Efficient Hypersonic Heating Rate Prediction for Three-Dimensional Vehicles Using Radial Basis Interpolation

An efficient method for predicting hypersonic heating rates over general three-dimensional vehicles is introduced. The radial basis interpolation method is employed to make the proposed approach applicable to various mesh types, including triangular, quadrilateral, hybrid, and polygonal meshes. The Gaussian kernel is meticulously selected to prevent division by zero errors. Formulas for calculating the metric coefficients required by the axisymmetric analog method along the streamlines are derived, and the procedure for determining the adjustable parameter in the Gaussian kernel function is detailed. Furthermore, the method has been extended to include scenarios involving sideslip angles. The proposed method is validated on configurations that include a bent-nose biconic model, a spherically blunted cone, and a double-ellipsoid model in hypersonic flow. Numerical results indicate that 1) reasonable heating rates, which agree well with experimental measurements, can be predicted using the proposed method; 2) the method is applicable to surfaces with various mesh types, especially polygonal meshes, and therefore offers lower computational costs and enhanced shape applicability; and 3) the proposed method is effective for scenarios involving sideslip angles, making it more suitable for general engineering problems.