A conservative finite elements approach to overland flow: the control volume finite element formulation

Abstract

This paper proposes the control volume finite element (CVFE) method, a locally conservative formulation of the better known finite elements (FE) approach, to deal more effectively with overland flow. The two-dimensional overland flow problem is introduced and several approaches available in the literature are briefly reported. The partial differential equations describing overland and channel processes are then presented and a consistent two-dimensional formulation for the head losses is introduced. The derivation of the CVFE discrete formulation is preceded by a discussion on the classical integrated finite difference (IFD) and FE approaches, together with their advantages and disadvantages. The CVFE formulation is shown to improve on both approaches, resulting in a better representation of the gradients than that of the IFD approach and, in contrast to the FE, allows for the conservation of mass at local scale. The preliminary results obtained with a CVFE computer code are presented and compared with analytical solutions. Finally, several computational aspects are discussed, such as the formulation of the time integration, the representation of the water volumes pertaining to each node of the space discretization mesh and the explicit imposition of the local mass balance.