implicit finite volume (FV) non-oscillatory forward-in-time (NFT) integration scheme enhanced by MPI parallelization. The developed model is applied for a systematic investigation of stratified flow patterns arising for a range of Froude numbers Fr ∈ [0.1,∞] at Reynolds numbers Re = 200 and Re = 300, for which the neutrally stratified flows induces distinctly different near-wake features

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

The ESCAPE project: Energy-efficient Scalable Algorithms for Weather Prediction at Exascale

Abstract. In the simulation of complex multi-scale flows arising in weather and climate modelling, one of the biggest challenges is to satisfy strict service requirements in terms of time to solution and to satisfy budgetary constraints in terms of energy to solution, without compromising the accuracy and stability of the application. These simulations require algorithms that minimise the energy footprint along with the time required to produce a solution, maintain the physically required level of accuracy, are numerically stable, and are resilient in case of hardware failure. The European Centre for Medium-Range Weather Forecasts (ECMWF) led the ESCAPE (Energy-efficient Scalable Algorithms for Weather Prediction at Exascale) project, funded by Horizon 2020 (H2020) under the FET-HPC (Future and Emerging Technologies in High Performance Computing) initiative. The goal of ESCAPE was to develop a sustainable strategy to evolve weather and climate prediction models to next-generation computing technologies. The project partners incorporate the expertise of leading European regional forecasting consortia, university research, experienced high-performance computing centres, and hardware vendors. This paper presents an overview of the ESCAPE strategy: (i) identify domain-specific key algorithmic motifs in weather prediction and climate models (which we term Weather & Climate Dwarfs), (ii) categorise them in terms of computational and communication patterns while (iii) adapting them to different hardware architectures with alternative programming models, (iv) analyse the challenges in optimising, and (v) find alternative algorithms for the same scheme. The participating weather prediction models are the following: IFS (Integrated Forecasting System); ALARO, a combination of AROME (Application de la Recherche à l'Opérationnel à Meso-Echelle) and ALADIN (Aire Limitée Adaptation Dynamique Développement International); and COSMO–EULAG, a combination of COSMO (Consortium for Small-scale Modeling) and EULAG (Eulerian and semi-Lagrangian fluid solver). For many of the weather and climate dwarfs ESCAPE provides prototype implementations on different hardware architectures (mainly Intel Skylake CPUs, NVIDIA GPUs, Intel Xeon Phi, Optalysys optical processor) with different programming models. The spectral transform dwarf represents a detailed example of the co-design cycle of an ESCAPE dwarf. The dwarf concept has proven to be extremely useful for the rapid prototyping of alternative algorithms and their interaction with hardware; e.g. the use of a domain-specific language (DSL). Manual adaptations have led to substantial accelerations of key algorithms in numerical weather prediction (NWP) but are not a general recipe for the performance portability of complex NWP models. Existing DSLs are found to require further evolution but are promising tools for achieving the latter. Measurements of energy and time to solution suggest that a future focus needs to be on exploiting the simultaneous use of all available resources in hybrid CPU–GPU arrangements

A multidimensional positive definite remapping algorithm for unstructured meshes

We report on developments of a second-order, conservative, sign-preserving remapping scheme for Arbitrary Lagrangian-Eulerian (ALE) methods operating on unstructured meshes. The remapping uses concepts of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA).The non-oscillatory infinite gauge option of MPDATA remapping is derived in volume coordinates and is based upon a general and compact edge-based data structure, developed for use within an arbitrary finite volume framework. A Flux Corrected Transport style of limiting ensures monotonicity preservation, while the construction of volume coordinates utilises median dual polygonal finite volume cells.Theoretical developments are supported by numerical testing involving idealised cases with prescribed mesh movement for advection of scalars. The numerical investigations include an asymptotic mesh convergence study and comparisons with both MPDATA and Van Leer MUSCL remapping schemes operating on Cartesian meshes. The results demonstrate that the proposed scheme is suitable for providing accurate ALE remapping for unstructured meshes.</div

Simulations of stably stratified flow past two spheres at Re = 300

Flows past two spheres immersed in a horizontally moving, linearly-stratified fluid are investigated at a moderate Reynolds number of 300. Characterisation of flow patterns considers representative geometrical configurations defined by varying both the distance between the spheres and their relative orientation to the free stream direction. Simulations are performed on unstructured meshes chosen to accurately resolve the dynamics of fluids in regions close to the spheres for Froude numbers Fr ∈ [0.25,∞]. Results illustrate the evolution of boundary layers, separation, and the wakes interaction under the influence of a gravity induced buoyancy force. Computations utilise a limited area, nonhydrostatic model employing Non-oscillatory Forward-in-Time (NFT) integration based on the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA). The model solves the Navier-Stokes equations in the incompressible Boussinnesq limit, suitable for describing a range of mesoscale atmospheric flows. Results demonstrate that stratification progressively dominates the flow patterns as the Froude number decreases and that the interactions between the two spheres’ wakes bear a resemblance to atmospheric flows past hills

Stratified flow past a sphere at moderate Reynolds numbers

A numerical study of stably stratified flows past spheres at Reynolds numbers Re= 200 and Re= 300 is reported. In these flow regimes, a neutrally stratified laminar flow induces distinctly different near-wake features. However, the flow behaviour changes significantly as the stratification increases and suppresses the scale of vertical displacements of fluid parcels. Computations for a range of Froude numbers Fr∈[0.1,∞] show that as Froude number decreases, the flow patterns for both Reynolds numbers become similar. The representative simulations of the lee-wave instability at Fr= 0.625 and the two-dimensional vortex shedding at Fr= 0.25 regimes are illustrated for flows past single and tandem spheres, thereby providing further insight into the dynamics of stratified flows past bluff bodies. In particular,the reported study examines the relative influence of viscosity and stratification on the dividing streamline elevation, wake structure and flow separation. The solutions of the Navier-Stokes equations in the incompressible Boussinesq limit are obtained on unstructured meshes suitable for simulations involving multiple bodies. Computations are accomplished using the finite volume, non-oscillatory forward-in-time (NFT) Multidimensional Positive Definite Transport Algorithm (MPDATA) based solver. The impact and validity of the numerical approximations, especially for the cases exhibiting strong stratification, are also discussed. Qualitative and quantitative comparisons with available laboratory experiments and prior numerical studies confirm the validity of the numerical approach.</div

Resilience and fault tolerance in high-performance computing for numerical weather and climate prediction

Progress in numerical weather and climate prediction accuracy greatly depends on the growth of the available computing power. As the number of cores in top computing facilities pushes into the millions, increased average frequency of hardware and software failures forces users to review their algorithms and systems in order to protect simulations from breakdown. This report surveys hardware, application-level and algorithm-level resilience approaches of particular relevance to time-critical numerical weather and climate prediction systems. A selection of applicable existing strategies is analysed, featuring interpolation-restart and compressed checkpointing for the numerical schemes, in-memory checkpointing, user-level failure mitigation and backup-based methods for the systems. Numerical examples showcase the performance of the techniques in addressing faults, with particular emphasis on iterative solvers for linear systems, a staple of atmospheric fluid flow solvers. The potential impact of these strategies is discussed in relation to current development of numerical weather prediction algorithms and systems towards the exascale. Trade-offs between performance, efficiency and effectiveness of resiliency strategies are analysed and some recommendations outlined for future developments