Abstract
In this contribution we describe a numerical method based on the application of a mesh free interpolation technique (Moving Least Squares (MLS)) for the development of a higher-order finite volume discretization useful on structured and unstructured grids. With this procedure it is possible to build a higher-order scheme in which the computation of the derivatives is performed in a truly three-dimensional way. We use a MLS approach to compute the successive derivatives needed for the approximation of variables at element interfaces using Taylor series. Due to the use of cubic (or higher) reconstructions with the MLS technique, viscous fluxes are also approximated with higher-order accuracy and can be directly computed at edges.
The higher-order accuracy achieved by this method makes it suitable for aeroacoustics problems and DNS and LES of turbulent flows. One of the advantages of the use of the meshfree method on a finite volume framework is that it is possible to exploit all the shock capturing techniques developed for finite volume methods, allowing the computation of compressible flows. Moreover, we also present the application of this interpolation technique to shock detection. We make use of its connection with wavelets, and develop a technique we believe superior to traditional shock capturing methods. This application could be included in a very natural way in the computations with the method presented herein.
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Nogueira, X., Cueto-Felgueroso, L., Colominas, I., Navarrina, F., Casteleiro, M. (2008). A Higher-Order Finite Volume Method Using Multiresolution Reproducing Kernels. In: Griebel, M., Schweitzer, M.A. (eds) Meshfree Methods for Partial Differential Equations IV. Lecture Notes in Computational Science and Engineering, vol 65. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79994-8_10
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DOI: https://doi.org/10.1007/978-3-540-79994-8_10
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