Summary
A numerical scheme for solving the Euler equations on locally h-adaptive grids with hanging nodes in two space dimensions is presented. The method consists of an integrated framework, including a novel grid generation technique using B-Splines, advanced adaptation criteria based on multiscale analysis and a flow solver which is capable to operate on arbitrary unstructured meshes with polygonal elements. An implicit finite volume method is developed to solve the conservation laws, employing a higher-order upwind scheme for the conservative fluxes. A variety of examples for stationary, inviscid flows have been studied to validate the new method. Firstly, the subsonic and transonic flow in a channel with a circular arc bump is investigated to assess the perfomance of the implicit scheme and to demonstrate the quality of the solution obtained with the adaptive algorithm. Secondly, the flow around a wing section has been considered in subsonic Mach number regime to study the advantage of the present method for smooth flows.
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Bramkamp, F., Ballmann, J. (2002). Solution of the Euler Equations on Locally Adaptive B-Spline Grids. In: Wagner, S., Rist, U., Heinemann, HJ., Hilbig, R. (eds) New Results in Numerical and Experimental Fluid Mechanics III. Notes on Numerical Fluid Mechanics (NNFM), vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45466-3_34
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DOI: https://doi.org/10.1007/978-3-540-45466-3_34
Publisher Name: Springer, Berlin, Heidelberg
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