Non-local formulation of heat transfer with phase change in domains with spherical and axial symmetries

Describing heat transfer in domains with strong non-linearities and discontinuities, e.g., propagating fronts between different phases, or growing cracks, is a challenge for classical approaches, where conservation laws are formulated as partial differential equations subsequently solved by discretisation methods such as the finite element method (FEM). An alternative approach for such problems is based on the non-local formulation; a prominent example is peridynamics (PD). Its numerical implementation however demands substantial computational resources for problems of practical interest. In many engineering situations, the problems of interest may be considered with either axial or spherical symmetry. Specialising the non-local description to such situations would decrease the number of PD particles by several orders of magnitude with proportional decrease of the computational time, allowing for analyses of larger domains or with higher resolution as required. This work addresses the need for specialisation by developing bond-based peridynamic formulations for physical problems with axial and spherical symmetries. The development is focused on the problem of heat transfer with phase change. The accuracy of the new non-local description is verified by comparing the computational results for several test problems with analytical solutions where available, or with numerical solutions by the finite element method.