Addressing the challenges of implementation of high-order finite volume schemes for atmospheric dynamics of unstructured meshes

The solution of the non-hydrostatic compressible Euler equations using Weighted Essentially Non-Oscillatory (WENO) schemes in two and three-dimensional unstructured meshes, is presented. Their key characteristics are their simplicity; accuracy; robustness; non-oscillatory properties; versatility in handling any type of grid topology; computational and parallel efficiency. Their defining characteristic is a non-linear combination of a series of high-order reconstruction polynomials arising from a series of reconstruction stencils. In the present study an explicit TVD Runge-Kutta 3rd -order method is employed due to its lower computational resources requirement compared to implicit type time advancement methods. The WENO schemes (up to 5th -order) are applied to the two dimensional and three dimensional test cases: a 2D rising

The ICON-1.2 hydrostatic atmospheric dynamical core on triangular grids – Part 1: Formulation and performance of the baseline version

Abstract. As part of a broader effort to develop next-generation models for numerical weather prediction and climate applications, a hydrostatic atmospheric dynamical core is developed as an intermediate step to evaluate a finite-difference discretization of the primitive equations on spherical icosahedral grids. Based on the need for mass-conserving discretizations for multi-resolution modelling as well as scalability and efficiency on massively parallel computing architectures, the dynamical core is built on triangular C-grids using relatively small discretization stencils. This paper presents the formulation and performance of the baseline version of the new dynamical core, focusing on properties of the numerical solutions in the setting of globally uniform resolution. Theoretical analysis reveals that the discrete divergence operator defined on a single triangular cell using the Gauss theorem is only first-order accurate, and introduces grid-scale noise to the discrete model. The noise can be suppressed by fourth-order hyper-diffusion of the horizontal wind field using a time-step and grid-size-dependent diffusion coefficient, at the expense of stronger damping than in the reference spectral model. A series of idealized tests of different complexity are performed. In the deterministic baroclinic wave test, solutions from the new dynamical core show the expected sensitivity to horizontal resolution, and converge to the reference solution at R2B6 (35 km grid spacing). In a dry climate test, the dynamical core correctly reproduces key features of the meridional heat and momentum transport by baroclinic eddies. In the aqua-planet simulations at 140 km resolution, the new model is able to reproduce the same equatorial wave propagation characteristics as in the reference spectral model, including the sensitivity of such characteristics to the meridional sea surface temperature profile. These results suggest that the triangular-C discretization provides a reasonable basis for further development. The main issues that need to be addressed are the grid-scale noise from the divergence operator which requires strong damping, and a phase error of the baroclinic wave at medium and low resolutions

Hybridised multigrid preconditioners for a compatible finite element dynamical core

Compatible finite element discretisations for the atmospheric equations of motion have recently attracted considerable interest. Semi-implicit timestepping methods require the repeated solution of a large saddle-point system of linear equations. Preconditioning this system is challenging since the velocity mass matrix is non-diagonal, leading to a dense Schur complement. Hybridisable discretisations overcome this issue: weakly enforcing continuity of the velocity field with Lagrange multipliers leads to a sparse system of equations, which has a similar structure to the pressure Schur complement in traditional approaches. We describe how the hybridised sparse system can be preconditioned with a non-nested two-level preconditioner. To solve the coarse system, we use the multigrid pressure solver that is employed in the approximate Schur complement method previously proposed by the some of the authors. Our approach significantly reduces the number of solver iterations. The method shows excellent performance and scales to large numbers of cores in the Met Office next-generation climate- and weather prediction model LFRic.Comment: 24 pages, 13 figures, 5 tables; accepted for publication in Quarterly Journal of the Royal Meteorological Societ

Two-dimensional evaluation of atham-fluidity, a nonhydrostatic atmospheric model using mixed continuous/discontinuous finite elements and anisotropic grid optimization

AbstractThis paper presents the first attempt to apply the compressible nonhydrostatic Active Tracer High-Resolution Atmospheric Model–Fluidity (ATHAM-Fluidity) solver to a series of idealized atmospheric test cases. ATHAM-Fluidity uses a hybrid finite-element discretization where pressure is solved on a continuous second-order grid while momentum and scalars are computed on a first-order discontinuous grid (also known as ). ATHAM-Fluidity operates on two- and three-dimensional unstructured meshes, using triangular or tetrahedral elements, respectively, with the possibility to employ an anisotropic mesh optimization algorithm for automatic grid refinement and coarsening during run time. The solver is evaluated using two-dimensional-only dry idealized test cases covering a wide range of atmospheric applications. The first three cases, representative of atmospheric convection, reveal the ability of ATHAM-Fluidity to accurately simulate the evolution of large-scale flow features in neutral atmospheres at rest. Grid convergence without adaptivity as well as the performances of the Hermite–Weighted Essentially Nonoscillatory (Hermite-WENO) slope limiter are discussed. These cases are also used to test the grid optimization algorithm implemented in ATHAM-Fluidity. Adaptivity can result in up to a sixfold decrease in computational time and a fivefold decrease in total element number for the same finest resolution. However, substantial discrepancies are found between the uniform and adapted grid results, thus suggesting the necessity to improve the reliability of the approach. In the last three cases, corresponding to atmospheric gravity waves with and without orography, the model ability to capture the amplitude and propagation of weak stationary waves is demonstrated. This work constitutes the first step toward the development of a new comprehensive limited area atmospheric model.This research has received funding from the European Union Seventh Framework Program (FP7/2007-2013) under Grant agreement 603663 for the research project PEARL (Preparing for Extreme And Rare events in coastaL regions). The EPSRC multiphase program grant MEMPHIS is also acknowledged.This is the author accepted manuscript. The final version is available from the American Meteorological Society via http://dx.doi.org/10.1175/MWR-D-15-0398.

A high-order finite-volume method for atmospheric flows on unstructured grids

This paper presents an extension of a Weighted Essentially Non-Oscillatory (WENO) type schemes for the compressible Euler equations on unstructured meshes for stratified atmospheric flows. The schemes could be extended for regional and global climate models dynamical cores. Their potential lies in their simplicity; accuracy; robustness; non-oscillatory properties; versatility in handling any type of grid topology; computational and parallel efficiency. Their defining characteristic is a non-linear combination of a series of high-order reconstruction polynomials arising from a series of reconstruction stencils. In the present study an explicit Strong Stability Preserving (SSP) Runge-Kutta 3rd-order method is employed for time advancement. The WENO schemes (up to 5th-order) are applied to the two dimensional and three dimensional test cases: a 2D rising thermal bubble; the 2D density current and the 3D Robert smooth bubble. The parallel performance of the schemes in terms of scalability and efficiency is also assessed

Physics–Dynamics Coupling in weather, climate and Earth system models: Challenges and recent progress

This is the final version. Available from American Meteorological Society via the DOI in this record.Numerical weather, climate, or Earth system models involve the coupling of components. At a broad level, these components can be classified as the resolved fluid dynamics, unresolved fluid dynamical aspects (i.e., those represented by physical parameterizations such as subgrid-scale mixing), and nonfluid dynamical aspects such as radiation and microphysical processes. Typically, each component is developed, at least initially, independently. Once development is mature, the components are coupled to deliver a model of the required complexity. The implementation of the coupling can have a significant impact on the model. As the error associated with each component decreases, the errors introduced by the coupling will eventually dominate. Hence, any improvement in one of the components is unlikely to improve the performance of the overall system. The challenges associated with combining the components to create a coherent model are here termed physics–dynamics coupling. The issue goes beyond the coupling between the parameterizations and the resolved fluid dynamics. This paper highlights recent progress and some of the current challenges. It focuses on three objectives: to illustrate the phenomenology of the coupling problem with references to examples in the literature, to show how the problem can be analyzed, and to create awareness of the issue across the disciplines and specializations. The topics addressed are different ways of advancing full models in time, approaches to understanding the role of the coupling and evaluation of approaches, coupling ocean and atmosphere models, thermodynamic compatibility between model components, and emerging issues such as those that arise as model resolutions increase and/or models use variable resolutions.Natural Environment Research Council (NERC)National Science FoundationDepartment of Energy Office of Biological and Environmental ResearchPacific Northwest National Laboratory (PNNL)DOE Office of Scienc