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Surface Gradient Algorithms for Unstructured Grid Panel Methods

Altena, Thomas Maarten (2024) Surface Gradient Algorithms for Unstructured Grid Panel Methods.

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Abstract:Advanced low-order panel methods based on the internal Dirichlet boundary conditions use piecewise constant source and dipole distributions to model inviscid, incompressible (potential) flow over complex geometries. In these formulations the perturbation velocity tangential to the surface in the nodes is obtained in a post-processing step from the surface gradient of the dipole distribution. Determining the surface gradient for unstructured grid panel methods is challenging with respect to accuracy, computational cost, and data structure complexity. In this research, the focus lies on two numerical approaches to determine the surface gradient at the panel corner points (nodes). In particular the Green-Gauss gradient reconstruction scheme is extensively tested to reconstruct the gradient of both linear and non-linear functions. This is done for structured and (highly) unstructured grids over flat and curved surfaces in 3D space. The tests revealed that linear functions can be represented exactly on flat surface grids, while on highly curved grids, such as over the surface of a sphere, the results reveal that the linear functions cannot be represented exactly anymore by the Green-Gauss method, but they can be approximated with at least first order accuracy on unstructured meshes. The least squares method on the other hand, is able to exactly reconstruct the gradient of linear functions on curved grids.
Item Type:Essay (Master)
Faculty:ET: Engineering Technology
Subject:52 mechanical engineering
Programme:Mechanical Engineering MSc (60439)
Link to this item:https://purl.utwente.nl/essays/101339
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