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Anisotropic kernels for particle flow simulation
Publikationstyp
Book Part
Date Issued
2023-12-14
Sprache
English
Author(s)
First published in
Number in series
148
Start Page
57
End Page
76
Citation
In: Iske, A., Rung, T. (eds) Modeling, Simulation and Optimization of Fluid Dynamic Applications. Lecture Notes in Computational Science and Engineering, vol 148. Springer, Cham. (2023)
Publisher DOI
Scopus ID
Publisher
Springer
ISBN
978-3-031-45157-7
978-3-031-45158-4
This contribution discusses the construction and the utility of anisotropic kernels for numerical fluid flow simulation. So far, commonly used radial kernels, such as Gaussians, (inverse) multiquadrics and polyharmonic splines, were proven to be powerful tools in various applications of multivariate scattered data approximation. Due to the well-known uncertainty principle, however, their resulting reconstruction methods are often critical when it comes to combine high order approximation with numerical stability. In many cases this leads to severe limitations, especially when it comes to fluid flow simulations. Therefore, more sophisticated kernel methods are required. In this paper, we show how to obtain anisotropic positive definite kernels from standard kernels rather directly. Our proposed construction yields a new class of more flexible kernels that are particularly useful for fluid flow simulations. To this end, the finite volume particle method is used as a prototype of our discussion, where scattered data approximation is needed in the recovery step of weighted essentially non-oscillatory (WENO) reconstructions. Supporting numerical examples and comparisons are provided.
DDC Class
510: Mathematics