Radiation Transport Equation Solving in Mediums with Voids. Specialized Algorithm in (x,y) Geometry

Special algorithm for numerical solution of transport equation in (x,y) geometry in vacuum cavity of arbitrary configuration is developed. Algorithm is based on opportunity to solve this equation in void analytically. Method is balance, positive and monotone, it meets some qualitative properties of solution correctly. The algorithm is local: when it calculates each cell, it uses information about presence or absence vacuum only in neighboring cells.