Numerical simulation of valley flood using an implicit diffusion wave model

Abstract

In this work, a diffusion wave overland flow model is presented for the efficient resolution of valley flood situations. The spatial discretization is done following an upwind finite volume scheme, applied in a non-structured triangular mesh. An implicit scheme is used for the temporal discretization, which involves the generation of a system of equations, one for each computational cell. The BiConjugate Gradient Stabilized (BiCGStab) method is used for the resolution of the system. The computational efficiency is measured by means of a CPU cost comparison between the explicit and implicit versions of the numerical scheme. In general, the diffusive model benefits from an implicit discretization becoming much more efficient than the explicit versión. Due to the nonlinearity of the diffusive wave equation, larger time steps do not always imply shorter computational times. The optimal time step size must be identified in every new problem. The diffusive wave model has been applied to a valley flooding case proposed by the UK Environmental Agency in order to compare its performance with that provided by commercial models.

Keywords

• Flujo superficial
• Inundación de valles
• Volúmenes finitos
• Modelo difusivo
• Esquemas implícitos