Conservation properties of convection difference schemes

Piacsek, S.; Williams, Gareth

doi:10.1016/0021-9991(70)90038-0

Cited by 244 publications

(122 citation statements)

References 9 publications

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“…It is desirable for the discrete solution to satisfy the analogous conservation property. This is because the weak instability caused by the nonlinear convection term can be avoided if the discrete convection form satisfies this conservation property and the usual CourantFriedrichs-Lewy number condition for linearized stability [26]. Now let us focus only on the spatial discretization and consider the semi-discrete evolution equation as…”

Section: Formally Second-order Methodsmentioning

confidence: 99%

An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity

Lai

Peskin

2000

Journal of Computational Physics

790

508

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A formally second-order accurate immersed boundary method is presented and tested in this paper. We apply this new scheme to simulate the flow past a circular cylinder and study the effect of numerical viscosity on the accuracy of the computation by comparing the numerical results with those of a first-order method. The numerical evidence shows that the new scheme has less numerical viscosity and is therefore a better choice for the simulation of high Reynolds number flows with immersed boundaries.

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Section: Formally Second-order Methodsmentioning

confidence: 99%

An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity

Lai

Peskin

2000

Journal of Computational Physics

790

508

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“…The time-differencing scheme is less diffusive than the leapflog approach, based on a square wave test. The approach is referred to as "angled derivative" [Roberts and Weiss, 1966] and has also been investigated by Piacsek and Williams [1970]. Even in the extreme square-wave test, the numerical diffusion is less than half the minimum explicit dif- …”

mentioning

confidence: 99%

A diabatic circulation experiment in a two‐dimensional photochemical model

Guthrie

Jackman²,

Herman³

et al. 1984

J. Geophys. Res.

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A two-dimensional photochemical model based on diabatic circulation has been used to simulate the behavior of N20, CFC13 (F-11), and CF2Cl• (F-12). The circulation is based on estimates of net heating from the ground to 60 kin. Eddy diffusion has been reduced with respect to other model studies with Kzz --2 x 103 cm • s-• everywhere above 100 mbar. Resulting tracer profiles show reasonable agreement with measured profiles in the tropics and fall off much more sharply with altitude than those produced by models using larger values of Kzz. The agreement obtained is at least as good as that obtained with adjustable, eddy diffusion parameters. The diabatic circulation treatment is more closely related to real physical processes and thus more easily interpreted. Diffusive mixing appears to be more important in determining the details of the tracer distributions than the basic morphology.

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“…The results presented here are obtained using the Boussinesq equations and a first-order Richardson-number-dependent mixing-length turbulence closure scheme. The secondorder-accurate scheme of Piacsek and Williams (1970) is used for advection of both velocity and potential temperature. A no-slip condition is imposed at the lower boundary (via a similarity condition for the surface stress), along with a zero-surface-heat-flux condition, and the Coriolis force is imposed with f = 10 −4 s −1 .…”

Section: The Numerical Modelmentioning

confidence: 99%

The effect of small‐scale hills on orographic drag

Brown

2007

Quart J Royal Meteoro Soc

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ABSTRACT:The purpose of this study is to investigate the extent to which the presence of hills with relatively short horizontal scales can influence the drag, due to mountain waves and flow blocking, exerted on the flow by larger-scale mountains. Numerical simulations of stratified flow over mountains are presented for flow over orography described by the linear superposition of broad mountains, whose length scales are large enough to generate mountain waves, and narrow corrugations, whose wavelengths fall below the minimum horizontal wavelength for stationary gravity waves. Results are presented for both two-and three-dimensional mountain shapes, and for a range of corrugation heights. It is shown that the corrugations can significantly reduce the amplitude of the mountain waves generated by the broader mountain, or they can suppress the unsteadiness of the wake. When these mechanisms make an important contribution to the total drag, this implies a significant drop in the total drag, compared to the sum of the contributions from the two scales of orography. From the point of view of drag parametrization, the extent to which the effect of the small-scale hills can be represented via an effective roughness length is investigated.  Crown

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Conservation properties of convection difference schemes

Cited by 244 publications

References 9 publications

An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity

An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity

A diabatic circulation experiment in a two‐dimensional photochemical model

The effect of small‐scale hills on orographic drag

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