Iterated upwind schemes for gas dynamics

A class of high-resolution schemes established in integration of anelastic equations is extended to fully compressible flows, and documented for unsteady (and steady) problems through a span of Mach numbers from zero to supersonic. The schemes stem from iterated upwind technology of the multidimensional positive definite advection transport algorithm (MPDATA). The derived algorithms employ standard and modified forms of the equations of gas dynamics for conservation of mass, momentum and either total or internal energy as well as potential temperature. Numerical examples from elementary wave-propagation, through computational aerodynamics benchmarks, to atmospheric small- and large-amplitude acoustics with intricate wave-flow interactions verify the approach for both structured and unstructured meshes, and demonstrate its flexibility and robustness

An edge-based unstructured mesh framework for atmospheric flows

This paper describes an unstructured/hybrid mesh framework providing a robust environment for multiscale atmospheric modeling. The framework builds on nonoscillatory forward-in-time MPDATA solvers using finite volume edge-based discretization, and admits meshes with arbitrarily shaped cells. The numerical formulation is equally applicable to global and limited area models. Theoretical considerations are supported with canonical examples of slab-symmetric, nonhydrostatic orographic problems in weakly and strongly stratified flow regimes and three-dimensional hydrostatic analogues of the strongly stratified case on a slowly and rapidly rotating sphere

An edge-based unstructured mesh discretisation in geospherical framework

An arbitrary finite-volume approach is developed for discretising partial differential equations governing fluid flows on the sphere. Unconventionally for unstructured-mesh global models, the governing equations are cast in the anholonomic geospherical framework established in computational meteorology. The resulting discretisation retains proven properties of the geospherical formulation, while it offers the flexibility of unstructured meshes in enabling irregular spatial resolution. The latter allows for a global enhancement of the spatial resolution away from the polar regions as well as for a local mesh refinement. A class of non-oscillatory forward-in-time edge-based solvers is developed and applied to numerical examples of three-dimensional hydrostatic flows, including shallow-water benchmarks, on a rotating sphere

A nonhydrostatic unstructured-mesh soundproof model for simulation of internal gravity waves

A semi-implicit edge-based unstructured-mesh model is developed that integrates nonhydrostatic soundproof equations, inclusive of anelastic and pseudo-incompressible systems of partial differential equations. The model builds on nonoscillatory forward-in-time MPDATA approach using finite-volume discretization and unstructured meshes with arbitrarily shaped cells. Implicit treatment of gravity waves benefits both accuracy and stability of the model. The unstructured-mesh solutions are compared to equivalent structured-grid results for intricate, multiscale internal-wave phenomenon of a non-Boussinesq amplification and breaking of deep stratospheric gravity waves. The departures of the anelastic and pseudo-incompressible results are quantified in reference to a recent asymptotic theory [Achatz et al. 2010, J. Fluid Mech., 663, 120-147)]

Simulation of all-scale atmospheric dynamics on unstructured meshes

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 pseudo-incompressible 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 weather-prediction models. Theoretical considerations are substantiated by calculations attesting to the versatility and efficacy of the NFTFV approach. Some prospective developments are also discussed

An unstructured-mesh atmospheric model for nonhydrostatic dynamics

A three-dimensional semi-implicit edge-based unstructured-mesh model is developed that integrates nonhydrostatic anelastic equations, suitable for simulation of small-to-mesoscale atmospheric flows. The model builds on nonoscillatory forward-in-time MPDATA approach using finite-volume discretization and admitting unstructured meshes with arbitrarily shaped cells. The numerical advancements are evaluated with canonical simulations of convective planetary boundary layer and strongly (stably) stratified orographic flows, epitomizing diverse aspects of highly nonlinear nonhydrostatic dynamics. The unstructured-mesh solutions are compared to equivalent results generated with an established structured-grid model and observation. © 2013 Elsevier Inc

3D MHD Modeling of the Impact of Subsurface Stratification on the Solar Dynamo

Various models of solar subsurface stratification are tested in the global EULAG-MHD solver to simulate diverse regimes of near-surface convective transport. Sub- and superadiabacity are altered at the surface of the model ($r > 0.95~R_{\odot}$) to either suppress or enhance convective flow speeds in an effort to investigate the impact of the near-surface layer on global dynamics. A major consequence of increasing surface convection rates appears to be a significant alteration of the distribution of angular momentum, especially below the tachocline where the rotational frequency predominantly increases at higher latitudes. These hydrodynamic changes correspond to large shifts in the development of the current helicity in this stable layer ($r<0.72R_{\odot}$), significantly altering its impact on the generation of poloidal and toroidal fields at the tachocline and below, acting as a major contributor towards transitions in the dynamo cycle. The enhanced near-surface flow speed manifests in a global shift of the toroidal field ($B_{\phi}$) in the butterfly diagram - from a North-South symmetric pattern to a staggered anti-symmetric emergence