This chapter presents TETHYS, a specialized simulation tool developed to study the hydrodynamic behaviour of graphene-based systems. TETHYS implements a set of governing equations derived from the hydrodynamic theory of two-dimensional electron systems, enabling detailed exploration of the electrohydrodynamics in Dirac materials. The chapter describes the numerical methods employed in the simulations, tailored to handle the unique properties of graphene’s electron flow. Various boundary conditions and numerical implementations are discussed, providing a comprehensive understanding of the simulation environment. The program is demonstrated with examples such as the Dyakonov-Shur instability and pulsatile electric flows, which showcase its capability to accurately simulate nonlinear and unstable behaviors in graphene systems. The chapter also highlights the importance of such tools in studying the dynamic behaviour of collective modes in 2D materials, offering insights into the development of novel electronic and photonic devices based on the principles of hydrodynamic instabilities.