Study on the inverse problem of central temperature of nuclear explosion in polar coordinates

This paper investigates the inverse problem of reconstructing the temperature at the center of a nuclear explosion using temperature observation data at different times within a polar coordinate system. The model possesses a singularity at r=0, which increases the difficulty of both theoretical analysis and numerical solution. Firstly, based on the physical characteristics of nuclear explosions, a heat conduction equation incorporating this singularity is established and discretized using numerical integration and the finite difference method, respectively. Secondly, for solving this inverse problem, an improved Landweber regularization iterative algorithm is proposed to invert the temperature at the explosion center and obtain numerical solutions. Numerical examples demonstrate that this method is stable and efficient. It can successfully reconstruct the temperature distribution at the explosion center and effectively handle the complex variations in different time and space scales present in nuclear explosions. Its noise resistance capability shows marked superiority over the traditional Landweber method.