一种保持二阶精度的反距离加权空间插值算法

An Inverse Distance Weighting Spatial Interpolation Algorithm with Second Order Accuracy

针对传统反距离加权(IDW)插值精度较低的缺陷,发展一种高精度插值算法.该插值算法采用迭代亏量校正技术(IDeC)对一次反距离加权插值结果进行修正,通过有限次迭代,理论上将计算精度提高至二阶.在基于结构化网格、非结构化网格的数值验证中,该插值算法的计算精度均保持在二阶左右.应用该算法针对二维圆形和三维球形界面重构时,算法提高了重构界面的光滑度,且计算精度保持为二阶.双层网格插值实验中,算法将速度和压力的绝对误差降低45%以上,得到的压力等值线更接近于初始场.

For low precision of traditional inverse distance weighting(IDW)interpolation,a high-precision interpolation algorithm is developed.Iterative defect correction(IDeC)is applied to correct IDW result,with which a second order accuracy is achieved theoretically within finite iterations.Numerical validations based on structured and unstructured grid are performed.It shows that,with this algorithm the second order accuracy is kept.Furthermore,the algorithm is adopted to surface reconstruction of a 2 D circle and a 3 D sphere,in which smoothness of reconstructed surface is improved and second order accuracy is maintained.In a two-layer mesh interpolation experiment,absolute error of velocity and pressure is reduced by more than 45%,and pressure contours are closer to the initial field.