Numerical errors in the presence of steep topography [electronic resource] : analysis and alternatives

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Tác giả:

Ngôn ngữ: eng

Ký hiệu phân loại: 621.45 Wind engines

Thông tin xuất bản: Livermore, Calif : Oak Ridge, Tenn. : Lawrence Livermore National Laboratory ; Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 2010

Mô tả vật lý: Size: PDF-file: 21 pages

Bộ sưu tập: Metadata

ID: 259560

It is well known in computational fluid dynamics that grid quality affects the accuracy of numerical solutions. When assessing grid quality, properties such as aspect ratio, orthogonality of coordinate surfaces, and cell volume are considered. Mesoscale atmospheric models generally use terrain-following coordinates with large aspect ratios near the surface. As high resolution numerical simulations are increasingly used to study topographically forced flows, a high degree of non-orthogonality is introduced, especially in the vicinity of steep terrain slopes. Numerical errors associated with the use of terrainfollowing coordinates can adversely effect the accuracy of the solution in steep terrain. Inaccuracies from the coordinate transformation are present in each spatially discretized term of the Navier-Stokes equations, as well as in the conservation equations for scalars. In particular, errors in the computation of horizontal pressure gradients, diffusion, and horizontal advection terms have been noted in the presence of sloping coordinate surfaces and steep topography. In this work we study the effects of these spatial discretization errors on the flow solution for three canonical cases: scalar advection over a mountain, an atmosphere at rest over a hill, and forced advection over a hill. This study is completed using the Weather Research and Forecasting (WRF) model. Simulations with terrain-following coordinates are compared to those using a flat coordinate, where terrain is represented with the immersed boundary method. The immersed boundary method is used as a tool which allows us to eliminate the terrain-following coordinate transformation, and quantify numerical errors through a direct comparison of the two solutions. Additionally, the effects of related issues such as the steepness of terrain slope and grid aspect ratio are studied in an effort to gain an understanding of numerical domains where terrain-following coordinates can successfully be used and those domains where the solution would benefit from the use of the immersed boundary method.
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