Abstract
We give a brief review of our recently proposed WENO finite volume method for Cartesian grids (Buchmüller, Helzel, J Sci Comput, 61:343–368, 2014, [3]), (Buchmüller et al. Appl Math Comput, 272:460–478, 2016, [4]), which increases the accuracy of the commonly used so-called dimension-by-dimension approach. The main ingredient is a transformation from high-order accurate interface-averaged values of the conserved quantities to high-order accurate point values. Using these point values of the conserved quantities, we can compute point values of the fluxes at the center of each grid cell interface. Finally, the reverse transformation is used in order to compute high-order accurate face-averaged numerical fluxes that can be used in a finite volume method. While we have recently concentrated on spatially two-dimensional test calculations, we will here present a new three-dimensional test problem, which confirms the accuracy and efficiency of our approach. This test problem, a rotated vortex, should be of general interest to researchers who want to test the accuracy of their three-dimensional schemes.
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Buchmüller, P., Dreher, J., Helzel, C. (2018). Improved Accuracy of High-Order WENO Finite Volume Methods on Cartesian Grids with Adaptive Mesh Refinement. In: Klingenberg, C., Westdickenberg, M. (eds) Theory, Numerics and Applications of Hyperbolic Problems I. HYP 2016. Springer Proceedings in Mathematics & Statistics, vol 236. Springer, Cham. https://doi.org/10.1007/978-3-319-91545-6_21
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DOI: https://doi.org/10.1007/978-3-319-91545-6_21
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