Friction decoupling and loss of rotational invariance in flooding models

TL;DR

This paper investigates how friction decoupling in flooding models affects the accuracy and rotational invariance of the results, revealing significant theoretical and numerical drawbacks.

Contribution

It provides a theoretical and numerical analysis showing that friction decoupling reduces force accuracy and causes loss of rotational invariance in flooding models.

Findings

Friction decoupling reduces the computed friction force.

Decoupled models lack rotational invariance.

Classic coupled models are more reliable.

Abstract

Friction decoupling, i.e. the computation of friction vector components making separate use of the corresponding velocity components, is common in staggered grid models of the SWE simplifications (Zero-Inertia and Local Inertia Approximation), due to the programming simplicity and to the consequent calculations speed-up. In the present paper, the effect of friction decoupling has been studied from the theoretical and numerical point of view. First, it has been found that friction vector decoupling causes the reduction of the computed friction force and the rotation of the friction force vector. Second, it has been demonstrated that decoupled-friction models lack of rotational invariance, i.e. model results depend on the alignment of the reference framework. These theoretical results have been confirmed by means of numerical experiments. On this basis, it is evident that the decoupling of the friction vector causes a major loss of credibility of the corresponding mathematical and numerical models. Despite the modest speed-up of decoupled-friction computations, classic coupled-friction models should be preferred in every case.