Coupling of two-dimensional hyperbolic and elliptic equations

We deal with the problem of interfacing an elliptic equation with a hyperbolic one in adjoining two-dimensional domains. We provide proper interface conditions and propose an iterative algorithm that alternates the solution of the elliptic equation and of the hyperbolic one within the respective subdomains. The spectral Chebyshev collocation method is used to discretize the result subproblems. Several numerical tests show that the iterative algorithm is very effective and that the computed solutions are quite accurate. This approach can be successfully applied to computational fluid dynamics problems, such as the simulation of flow around a body.