A conservative multi-tracer transport scheme for spectral-element spherical grids

Erath, Christoph; Nair, Ramachandran D.

doi:10.1016/j.jcp.2013.08.050

Cited by 17 publications

(23 citation statements)

References 27 publications

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“…For that reason our implementation provides at least the more simple overlap of pack/unpack with communication calls. It is important to mention that this approach can in principle be applied to any point-to-point communication stemming from the discretization of partial differential equations (PDEs) or other applications -one example being the semi-Lagrangian multitracer transport schemes implemented in HOMME by Erath et al (2012) and Erath and Nair (2014). We now describe the computation and data movement that can be performed while waiting for messages to be received in the SE and DG methods.…”

Section: Overlapping For the Dg Methodsmentioning

confidence: 99%

Asynchronous communication in spectral-element and discontinuous Galerkin methods for atmospheric dynamics – a case study using the High-Order Methods Modeling Environment (HOMME-homme_dg_branch)

Jamroz¹,

Klöfkorn²

2016

Geosci. Model Dev.

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Abstract. The scalability of computational applications on current and next-generation supercomputers is increasingly limited by the cost of inter-process communication. We implement non-blocking asynchronous communication in the High-Order Methods Modeling Environment for the time integration of the hydrostatic fluid equations using both the spectral-element and discontinuous Galerkin methods. This allows the overlap of computation with communication, effectively hiding some of the costs of communication. A novel detail about our approach is that it provides some data movement to be performed during the asynchronous communication even in the absence of other computations. This method produces significant performance and scalability gains in large-scale simulations.

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Section: Overlapping For the Dg Methodsmentioning

confidence: 99%

Asynchronous communication in spectral-element and discontinuous Galerkin methods for atmospheric dynamics – a case study using the High-Order Methods Modeling Environment (HOMME-homme_dg_branch)

Jamroz¹,

Klöfkorn²

2016

Geosci. Model Dev.

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“…Together with an easy search algorithm, which is needed to find the fluxes, the SPELT approach is very attractive for non-uniform grids. In [12] we show that the scheme works on non-uniform quadrilateral grids with a positivity preservation option. Additionally, we discuss how the scheme can be made monotonic with a flux-corrected transport approach in the spirit of [15].…”

Section: Spectral-element Lagrangian Transportmentioning

confidence: 99%

“…The SPELT scheme described in [12] is based on the multi-moment semi-Lagrangian scheme of [14]. SPELT is a third order accurate flux form scheme, which uses a biquadratic polynomial reconstruction (2D) on a single Eulerian cell.…”

Section: Spectral-element Lagrangian Transportmentioning

confidence: 99%

“…However, flux schemes have the strong property that they ensure mass conservation no matter how we approximate fluxes. Nevertheless, it is important to know for parallelization that if the flux approximation on an edge E is done separately more details on the flux approximation, in particular in the more difficult case of non-uniform grids, we refer to [12]. There, one can also find details on a quasi-monotone semi-Lagrangian (QMSL) filter and the flux-corrected transport (FCT) philosophy.…”

Section: Spectral-element Lagrangian Transportmentioning

confidence: 99%

“…A scheme based on the traditional philosophy of the semiLagrangian idea uses a spectral element reconstruction followed by a global optimization to preserve conservation of mass and monotonicity (with a divided and conquer strategy) [11]. In this work we give a review of the conservative SPectral-Element Lagrangian Transport (SPELT) scheme in HOMME [12] and the Conservative Semi-LAgrangian Multi-tracer transport scheme (CSLAM) in HOMME [13]. Both schemes in HOMME are mass conservative, multi-tracer efficient, third order accurate, scalable on parallel computers and have a positivity option.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Two conservative multi-tracer efficient semi-Lagrangian schemes for multiple processor systems integrated in a spectral element (climate) dynamical core

Erath

Taylor

Nair

2016

Communications in Applied and Industrial Mathematics

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In today's atmospheric numerical modeling, scalable and highly accurate numerical schemes are of particular interest. To address these issues Galerkin schemes, such as the spectral element method, have received more attention in the last decade. They also provide other state-of-the-art capabilities such as improved conservation. However, the tracer transport of hundreds of tracers, e.g., in the chemistry version of the Community Atmosphere Model, is still a performance bottleneck. Therefore, we consider two conservative semi-Lagrangian schemes. Both are designed to be multi-tracer efficient, third order accurate, and allow significantly longer time steps than explicit Eulerian formulations. We address the difficulties arising on the cubed-sphere projection and on parallel computers and show the high scalability of our approach. Additionally, we use the two schemes for the transport of passive tracers in a dynamical core and compare our results with a current spectral element tracer transport advection used by the High-Order Method Modeling Environment.

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A semi‐implicit, semi‐Lagrangian discontinuous Galerkin framework for adaptive numerical weather prediction

Tumolo

Bonaventura

2015

Quart J Royal Meteoro Soc

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We present an adaptive discretization approach for model equations typical of numerical weather prediction (NWP), which combines the semi-Lagrangian technique with a semiimplicit time discretization method, based on the Trapezoidal Rule second-order Backward Difference Formula scheme (TR-BDF2), and with a discontinuous Galerkin (DG) spatial discretization, with variable and adaptive element degree. The resulting method has full second-order accuracy in time, can employ polynomial bases of arbitrarily high degree in space, is unconditionally stable and can effectively adapt the number of degrees of freedom employed in each element at runtime, in order to balance accuracy and computational cost. Furthermore, although the proposed method can be implemented on arbitrary unstructured and non-conforming meshes, even its application on simple Cartesian meshes in spherical coordinates can reduce the impact of the coordinate singularity, by reducing the polynomial degree used in the polar elements. Numerical results are presented, obtained on classical benchmarks with two-dimensional models implementing discretizations of the shallowwater equations on the sphere and of the Euler equations on a vertical slice, respectively. The results confirm that the proposed method has a significant potential for NWP applications.

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A conservative multi-tracer transport scheme for spectral-element spherical grids

Cited by 17 publications

References 27 publications

Asynchronous communication in spectral-element and discontinuous Galerkin methods for atmospheric dynamics – a case study using the High-Order Methods Modeling Environment (HOMME-homme_dg_branch)

Asynchronous communication in spectral-element and discontinuous Galerkin methods for atmospheric dynamics – a case study using the High-Order Methods Modeling Environment (HOMME-homme_dg_branch)

Two conservative multi-tracer efficient semi-Lagrangian schemes for multiple processor systems integrated in a spectral element (climate) dynamical core

A semi‐implicit, semi‐Lagrangian discontinuous Galerkin framework for adaptive numerical weather prediction

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