An alternative Galerkin formulation for streamline problems

An accurate numerical visualization for streamlines of fluid flows is a fundamental tool in computational fluid dynamics. However, the standard finite element formulation to compute streamlines suffers from the disadvantage of requiring the determination of boundary integrals. This shortcoming requires the implementation of two distinct mappings in the finite element code, one for the interior domain employing two-dimensional elements and another with one-dimensional elements to approximate the boundary domain. We introduce an efficient way to determine the streamlines for the above-mentioned flows, which does not need the computation of contour integrals. In order to illustrate the good performance of the alternative formulation proposed, we capture the streamlines of two classical viscous models: Stokes and Navier-Stokes flows