A Numerical Scheme for the Solution of the Vector Parabolic Equation Governing the Radio Wave Propagation in Straight and Curved Rectangular Tunnels

A high-frequency field prediction model, useful to evaluate the radio wave propagation in realistic tunnels having rectangular cross-section, is presented. The model is based on a hybrid implicit/explicit finite-difference numerical scheme adopted to solve the vector parabolic equation (VPE) governing the electromagnetic field propagation in straight and curved tunnels. To model the materials forming the tunnel walls, mixed Dirichlet-Von Neumann boundary conditions are employed. In this way, all the relevant field propagation processes are properly taken into account. To show the feasibility of the proposed numerical method, results concerning the spatial distribution of the electromagnetic field and the power flux in straight and curved rectangular tunnels are provided. An analysis concerning the convergence properties of the proposed numerical scheme is also reported.