A Class of Semi-Lagrangian Approximations for Fluids

Smolarkiewicz, Piotr K.; Pudykiewicz, Janusz A.

doi:10.1175/1520-0469(1992)049<2082:acosla>2.0.co;2

Cited by 205 publications

(129 citation statements)

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“…where ( (58)- (59) are solved by applying two iterations of a simple fixedpoint algorithm (Smolarkiewicz and Pudykiewicz, 1992) and determine all departure points (…”

Section: A Description Of the Slsv Time Discretization For The Regulamentioning

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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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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“…where ( (58)- (59) are solved by applying two iterations of a simple fixedpoint algorithm (Smolarkiewicz and Pudykiewicz, 1992) and determine all departure points (…”

Section: A Description Of the Slsv Time Discretization For The Regulamentioning

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 PDEs in this case are seen as physical constraints on the path that can be followed to connect two states in the four-dimensional time-space continuum [93], as depicted in Fig. 4.…”

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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“…It can 125 be run parallel up to a domain decomposition in three dimensions. The name EULAG refers to the ability of solving the equations of motions either in an EUlerian (flux form) (Smolarkiewicz and Margolin (1993)) or in a semi-LAGrangian (advective form) (Smolarkiewicz and Pudykiewicz (1992)) mode. A comprehensive description and discussion of EULAG can be found in Smolarkiewicz and Margolin (1998) and Prusa et al (2008).…”

Section: Numerical Modelmentioning

confidence: 99%

The impact of the diurnal cycle of the atmospheric boundary layer on physical variables relevant for wind energy applications

Englberger¹,

Dörnbrack²

2016

Preprint

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Abstract. This paper provides a quantification of the temporal evolution of physical variables in the atmospheric boundary layer (ABL) relevant for wind energy applications. For this purpose, we use the unique dataset gathered during the BLLAST (Boundary Layer Late Afternoon and Sun- This results in a quantification of the diurnal cycle influence on the vertical wind shear, the stratifi-10 cation and the turbulence intensity in the atmosphere. Further, the impact of different heterogeneous surface conditions on shear near the surface layer of the ABL is investigated.

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A Class of Semi-Lagrangian Approximations for Fluids

Cited by 205 publications

References 0 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

The impact of the diurnal cycle of the atmospheric boundary layer on physical variables relevant for wind energy applications

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