A 3-D poisson solver based on conjugate gradients compared to standard iterative methods and its performance on vector computers

Kapitza, Hartmut; Eppel, D.

doi:10.1016/0021-9991(87)90067-2

Cited by 30 publications

(11 citation statements)

References 18 publications

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“…The discrete form of the elliptical pressure equation (15) is solved iteratively with the idealised generalised conjugate gradient (IGCG)-method as described by Kapitza and Eppel (1986). To account for grid cells that are intersected by orography, the discretised pressure equation has been expanded by so-called 'cell boundary weight factors'.…”

Section: Methodsmentioning

confidence: 99%

A new large-eddy simulation model for simulating air flow and warm clouds above highly complex terrain. Part I: The dry model

Reinert

Wirth

Eichhorn

et al. 2007

Boundary-Layer Meteorol

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This paper presents the dry version of a new large-eddy simulation (LES) model, which is designed to simulate air flow and clouds above highly complex terrain. The model is three-dimensional and nonhydrostatic, and the governing equations are sound filtered by use of the anelastic approximation. A fractional step method is applied to solve the equations on a staggered Cartesian grid. Arbitrarily steep and complex orography can be accounted for through the method of viscous topography. The dynamical model core is validated by comparing the results for a spreading density current against a benchmark solution. The model accuracy is further assessed through the simulation of turbulent flow across a quasi two-dimensional ridge. The results are compared with wind-tunnel data. The method of viscous topography is not restricted to moderately sloped terrain. Compared to models using curvilinear grids, it allows this model to be applied to a much wider range of flows. This is illustrated through the simulation of an atmospheric boundary-layer flow over a surface mounted cube. The results show that the dry model version is able to accurately represent the complex flow in the vicinity of three-dimensional obstacles. It is concluded that the method of viscous topography was successfully implemented into a micrometeorological LES model. As will be shown in Part II, this allows the detailed study of clouds in highly complex terrain.

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Section: Methodsmentioning

confidence: 99%

A new large-eddy simulation model for simulating air flow and warm clouds above highly complex terrain. Part I: The dry model

Reinert

Wirth

Eichhorn

et al. 2007

Boundary-Layer Meteorol

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“…At each iteration, the linear system in (20) is to be solved, for example, by some number of preconditioned conjugate gradient iterations. Application of block tridiagonal preconditioning based on the discretization of the vertical derivatives terms, as suggested in [13,14], yields a quite efficient solution algorithm. Furthermore, the tolerance used in the stopping criterion for the conjugate gradient is rescaled with the norm of the right hand side of the linear system (see, e.g., [29]).…”

Section: Convergence Of the Nonlinear Iterationsmentioning

confidence: 99%

A Semi-implicit Semi-Lagrangian Scheme Using the Height Coordinate for a Nonhydrostatic and Fully Elastic Model of Atmospheric Flows

Bonaventura

2000

Journal of Computational Physics

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“…The mesoscale nonhydrostatic pressure contribution p2 is calculated by a conjugate gradient method (Kapitza and Eppel, 1987). To suppress nonlinear numerical instability, a 7-point filter is applied at each time step (Shapiro,197 1).…”

Section: Christof Liipkes and K Heinke Schlijnzenmentioning

confidence: 99%

Modelling the arctic convective boundary-layer with different turbulence parameterizations

Lüpkes

Schlünzen²

1996

Boundary-Layer Meteorol

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Different parameterizations of subgrid-scale fluxes are utilized in a nonhydrostatic and anelastic mesoscale model to study their influence on simulated Arctic cold air outbreaks. A local closure, a profile closure and two nonlocal closure schemes are applied, including an improved scheme, which is based on other nonlocal closures. It accounts for continuous subgrid-scale fluxes at the top of the surface layer and a continuous Prandtl number with respect to stratification. In the limit of neutral stratification the improved scheme gives eddy diffusivities similar to other parameterizations, whereas for strong unstable stratifications they become much larger and thus turbulent transports are more efficient. It is shown by comparison of model results with observations that the application of simple nonlocal closure schemes results in a more realistic simulation of a convective boundary layer than that of a local or a profile closure scheme. Improvements are due to the nonlocal formulation of the eddy diffusivities and to the inclusion of heat transport, which is independent of local gradients (countergradient transport).

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A 3-D poisson solver based on conjugate gradients compared to standard iterative methods and its performance on vector computers

Cited by 30 publications

References 18 publications

A new large-eddy simulation model for simulating air flow and warm clouds above highly complex terrain. Part I: The dry model

A new large-eddy simulation model for simulating air flow and warm clouds above highly complex terrain. Part I: The dry model

A Semi-implicit Semi-Lagrangian Scheme Using the Height Coordinate for a Nonhydrostatic and Fully Elastic Model of Atmospheric Flows

Modelling the arctic convective boundary-layer with different turbulence parameterizations

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