Allen, CB

Rendall, TCS

A greedy method, for choosing an optimum reduced set of control points, is integrated with radial basis function interpolation and evaluated for the purpose of interpolating large volume data sets in CFD. Given a function defined at a set of points, the greedy method selects a small subset of these points that is sufficient to keep the interpolation error at all the remaining points below a chosen bound. This is equivalent to a type of data compression, and would have useful storage, post-processing and computational applications in CFD. To test the method in terms of both the point selection scheme and the suitability of reduced control point volume interpolation, a trial application of the interpolation to velocity fields in CFD volume meshes is considered. To optimise the point selection process, and attempt to be able to capture multiple length scales, a variable support radius formulation has also been included. Structured and unstructured mesh cases are considered for aerofoils, a wing case, and a wing-body case. For smooth volume functions the method is shown to work extremely well, producing accurate velocity interpolations using a very small number of the cells in the mesh. For general complex fields, i.e. non-smooth and including large gradients at multiple length scales, the method is still shown to be effective and, significantly, the accuracy of the method appears independent of mesh size.A greedy method, for choosing an optimum reduced set of control points, is integrated with radial basis function interpolation and evaluated for the purpose of interpolating large volume data sets in CFD. Given a function defined at a set of points, the greedy method selects a small subset of these points that is sufficient to keep the interpolation error at all the remaining points below a chosen bound. This is equivalent to a type of data compression, and would have useful storage, post-processing and computational applications in CFD. To test the method in terms of both the point selection scheme and the suitability of reduced control point volume interpolation, a trial application of the interpolation to velocity fields in CFD volume meshes is considered. To optimise the point selection process, and attempt to be able to capture multiple length scales, a variable support radius formulation has also been included. Structured and unstructured mesh cases are considered for aerofoils, a wing case, and a wing-body case. For smooth volume functions the method is shown to work extremely well, producing accurate velocity interpolations using a very small number of the cells in the mesh. For general complex fields, i.e. non-smooth and including large gradients at multiple length scales, the method is still shown to be effective and, significantly, the accuracy of the method appears independent of mesh size

Evaluation of radial basis functions for CFD volume data interpolation

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