Abstract
Smoothness-Increasing Accuracy-Conserving (SIAC) filters for Discontinuous Galerkin (DG) methods are designed to increase the smoothness and improve the convergence rate of the DG solution through post-processing. These advantages can be exploited during flow visualization, for example by applying the SIAC filter to DG data before streamline computations. However, introducing these filters in engineering applications can be challenging since the filter is based on a convolution over an area of [(r + ℓ + 1)h]d, where d is the dimension, h is the uniform element length, and r and ℓ depend on the construction of the filter. This can become computationally prohibitive as the dimension increases. However, by exploiting the underlying mathematical framework, this problem can be overcome in order to realize a technique that allows for appropriate filtering along a streamline curve. Numerical experiments of such an idea were proposed in Walfisch et al. (J Sci Comput 38(2):164–184, 2009). Here, we review the introduction of the Line SIAC post-processing filter by Docampo et al. (SIAM J Sci Comput 39(5):A2179–A2200, 2017), which showed how the underlying mathematics can be exploited to make the SIAC filter more tractable and illustrate the promise of LSIAC in assisting in streamline visualization.
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Acknowledgements
This research was sponsored by the European Office of Aerospace Research and Development (EOARD) under the U.S. Air Force Office of Scientific Research (AFOSR) under grant number FA8655-13-1-3017.
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Ryan, J.K., Docampo-Sanchez, J. (2020). One-Dimensional Line SIAC Filtering for Multi-Dimensions: Applications to Streamline Visualization. In: van Brummelen, H., Corsini, A., Perotto, S., Rozza, G. (eds) Numerical Methods for Flows. Lecture Notes in Computational Science and Engineering, vol 132. Springer, Cham. https://doi.org/10.1007/978-3-030-30705-9_13
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