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High Order Accurate and Efficient Computation Via Wavelet Transformation Method

Hyungmin Kang, Dohyung Lee

Abstract


An adaptive wavelet transformation method with high order accuracy is proposed to enable efficient and accurate flow computations. The main algorithm is as follows; 3rd order of wavelet decomposition and thresholding are applied to a CFD dataset and the positions of crucial features in the dataset are searched with maintaining the original numerical accuracy of a conventional solver and the dataset is automatically adapted to local features of a solution. After the wavelet transformation, 3rd order spatial and temporal accurate high order interpolation scheme with Multidimensional Limiting Process (MLP) are performed only at the included points in the adapted dataset. In the other
points, high order of interpolation method is utilized in order to construct residual values. This high order interpolation scheme with high order adaptive wavelet transformation was applied to unsteady Euler flow computations. Through these processes, both computational efficiency and
numerical accuracy are guaranteed in case of high order accurate unsteady flow computations.

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References


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DOI: http://dx.doi.org/10.21535%2FProICIUS.2010.v6.481

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