径向基函数在高超声速热流插值中支撑点选择的判据研究

Research on criterion of support point selection of radial basis function in hypersonic heat flux interpolation

摘要:

在使用径向基函数进行高超声速热流插值时，为了避免传统单一绝对误差判据选择得到的支撑点在热流较小处插值不准确的问题，提出一种双重误差判据下的径向基函数插值过程。这一过程首先使用绝对误差判据选择一定数量的支撑点，再使用相对误差判据标准选择另一部分点。通过数值实验验证同时采用以绝对误差和相对误差为标准选取支撑点的方法，结果表明：采用双重误差判据可以同时保证了热流较大与较小处的插值精度，尤其能避免传统单一绝对误差判据导致插值结果中容易出现负热流的问题。

Abstract:

In order to avoid the problem that the support points selected by the traditional single absolute error criterion are not interpolated accurately when the heat flux is small when the radial basis function is used for hypersonic heat flux interpolation. In this paper, a radial basis function interpolation procedure with double error criterion is proposed. In this process, the absolute error criterion is used to select a certain number of support points, and then the relative error criterion is used to select another part of points. The numerical experiments show that the double error criterion can ensure the interpolation accuracy at both large and small heat flux and can avoid the problem of negative heat flux which is easy to appear in the interpolation results caused by the traditional single absolute error criterion.