Examination of the upwind (donor-cell) formulation in control volume finite-element methods for fluid flow and heat transfer

The upwind (donor-cell) methodology has been explored in the framework of control volume-based finite-element methods using triangular elements. The key advantage of the upwind procedure is that it ensures positive discretization coefficients and hence a stable numerical analog that avoids any undershoots/overshoots. However, the upwind procedure does increase the cross-wind diffusion. Four test problems are solved to study the performance of the scheme.