Construction of a peridynamic model for transient advection-diffusion problems

We introduce a transient advection-diffusion peridynamic model using a constructive approach. We verify our model against the classical model in 1D and 2D, and we find that in the limit of the peridynamic horizon going to zero the peridynamic solutions converge to the classical ones. We find that a hybrid between upwind and central models performs better in advection-dominated cases. We compute solutions to sample problems in heterogeneous domains for two different conditions and observe the contrast between the solutions depending on microstructure and material properties. Remarkably, no extra effort was required in producing solutions for the complex, heterogeneous cases.