An Efficient Two‐Time‐Level Semi‐Lagrangian Semi‐Implicit Integration Scheme

Temperton, Clive; Staniforth, Andrew

doi:10.1002/qj.49711347714

Cited by 151 publications

(85 citation statements)

References 20 publications

(16 reference statements)

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“…In that regard, the method is similar to 2-TL implementations of the SISL method (Temperton and Staniforth, 1987;McDonald and Bates, 1987). Note, however, that no velocity extrapolation from previous time steps is required for the SL part of the algorithm.…”

Section: Discussionmentioning

confidence: 99%

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A regularization approach for a vertical‐slice model and semi‐Lagrangian Störmer–Verlet time stepping

Hundertmark

Reich

2007

Quart J Royal Meteoro Soc

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ABSTRACT:In this paper, we provide a systematic derivation of regularized equations for a non-hydrostatic and compressible vertical-slice model of the dry atmosphere. The derivation is based on an analysis of a semi-implicit discretization of the equations of motion and a recent regularized formulation is obtained as a special case. An implementation of the regularized equations, using a recent second-order, centred-in-time, two-time-level semi-Lagrangian Störmer-Verlet method, is discussed and a series of numerical experiments is conducted.

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Section: Discussionmentioning

confidence: 99%

“…The analysis is based on earlier work by Frank et al (2005) and Wood et al (2006) on regularized SWEs and their link to SI and SI semi-Lagrangian (SISL) methods (e.g. Robert, 1982;Temperton and Staniforth, 1987;Tanguay et al, 1990).…”

Section: Introductionmentioning

confidence: 99%

A regularization approach for a vertical‐slice model and semi‐Lagrangian Störmer–Verlet time stepping

Hundertmark

Reich

2007

Quart J Royal Meteoro Soc

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“…The most common PBTI strategy employed in NWP is the Semi-Lagrangian (SL) scheme that revolutionized the field two decades ago [94,98]. Pure Lagrangian approaches, where the exact solution at the next time step is sought by translating the flow information on the mesh at the current time level along the trajectory integrals, with remapping only for postprocessing purposes, have never been adopted into operational NWP models.…”

Section: Path-based Time-integration (Pbti)mentioning

confidence: 99%

Current and Emerging Time-Integration Strategies in Global Numerical Weather and Climate Prediction

Mengaldo

Wyszogrodzki

Diamantakis

et al. 2018

Arch Computat Methods Eng

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The continuous partial differential equations governing a given physical phenomenon, such as the Navier-Stokes equations describing the fluid motion, must be numerically discretized in space and time in order to obtain a solution otherwise not readily available in closed (i.e., analytic) form. While the overall numerical discretization plays an essential role in the algorithmic efficiency and physically-faithful representation of the solution, the time-integration strategy commonly is one of the main drivers in terms of cost-to-solution (e.g., time-or energy-to-solution), accuracy and numerical stability, thus constituting one of the key building blocks of the computational model. This is especially true in time-critical applications, including numerical weather prediction (NWP), climate simulations and engineering. This review provides a comprehensive overview of the existing and emerging time-integration (also referred to as time-stepping) practices used in the operational global NWP and climate industry, where global refers to weather and climate simulations performed on the entire globe. While there are many flavors of time-integration strategies, in this review we focus on the most widely adopted in NWP and climate centers and we emphasize the reasons why such numerical solutions were adopted. This allows us to make some considerations on future trends in the field such as the need to balance accuracy in time with substantially enhanced time-to-solution and associated implications on energy consumption and running costs. In addition, the potential for the co-design of time-stepping algorithms and underlying high performance computing hardware, a keystone to accelerate the computational performance of future NWP and climate services, is also discussed in the context of the demanding operational requirements of the weather and climate industry.

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“…This procedure was first proposed in [30] for finite difference semi-Lagrangian methods and studied for finite elements in [7,8], among others. It is also known that…”

Section: Formulation Of Convection Fractional Stagementioning

confidence: 99%

A Galerkin-Characteristic Method for Large-Eddy Simulation of Turbulent Flow and Heat Transfer

El‐Amrani¹,

Seaı̈d²

2008

SIAM J. Sci. Comput.

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract. This work aims at the development of a nonoscillatory Galerkin-characteristic method for large-eddy simulation of turbulent flow and heat transfer. The method is based on combining the modified method of characteristics with a Galerkin finite element discretization of the incompressible Navier-Stokes/Boussinesq equations in primitive variables. It can be interpreted as a fractional step technique where the convective part and the Stokes/Boussinesq part are treated separately. A limiting procedure is implemented for the reconstruction of numerical solutions at the departure points. The main feature of the proposed Galerkin-characteristic method is that, due to the Lagrangian treatment of convection, the standard Courant-Friedrichs-Levy condition is relaxed, and the time truncation errors are reduced in the Stokes/Boussinesq part. To solve the generalized Stokes/Boussinesq problem we implement a conjugate gradient algorithm. This method avoids projection techniques and does not require any special correction for the pressure. We verify the method for an advection-diffusion equation with a known analytical solution and for the benchmark problem of mixed convection flow in a squared cavity. We also present numerical results for a problem of heat transport in the Strait of Gibraltar. The Galerkin-characteristic method has been found to be feasible and satisfactory.Key words. Galerkin-characteristic method, large-eddy simulation, heat transfer, finite element method, mixed convection, sea-surface temperature AMS subject classifications. 76F35, 74S05, 65M25DOI. 10.1137/080720711 1. Introduction. The large-eddy simulation (LES) equations for incompressible thermal flows are obtained by applying a spatial filtering to the Navier-Stokes equations subject to the Boussinesq approximation; see [5,4,17,23,16,12] and the references therein. However, this procedure introduces a term called a subgrid stress tensor which needs to be modelled. This term has to be seen as the interaction between the large and small scales in the system. In the current study, we will concentrate on a subgrid problem based on the Smagorinsky model [27]. The LES is normally performed on grids that are just fine enough to resolve the large flow scales, and numerical errors on such grids can have large effects on the simulation results. Although in the literature (see [12] and references therein) many numerical schemes have been presented, it is still not clear what the effect of the numerical and modelling errors in...

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An Efficient Two‐Time‐Level Semi‐Lagrangian Semi‐Implicit Integration Scheme

Cited by 151 publications

References 20 publications

A regularization approach for a vertical‐slice model and semi‐Lagrangian Störmer–Verlet time stepping

A regularization approach for a vertical‐slice model and semi‐Lagrangian Störmer–Verlet time stepping

Current and Emerging Time-Integration Strategies in Global Numerical Weather and Climate Prediction

A Galerkin-Characteristic Method for Large-Eddy Simulation of Turbulent Flow and Heat Transfer

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