ON A BI-LAYER SHALLOW WATER MODEL WITH RIGID-LID HYPOTHESIS

Abstract

In this paper, we present a new model for a bi-layer shallow water problem using the rigid-lid hypothesis. This model follows from the usual bi-layer model and can drastically decrease the computational time of simulation. But some mathematical and numerical difficulties appear. Particularly, we observe in the equations some terms in the form of 1/hi (where hi is the thickness of the layer) and we are not able to prove that hi > 0. To circumvent this difficulty, we replace in these terms hi by Hi > β > 0, where Hi is a characteristic thickness of the layer. This hypothesis is realistic if the fluctuations of hi are small, which is generally the case. Then, we prove existence and regularity results for this approximated problem which shows the convergence of the numerical scheme. Next, we present some comparative results in an idealized configuration between this model and the classical bi-layer shallow water model.