A [Summary] The control of the power exhaust in tokamaks is still an open issue for the future fusion operations. The heat loads on divertor and limiter PFCs is largely determined by the physics of the Scrape-Off Layer (SOL), and therefore it depends mainly on the geometry of the magnetic surfaces and on the geometry of wall components. A better characterization of the heat exhaust mechanisms requires therefore to improve the capabilities of the transport codes in terms of geometrical description of the wall components and in terms of the description of the magnetic geometry. The possibility of dealing with evolving magnetic configurations becomes also critical: during start-up or control operations, for example, the evolution of particles and heat fluxes is little known, although being critical for the safety of the machine. Hence, among the new capabilities of future transport codes will be the possibility of accurately describe the reactor chamber, and the flexibility with respect the magnetic configuration. In particular, avoiding expensive re-meshing of the computational domain in case of evolving equilibrium is mandatory. In order to fulfill these requirements, in this work a fluid solver based on non-aligned discretization is used to solve the plasma-edge transport equations for density, momentum and energies. Preliminary tests on non-structured meshes and realistic geometries/physical parameters show the pertinency of this novel approach.