Completely Conservative and Oscillationless Semi-Lagrangian Schemes for Advection Transportation

Xiao, Feng; Yabe, Takashi

doi:10.1006/jcph.2001.6746

Cited by 110 publications

(115 citation statements)

References 39 publications

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“…P n i±1/2 and V n i for the ith cell, the reconstruction polynomial n i (x) in (3) is found with the coefficients given in (5). Considering the problems with constant speed, the right-hand side term of (7) vanishes.…”

Section: Basic Formulation In One Dimensionmentioning

confidence: 99%

“…Among others, a class of conservative semi-Lagrangian schemes, which follow the underlying concept of the CIP (Cubic Polynomial Interpolation [2] or more generally Constrained Interpolation Profile [3]) method and are so-called CIP (Constrained Interpolation Profile) Conservative Semi-Lagrangian (CIP-CSL) schemes, were proposed in [4][5][6][7][8] by introducing multi moments [9,10] as the computational variables. A convenient and efficient transport model with numerical conservation can be constructed by making use of two kinds of moments, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…The major difference from the existing CIP-CSL schemes [4][5][6][7][8] is that the numerical flux in the present scheme is computed from the values sampled along the semi-Lagrangian trajectory instead of the rigorous integration of the interpolation function, and only two kinds of moments, i.e. PV and VIA, are used as the computational variables even in multi-dimensional cases.…”

Section: Introductionmentioning

confidence: 99%

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A multi‐moment transport model on cubed‐sphere grid

Xiao

et al. 2010

Numerical Methods in Fluids

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SUMMARYA conservative, single-cell-based semi-Lagrangian transport model is proposed in this paper. Using multimoment concept, an additional moment, i.e. volume-integrated average (VIA), is treated as the model variable besides the point value (PV) updated in the traditional semi-Lagrangian schemes. A quadratic interpolation function is constructed based on local degrees of freedom defined within each single cell. The PV moment is advanced by the semi-Lagrangian formulation, whereas the VIA moment is updated by a finite volume formulation to rigorously ensure the numerical conservation. The numerical fluxes are computed from the PV moments defined along the boundary edges of the control volume. The scheme is extended to the spherical geometry through the application of the cubed-sphere grid that eliminates the polar singularity in the conventional longitude/latitude coordinates by using the quasi-uniform grid spacing covering the whole sphere. The single-cell-based scheme is well suited for the treatment of the connections between different patches. A simple quasi-monotone limiter to the PV moment is applied to suppress non-physical oscillations. The proposed scheme has been validated via representative benchmark tests and the performance is competitive to other existing transport schemes.

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Section: Basic Formulation In One Dimensionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A multi‐moment transport model on cubed‐sphere grid

Xiao

et al. 2010

Numerical Methods in Fluids

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“…This is part of the reason why it has received such interest from the atmospheric sciences community [23,26,24,55], as well as the compressible flow community [25,43] where the acoustic time step restrictions can be severe. We refer the reader to a particularly interesting body of work that considers a number of methods for making semi-Lagrangian schemes conservative, considering one spatial dimension, multiple spatial dimensions with splitting, multiple spatial dimensions without splitting, and even obtaining conservation from a non-conservative form [49,52,39,51,48].…”

Section: Introductionmentioning

confidence: 99%

An unconditionally stable fully conservative semi-Lagrangian method

Lentine

Gretarsson

Fedkiw

2011

Journal of Computational Physics

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Semi-Lagrangian methods have been around for some time, dating back at least to [3]. Researchers have worked to increase their accuracy, and these schemes have gained newfound interest with the recent widespread use of adaptive grids where the CFL-based time step restriction of the smallest cell can be overwhelming. Since these schemes are based on characteristic tracing and interpolation, they do not readily lend themselves to a fully conservative implementation. However, we propose a novel technique that applies a conservative limiter to the typical semi-Lagrangian interpolation step in order to guarantee that the amount of the conservative quantity does not increase during this advection. In addition, we propose a new second step that forward advects any of the conserved quantity that was not accounted for in the typical semi-Lagrangian advection. We show that this new scheme can be used to conserve both mass and momentum for incompressible flows. For incompressible flows, we further explore properly conserving kinetic energy during the advection step, but note that the divergence free projection results in a velocity field which is inconsistent with conservation of kinetic energy (even for inviscid flows where it should be conserved). For compressible flows, we rely on a recently proposed splitting technique that eliminates the acoustic CFL time step restriction via an incompressible-style pressure solve. Then our new method can be applied to conservatively advect mass, momentum and total energy in order to exactly conserve these quantities, and remove the remaining time step restriction based on fluid velocity that the original scheme still had.

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“…This lack has often been dealt with by the use of a 'mass fixer', whereby global mass conservation is restored diagnostically (Priestley, 1993). To avoid this ad hoc procedure, a number of schemes have been proposed that inherently conserve mass (Rancić, 1992(Rancić, , 1995Laprise and Plante, 1995;Leslie and Purser, 1995;Lin and Rood, 1996;Xiao and Yabe, 2001;Nair and Machenhauer, 2002;Nair et al, , 2003Kaas, 2008), including the SLICE scheme (Zerroukat et al, 2002(Zerroukat et al, , 2004(Zerroukat et al, , 2005(Zerroukat et al, , 2006(Zerroukat et al, , 2007. Recently, some of these schemes have been applied in the context of coupled atmospheric equation sets (Lauritzen et al, 2006(Lauritzen et al, , 2008.…”

Section: Introductionmentioning

confidence: 99%

An improved version of SLICE for conservative monotonic remapping on a C‐grid

Zerroukat

Wood

Staniforth

2009

Quart J Royal Meteoro Soc

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This Note presents some further developments to the Semi-Lagrangian Inherently Conservative and Efficient (SLICE) scheme. The revised scheme, termed C-SLICE, is designed to exploit the good dispersion properties of a C-grid staggering of mass and momentum variables in atmospheric models. Furthermore, several simplifications are made to the SLICE scheme, leading to improved computational efficiency without loss of accuracy. The revised scheme is evaluated using some standard tests from the literature.

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Completely Conservative and Oscillationless Semi-Lagrangian Schemes for Advection Transportation

Cited by 110 publications

References 39 publications

A multi‐moment transport model on cubed‐sphere grid

A multi‐moment transport model on cubed‐sphere grid

An unconditionally stable fully conservative semi-Lagrangian method

An improved version of SLICE for conservative monotonic remapping on a C‐grid

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