Numerical Solutions of DCR Problems for Anisotropic FGMs of Spatio-Temporal Dependent Properties and a Source Inclusion

A combined Laplace transform (LT) and domain-boundary element method (DBEM) are utilized to obtain numerical solutions for an unsteady spatio-temporal coefficient diffusion-convection-reaction (DCR) equation with arbitrary initial condition and source terms, addressing problems in a distinct class of anisotropic functionally graded materials (FGMs). The process involves deriving a domain-boundary integral equation by transforming the variable coefficient equation into a constant coefficient equation and applying the Laplace transform. Numerical solutions are then obtained using the standard domain-boundary element method and the Stehfest formula. This study includes cases for compressible or incompressible flows, and demonstrates the accuracy of the numerical solutions.