Molecular communication (MC) is a promising paradigm for information transmission in complex environments, such as living cells and porous media. While most existing works consider standard diffusion, where the mean square displacement (MSD) of information molecules (IMs) scales linearly with time, this dissertation focuses on sub-diffusive dynamics in crowded and complex environments. The primary objectives of this research are to model, simulate, and analyze the performance of MC systems in sub-diffusive environments.

With the algorithm's suitability for exploiting current petascale and next-generation exascale supercomputers, stable and structure-preserving properties are necessary to develop predictive computational tools. This dissertation uses the mimetic properties of SBP-SAT operators and the structure-preserving property of a new relaxation procedure for Runge--Kutta schemes to construct nonlinearly stable full discretizations for non-reactive compressible computational fluid dynamics (CFD) and reaction-diffusion models.