AbstractA mathematical model and a numerical method for studying two-dimensional plane gas flows through thermal accumulators based on granular or capsular phase change materials (PCMs) are proposed. The considered objects are modeled as porous media with phase transitions occurring in the condensed component. The study is based on methods of heterogeneous continuum mechanics without detailing the processes inside individual particles. The proposed numerical method combines explicit and implicit finite-difference schemes. The method is described in detail, and its convergence is experimentally analyzed. The heating of smoothly narrowing and smoothly expanding thermal accumulators consisting of granular PCM is studied. It is shown that heating in such objects near the inclined walls occurs more slowly than in their central part even in the absence of heat transfer through the sidewalls.