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Spatial Computational Modes in the Centered Finite-Differencing Schemes

Chungu LuNOAA/OAR/Forecast Systems Laboratory, Boulder, Colorado, and Cooperative Institute for Research in the Atmosphere, Colorado State University, Fort Collins, Colorado

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Yuanfu XieNOAA/OAR/Forecast Systems Laboratory, Boulder, Colorado, and Cooperative Institute for Research in the Atmosphere, Colorado State University, Fort Collins, Colorado

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Abstract

The computational modes associated with a centered finite-differencing scheme in space are studied. The existence and impact of these computational modes in a numerical solution are demonstrated with the use of theoretical analyses and numerical experiments.

The results show that the computational modes due to a spatial discretization can have a detrimental effect on the numerical solution in situations where flows are evolved near shock (or having large spatial derivative). The numerical diffusion can reduce the impact of the computational modes, but can also impose an adverse effect on the physical modes.

Corresponding author address: Dr. Chungu Lu, NOAA/OAR/Forecast Systems Laboratory, Boulder, CO 80303.

Email: lu@fsl.noaa.gov

Abstract

The computational modes associated with a centered finite-differencing scheme in space are studied. The existence and impact of these computational modes in a numerical solution are demonstrated with the use of theoretical analyses and numerical experiments.

The results show that the computational modes due to a spatial discretization can have a detrimental effect on the numerical solution in situations where flows are evolved near shock (or having large spatial derivative). The numerical diffusion can reduce the impact of the computational modes, but can also impose an adverse effect on the physical modes.

Corresponding author address: Dr. Chungu Lu, NOAA/OAR/Forecast Systems Laboratory, Boulder, CO 80303.

Email: lu@fsl.noaa.gov

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