Stable Centered-Difference Schemes, Based on an Unstaggered A Grid, That Eliminate Two-Grid Interval Noise

Kar, Sajal K.

doi:10.1175/1520-0493(2000)128<3643:scdsbo>2.0.co;2

Cited by 5 publications

(6 citation statements)

References 8 publications

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“…Several notable exceptions that use an A-grid have relied on higher-order discretisations (Dietrich, 1997) or other forms of built-in filtering (Kar, 1999) in order to control computational modes. More generally, the pressure-velocity decoupling problem of collocated schemes had also been recognised early in the history of incompressible flow solvers (Harlow and Welch, 1965) and more recently solutions have been developed (Lai, Bell, and Colella, 1993;Rider, 1995;Almgren, Bell, and Crutchfield, 2001).…”

Section: Spatial Discretisationmentioning

confidence: 99%

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A tree-based solver for adaptive ocean modelling

Popinet

Rickard

2007

Ocean Modelling

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The development of an adaptive (in space and time) ocean model from an existing adaptive finite-volume Navier-Stokes model is described. A flexible and efficient quadtree spatial discretisation is used which requires collocation of all variables (i.e. an A-grid discretisation). We demonstrate that the use of an approximate projection method allows for implicit damping of instabilities generally associated with the A-grid, at the expense of a relatively small amount of numerical energy dissipation, while accurately preserving dispersive properties and geostrophic balance. The finite-volume formulation also maintains second-order spatial accuracy at all solid boundaries. Test cases demonstrate the efficacy of the adaptive ocean model, and the advantages it has in terms of efficient representation of multi-scale behaviour within a single model. The model is freely available as open-source code. * (s.popinet|g.rickard)@niwa.co.nz

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Section: Spatial Discretisationmentioning

confidence: 99%

“…Aside from the inherent instability of a scheme containing computational modes (Lai, Bell, and Colella, 1993;Kar, 1999), the wide stencil of the Laplacian greatly complicates the solution of (6) when a non-uniform resolution is used (Popinet, 2003). The standard compact Laplacian…”

Section: Exact and Approximate Projectionsmentioning

confidence: 99%

A tree-based solver for adaptive ocean modelling

Popinet

Rickard

2007

Ocean Modelling

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“…Note that Randal [15] proposed that modified B grid and shallow water equations be used in order to avoid the grid separation, while Kar [11] addressed an analogous problem on the A grid.…”

Section: Shallow-water Equation Modelmentioning

confidence: 99%

“…The two techniques are equivalent for the governing linear gravity wave equations without advection. A similar technique for the A grid was proposed by Kar [11].…”

Section: Experiments With Divergence Correctionmentioning

confidence: 99%

Method for efficient prevention of gravity wave decoupling on rectangular semi-staggered grids

Ničković

Djurdjević

Vujadinović

et al. 2011

Journal of Computational Physics

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“…using a compact five-point stencil. This particular choice helps eliminate grid-scale gravity wave noise on the unstaggered A grid as shown in Kar (2000). The resulting space-discrete form of the elliptic Eq.…”

Section: B Space Discretization Of the Equationsmentioning

confidence: 99%

A Semi-Implicit Runge–Kutta Time-Difference Scheme for the Two-Dimensional Shallow-Water Equations

Kar

2006

Monthly Weather Review

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A semi-implicit, two time-level, three-step iterative time-difference scheme is proposed for the two-dimensional nonlinear shallow-water equations in a conservative flux form. After a semi-implicit linearization of the governing equations, the linear gravity wave terms are time discretized implicitly using a second-order trapezoidal scheme applied over each iterative step, whereas the nonlinear terms including horizontal advection and other terms left over from the semi-implicit linearization are time discretized explicitly using a third-order Runge–Kutta scheme. The effectiveness of the scheme in terms of numerical accuracy, stability, and efficiency is established through a forced initial-boundary value problem studied using a two-dimensional shallow-water model.

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Stable Centered-Difference Schemes, Based on an Unstaggered A Grid, That Eliminate Two-Grid Interval Noise

Cited by 5 publications

References 8 publications

A tree-based solver for adaptive ocean modelling

A tree-based solver for adaptive ocean modelling

Method for efficient prevention of gravity wave decoupling on rectangular semi-staggered grids

A Semi-Implicit Runge–Kutta Time-Difference Scheme for the Two-Dimensional Shallow-Water Equations

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