A novel inversion approach for identifying the shape of cavity by combining Gappy POD with direct inversion scheme

Abstract

A novel inversion method is proposed for the identification of cavity shape by combining Gappy proper orthogonal decomposition (POD) with a direct inversion scheme. Firstly, the virtual boundary is introduced to construct a new computing domain, and the virtual boundary condition formed by polynomial of increasing order one by one is imposed on the virtual boundary, and then the needed snapshot to generate the POD vector is calculated with the boundary element method (BEM). Secondly, the full-field temperature data are reconstructed by Gappy POD using partial measurement data. Finally, the shape of cavity is identified by searching the isothermal. In order to improve the ability of the proposed method to adapt to the inversion of complex geometry problems, we propose an adaptive modified virtual boundary technique. Numerical examples show that the present method even for complex geometry such as pear shape, can not only obtain high precision inversion results, but also has a good tolerance of noise.