A study of the effects of grid non-orthogonality on the solution of shallow water equations in boundary-fitted coordinate systems

Sankaranarayanan, S.; Spaulding, Malcolm L.

doi:10.1016/s0021-9991(02)00042-6

Cited by 31 publications

(23 citation statements)

References 13 publications

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“…A detailed study on the effects of grid non-orthogonality carried by Sankaranarayanan and Spaulding (2003) reveals that truncation error terms due to first and second derivative terms are functions of grid angle and aspect ratio in a way that root-mean-square (rms) errors in surface elevation and velocities sharply increase as the grid resolution decreases for curvilinear grids with a grid angle less than 45 • (Thompson et al, 1985;Nielsen and Skovgaard, 2005).…”

Section: F F Pereira Et Al: Assessment Of Numerical Schemesmentioning

confidence: 99%

Assessment of numerical schemes for solving the advection–diffusion equation on unstructured grids: case study of the Guaíba River, Brazil

Pereira

Fragoso

Uvo

et al. 2013

Nonlin. Processes Geophys.

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Abstract. In this work, a first-order upwind and a high-order flux-limiter schemes for solving the advection-diffusion equation on unstructured grids were evaluated. The numerical schemes were implemented as a module of an unstructured two-dimensional depth-averaged circulation model for shallow lakes (IPH-UnTRIM2D), and they were applied to the Guaíba River in Brazil. Their performances were evaluated by comparing mass conservation balance errors for two scenarios of a passive tracer released into the Guaíba River. The circulation model showed good agreement with observed data collected at four water level stations along the Guaíba River, where correlation coefficients achieved values up to 0.93. In addition, volume conservation errors were lower than 1 % of the total volume of the Guaíba River. For all scenarios, the higher order flux-limiter scheme has been shown to be less diffusive than a first-order upwind scheme. Accumulated conservation mass balance errors calculated for the flux limiter reached 8 %, whereas for a first-order upwind scheme, they were close to 18 % over a 15-day period. Although both schemes have presented mass conservation errors, these errors are assumed negligible compared with kinetic processes such as erosion, sedimentation or decay rates.

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Section: F F Pereira Et Al: Assessment Of Numerical Schemesmentioning

confidence: 99%

Assessment of numerical schemes for solving the advection–diffusion equation on unstructured grids: case study of the Guaíba River, Brazil

Pereira

Fragoso

Uvo

et al. 2013

Nonlin. Processes Geophys.

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“…Because of the nonorthogonality of the grids and the curvilinear boundaries, the boundary-fitted-coordinate method (BFC) [13,14] was adopted. The governing equation, Eq.…”

Section: Governing Equations In Curvilinear Coordinatesmentioning

confidence: 99%

Role of characteristic modes in the dynamics of wave pattern in the Czochralski oxide crystal growth

Jing

Chen

et al. 2012

Journal of Crystal Growth

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a b s t r a c tWave pattern is a flow pattern observed on the free surface of oxide melt in the Czockralski crucible. Wave pattern exhibits regular folds in the azimuthal direction. In this paper three-dimensional flows of the LiNbO 3 melt in a Czockralski crucible of radius r c ¼ 100 mm and crystal radius r s ¼ 50 mm were investigated. The crucible is still and the crystal is rotating at a rate O s . The flow is assumed to be laminar. The governing equations of the melt flows were solved by a block-structured boundary-fittedcoordinate method. Massive numerical simulations were first conducted to obtain several stable n-folded wave patterns by changing aspect ratio A¼ h/r c and O s , where h is the depth of the oxide melt. The proper orthogonal decomposition was then applied to extract the characteristic modes of the n-folded original wave patterns. The spatial feature of the characteristic modes and the role of the characteristic modes in the dynamic process of the original wave patterns were finally analyzed. Some interesting conclusions are obtained. The characteristic modes of the wave patterns show strong spatial feature. The characteristic modes have more folds in the azimuthal direction than the original wave patterns; the characteristic modes appear in group; with the increase of group order, the number of folds in the azimuthal direction is increased regularly by n for the n-folded original wave pattern. The study of the dynamic process shows that the original wave pattern is a traveling wave, which is formed by the dominant characteristic modes.

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“…At present, the CTF-coordinate has been widely applied in atmospheric and oceanic models (Bleck, 2002;Wang et al, 2004;Davies et al, 2005;Madec, 2008;Skamarock et al, 2008Skamarock et al, , 2012Wallcraft et al, 2009;Skamarock et al, 2012;Schättler et al, 2013). The steep vertical layers and the non-orthogonal vertical computational grids of the CTF-coordinate over steep terrain, however, induce significant advection errors in a model (Thompson et al, 1985;Sharman et al, 1988;Pielke, 2002;Sankaranrayanan and Spaulding, 2003;Steppeler et al, 2003;Ji et al, 2005;Li et al, 2012;Mesinger et al, 2012). Many methods have been proposed to reduce the advection errors in the CTF-coordinate.…”

Section: Introductionmentioning

confidence: 99%

Advection errors in an orthogonal terrain‐following coordinate: idealized 2‐D experiments using steep terrains

Zou

et al. 2016

Atmospheric Science Letters

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This study illustrated the importance of smoothed vertical layers and orthogonal grids in an orthogonal terrain-following coordinate (an OTF-coordinate) in reducing advection errors over steep terrain. Three coordinates, namely, classic terrain-following coordinate, hybrid terrain-following coordinate (HTF-coordinate) and OTF-coordinate, were employed in Schär-type advection experiments for various terrains. The results demonstrated that the OTF-coordinate could diminish the grids with high skewness in the HTF-coordinate over steep terrain; the orthogonal grids share the same importance in reducing advection errors with smoothed vertical layers. Therefore, the advection errors in the OTF-coordinate are considerably reduced than those in the corresponding HTF-coordinate over steep terrain.

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A study of the effects of grid non-orthogonality on the solution of shallow water equations in boundary-fitted coordinate systems

Cited by 31 publications

References 13 publications

Assessment of numerical schemes for solving the advection–diffusion equation on unstructured grids: case study of the Guaíba River, Brazil

Assessment of numerical schemes for solving the advection–diffusion equation on unstructured grids: case study of the Guaíba River, Brazil

Role of characteristic modes in the dynamics of wave pattern in the Czochralski oxide crystal growth

Advection errors in an orthogonal terrain‐following coordinate: idealized 2‐D experiments using steep terrains

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