Accuracy assessment of inverse-distance weighted interpolation in the immersed boundary method

Inverse-distance weighted (IDW) interpolation has been recommended in the immersed boundary method. The interpolation is simple and flexible. However, its accuracy is still not clear yet. We establish a theorem for the error estimation of the IDW interpolation and assess its numerical accuracy on a Cartesian mesh. The accuracy is evaluated and discussed using several analytical functions. Some numerical examples are presented to illustrate the performance and validate the accuracy using a ghost-cell immersed boundary method. These includes flow past a circular cylinder, flow over a sphere, and oceanic flow around an island. These results show significant improvement in terms of the accuracy and stability.