Solution of the Div-Curl Problem in Generalized Curvilinear Coordinates

We propose a method for solving the div-curl problem on a structured nonorthogonal curvilinear grid. The differential operators are discretized using a MAC-scheme for the unknowns in such a way that the discrete counterparts of the usual vector analysis relations are satisfied. The derived discrete problem is then solved by performing a Helmholtz-type decomposition of the unknown vector field. This allows us to obtain a vector field for which both divergence and curl are satisfied to within machine accuracy. The method is validated for several configurations in two and three dimensions, and its accuracy is numerically checked.