Analysis of a double layer shallow water model with free surface
نویسنده
چکیده
A double layer shallow water model is established, departing from 3D Euler incompressible equations with free surface. On the one hand, the model is augmented with curl, as a new unknown. A result of existence and uniqueness is proved for a smooth initial condition (i.e. in Sobolev spaces) using criteria from [2]. On the other hand, the system without curl is considered. In order to treat more physically relevant solutions (for instance shocks), we study the domain of hyperbolicity of this system. The main difference with rigid lid model is that hyperbolicity is composed of two subdomains. A second order expansion of eigenvalues of the system is performed. We compare numerical results with other publications on this pattern (see [1], [3] or [4]).
منابع مشابه
Numerical Simulation of Free Surface in the Case of Plane Turbulent Wall Jets in Shallow Tailwater
Wall-jet flow is an important flow field in hydraulic engineering, and its applications include flow from the bottom outlet of dams and sluice gates. In this paper, the plane turbulent wall jet in shallow tailwater is simulated by solving the Reynolds Averaged Navier-Stokes equations using the standard turbulence closure model. This study aims to explore the ability of a time splitting method ...
متن کاملLocal Well-posedness of the Multi-layer Shallow Water Model with Free Surface∗
In this paper, we address the question of the hyperbolicity and the local wellposedness of the multi-layer shallow water model, with free surface, in two dimensions. We first provide a general criterion that proves the symmetrizability of this model, which implies hyperbolicity and local well-posedness in Hs(R2), with s > 2. Then, we analyze rigorously the eigenstructure associated to this mode...
متن کاملLocal Well-Posedness of the Two-Layer Shallow Water Model with Free Surface
In this paper, we address the question of the hyperbolicity and the local wellposedness of the two-layer shallow water model, with free surface, in two dimensions. We first provide a general criterion that proves the symmetrizability of this model, which implies hyperbolicity and local well-posedness in Hs(R2), with s > 2. Then, we analyze rigorously the eigenstructure associated to this model ...
متن کاملA Note on Free Vibration of a Double-beam System with Nonlinear Elastic Inner Layer
In this note, small amplitude free vibration of a double-beam system in presence of inner layer nonlinearity is investigated. The nonlinearity is due to inner layer material and is not related to large amplitude vibration. At first, frequencies of a double-beam system with linear inner layer are studied and categorized as synchronous and asynchronous frequencies. It is revealed that the inner l...
متن کاملHyperbolicity of the multi-layer shallow-water model with free surface
Considering n fluids, which are homogeneous, inviscid, incompressible and without surface tension, the 3D Euler equations with long wave assumptions provide the multi-layer shallow-water model with free surface. Since salinity is assumed discontinuous, these equations can be used to describe the oceans. The study of the hyperbolicity of this quasi-linear PDEs system is divided in two parts. Fir...
متن کامل