7,254 research outputs found
Parallel-in-Time Multi-Level Integration of the Shallow-Water Equations on the Rotating Sphere
The modeling of atmospheric processes in the context of weather and climate
simulations is an important and computationally expensive challenge. The
temporal integration of the underlying PDEs requires a very large number of
time steps, even when the terms accounting for the propagation of fast
atmospheric waves are treated implicitly. Therefore, the use of
parallel-in-time integration schemes to reduce the time-to-solution is of
increasing interest, particularly in the numerical weather forecasting field.
We present a multi-level parallel-in-time integration method combining the
Parallel Full Approximation Scheme in Space and Time (PFASST) with a spatial
discretization based on Spherical Harmonics (SH). The iterative algorithm
computes multiple time steps concurrently by interweaving parallel high-order
fine corrections and serial corrections performed on a coarsened problem. To do
that, we design a methodology relying on the spectral basis of the SH to
coarsen and interpolate the problem in space. The methods are evaluated on the
shallow-water equations on the sphere using a set of tests commonly used in the
atmospheric flow community. We assess the convergence of PFASST-SH upon
refinement in time. We also investigate the impact of the coarsening strategy
on the accuracy of the scheme, and specifically on its ability to capture the
high-frequency modes accumulating in the solution. Finally, we study the
computational cost of PFASST-SH to demonstrate that our scheme resolves the
main features of the solution multiple times faster than the serial schemes
The remapped particle-mesh advection scheme
We describe the remapped particle-mesh method, a new mass-conserving method
for solving the density equation which is suitable for combining with
semi-Lagrangian methods for compressible flow applied to numerical weather
prediction. In addition to the conservation property, the remapped
particle-mesh method is computationally efficient and at least as accurate as
current semi-Lagrangian methods based on cubic interpolation. We provide
results of tests of the method in the plane, results from incorporating the
advection method into a semi-Lagrangian method for the rotating shallow-water
equations in planar geometry, and results from extending the method to the
surface of a sphere
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Computational modes and grid imprinting on five quasi-uniform spherical C-grids
Currently, most operational forecasting models use latitude-longitude grids, whose convergence of meridians towards the poles limits parallel scaling. Quasi-uniform grids might avoid this limitation. Thuburn et al, JCP, 2009 and Ringler et al, JCP, 2010 have developed a method for arbitrarily-structured, orthogonal C-grids (TRiSK), which has many of the desirable properties of the C-grid on latitude-longitude grids but which works on a variety of quasi-uniform grids. Here, five quasi-uniform, orthogonal grids of the sphere are investigated using TRiSK to solve the shallow-water equations.
We demonstrate some of the advantages and disadvantages of the hexagonal and triangular icosahedra, a Voronoi-ised cubed sphere, a Voronoi-ised skipped latitude-longitude grid and a grid of kites in comparison to a full latitude-longitude grid. We will show that the hexagonal-icosahedron gives the most accurate results (for least computational cost). All of the grids suffer from spurious computational modes; this is especially true of the kite grid,
despite it having exactly twice as many velocity degrees of freedom as height degrees of freedom. However, the computational modes are easiest to control on the hexagonal icosahedron since they consist of vorticity oscillations on the dual grid which can be controlled using a diffusive advection scheme for potential vorticity
Spectral/hp element methods: recent developments, applications, and perspectives
The spectral/hp element method combines the geometric flexibility of the
classical h-type finite element technique with the desirable numerical
properties of spectral methods, employing high-degree piecewise polynomial
basis functions on coarse finite element-type meshes. The spatial approximation
is based upon orthogonal polynomials, such as Legendre or Chebychev
polynomials, modified to accommodate C0-continuous expansions. Computationally
and theoretically, by increasing the polynomial order p, high-precision
solutions and fast convergence can be obtained and, in particular, under
certain regularity assumptions an exponential reduction in approximation error
between numerical and exact solutions can be achieved. This method has now been
applied in many simulation studies of both fundamental and practical
engineering flows. This paper briefly describes the formulation of the
spectral/hp element method and provides an overview of its application to
computational fluid dynamics. In particular, it focuses on the use the
spectral/hp element method in transitional flows and ocean engineering.
Finally, some of the major challenges to be overcome in order to use the
spectral/hp element method in more complex science and engineering applications
are discussed
The upper-atmosphere extension of the ICON general circulation model (version: Ua-icon-1.0)
How the upper-atmosphere branch of the circulation contributes to and interacts with the circulation of the middle and lower atmosphere is a research area with many open questions. Inertia-gravity waves, for instance, have moved in the focus of research as they are suspected to be key features in driving and shaping the circulation. Numerical atmospheric models are an important pillar for this research. We use the ICOsahedral Non-hydrostatic (ICON) general circulation model, which is a joint development of the Max Planck Institute for Meteorology (MPI-M) and the German Weather Service (DWD), and provides, e.g., local mass conservation, a flexible grid nesting option, and a non-hydrostatic dynamical core formulated on an icosahedral-triangular grid. We extended ICON to the upper atmosphere and present here the two main components of this new configuration named UA-ICON: an extension of the dynamical core from shallow- to deep-atmosphere dynamics and the implementation of an upper-atmosphere physics package. A series of idealized test cases and climatological simulations is performed in order to evaluate the upper-atmosphere extension of ICON. © Author(s) 2019
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