Using radial basis function-generated finite differences (RBF-FD) to solve heat transfer equilibrium problems in domains with interfaces

When thermal diffusivity does not vary smoothly within a computational domain, standard numerical methods for solving heat equilibrium problems often converge to an inaccurate solution. In the present paper, we discuss a mesh-free, radial basis function-generated finite difference (RBF-FD)-based method for designing stencil weights that can be applied directly to data that crosses an interface. The approach produces a very accurate solution when thermal diffusivity varies smoothly on either side of an interface. It continues to produce high-quality results when a region between two interfaces is much smaller that the distance between adjacent discrete data nodes in the domain (as becomes the case for thin, nearly insulating layers). We give several test cases that demonstrate the method solving heat equilibrium problems to 4th-order accuracy in the presence of smoothly-curved interfaces.