Related papers: Least action principle for an integrable shallow w…
We consider a layer of an inviscid fluid with free surface which is subject to vertical high-frequency vibrations. We derive three asymptotic systems of equations that describe slowly evolving (in comparison with the vibration frequency)…
We propose a simple algebraic method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid. The problem reduces to consecutively solving three linear partial differential equations for a…
A system of identical particles interacting through an isotropic potential that allows for two preferred interparticle distances is numerically studied. When the parameters of the interaction potential are adequately chosen, the system…
We investigate stationary solutions of a thin-film model for liquid two-layer flows in an energetic formulation that is motivated by its gradient flow structure. The goal is to achieve a rigorous understanding of the contact-angle…
The two-dimensional shallow water equations with a particular bottom and the Coriolis's force $f=f_{0}+\Omega y$ are studied in this paper. The main goal of the paper is to describe all invariant solutions for which the reduced system is a…
We introduce a physically relevant stochastic representation of the rotating shallow water equations. The derivation relies mainly on a stochastic transport principle and on a decomposition of the fluid flow into a large-scale component and…
We propose a method to stabilise a solution to equations describing the interface of thin liquid films falling under gravity with a finite number of actuators and restricted observations. As for many complex systems, full observation of the…
The present work focuses on the numerical approximation of the weak solutions of the shallow water model over a non-flat topography. In particular, we pay close attention to steady solutions with nonzero velocity. The goal of this work is…
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups…
In this article we consider the inhomogeneous incompressible Euler equations describing two fluids with different constant densities under the influence of gravity as a differential inclusion. By considering the relaxation of the…
The shear shallow water model is an extension of the classical shallow water model to include the effects of vertical shear. It is a system of six non-linear hyperbolic PDE with non-conservative products. We develop a high-order entropy…
A model for internal interfacial waves between two layers of fluid in the presence of current and variable bottom is studied in the flat-surface approximation. Fluids are assumed to be incompressible and inviscid. Another assumption is that…
We propose a variational symplectic numerical method for the time integration of dynamical systems issued from the least action principle. We assume a quadratic internal interpolation of the state and we approximate the action in a small…
A minimalist approach to the linear stability problem in fluid dynamics is developed that ensures efficiency by utilizing only the essential elements required to find the eigenvalues for given boundary conditions. It is shown that the…
An equilibrium theory of classical fluids based on the space distribution among the particles is derived in the framework of the energy minimization method. This study is motivated by current difficulties of evaluation of optical properties…
A three-dimensional mathematical model of a viscous incompressible fluid with two stiff particles is investigated in the near-contact regime. When one of the particles approaches the other motionless particle with prescribed translational…
This paper is concerned with a numerical simulation of shape optimization in a two-dimensional viscous incompressible flow governed by Navier--Stokes equations with mixed boundary conditions containing the pressure. The minimization problem…
We consider an abstract functional-differential equation derived from the pressure-less Euler system with variable coefficients that includes several systems of partial differential equations arising in the fluid mechanics. Using the method…
This work investigates the topical problem of balancing the shallow water equations over the bottom steps of different heights. The current approaches in the literature are essentially based on mathematical analysis of the hyperbolic system…
An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equations disintegrates into independent equations for non-resonance systems.…