NUMERICAL RESOLUTION OF THE DIVERGENCE-CU RL PROBLEM IN GENERALIZED CURVILINEAR COORDINATES

We present a numerical algorithm for solving the divergence-curl probl em for which the vector field is split using a Helmholtz decomposition . Consequently, the solution method proceeds in two steps: first, find a vector field that has the desired curl; then solve a Poisson equati on with Neumann-type boundary conditions. The definition of the discre te differential operators allows us to satisfy the usual vector identi ties of the continuum. A discrete equivalence between the original pro blem and the proposed method is demonstrated.