Abstract
After recalling the most classical multiple flow direction algorithms (MFD), we establish their equivalence with a well chosen discretization of Manning–Strickler models for water flow. From this analogy, we derive a new MFD algorithm that remains valid on general, possibly non conforming meshes. We also derive a convergence theory for MFD algorithms based on the Manning–Strickler models. Numerical experiments illustrate the good behavior of the method even on distorted meshes.
Highlights
Overland water flow plays a major role in hydrogeology at many time scales, from million of years for stratigraphic studies of interest for the oil and gas industry to several days or weeks for predicting river flooding and landslides
From the equivalence between the multiple flow directions algorithms (MFD) algorithms and the two-point flux approximation (TPFA) scheme for the stationary Manning– Strickler model, an obvious way of generalizing MFD algorithms to general meshes consists in replacing the TPFA flux reconstruction formula by more advanced flux reconstruction techniques that are still valid on general meshes
We have established the equivalence between a classical family of multiple flow direction algorithms and the TPFA scheme applied to a family of stationary Manning–Strickler models
Summary
Overland water flow plays a major role in hydrogeology at many time scales, from million of years for stratigraphic studies of interest for the oil and gas industry to several days or weeks for predicting river flooding and landslides. It was clear that replacing the TPFA scheme that requires a strong orthogonality hypothesis on meshes to remain valid by more advanced flux approximation schemes would allow us to derive MFD algorithms adapted to general meshes This equivalence will allow us to derive a theoretical framework within which we will be able to study the convergence properties of MFD algorithms. The paper will be organized as follows: after describing the data and meshes, we recall the most classical multiple flow direction algorithms, and reformulate them in a more algebraic fashion Using this reformulation we explain how they are linked with the TPFA scheme for a family of Manning–Strickler models. We study the convergence properties of all methods and conclude by some numerical illustrations
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