Related papers: Least action principle for an integrable shallow w…
We introduce a new minimisation principle for Poisson equation using two variables: the solution and the gradient of the solution. This principle allows us to use any conforming finite element spaces for both variables, where the finite…
We describe the physical hypothesis in which an approximate model of water waves is obtained. For an irrotational unidirectional shallow water flow, we derive the Camassa-Holm equation by a variational approach in the Lagrangian formalism.
A nonlinear sea-ice problem is considered in a least-squares finite element setting. The corresponding variational formulation approximating simultaneously the stress tensor and the velocity is analysed. In particular, the least-squares…
The algebro-geometric approach for integrability of semi-Hamiltonian hydrodynamic type systems is presented. This method is significantly simplified for so-called symmetric hydrodynamic type systems. Plenty interesting and physically…
Backward parabolic equations, such as the backward heat equation, are classical examples of ill-posed problems where solutions may not exist or depend continuously on the data. In this work, we study a least squares finite element method to…
In this paper, we prove the existence and uniqueness of the solutions for the 2D viscous shallow water equations with low regularity assumptions on the initial data as well as the initial height bounded away from zero.
We consider a control system describing the interaction of water waves with a partially immersed rigid body constraint to move only in the vertical direction. The fluid is modeled by the shallow water equations. The control signal is a…
We consider a model of a binary mixture of two immiscible compressible fluids. We propose a numerical scheme and discuss its basic properties: Stability, consistency, convergence. The convergence is established via the method of generalized…
We present a novel discrete velocity kinetic framework to consistently recover the viscous shallow water equations. The proposed model has the following fundamental advantages and novelties: (a) A novel interpretation and general framework…
We adapt the precise definition of the flowing effective action in order to obtain a functional flow equation with simple properties close to physical intuition. The simplified flow equation is invariant under local gauge transformations…
We present a first order scheme based on a staggered grid for the shallow water equations with topography in two space dimensions, which enjoys several properties: positivity of the water height, preservation of constant states, and weak…
In this paper we analyze the convergence of the splitting method for shallow water equations. In particular, we give an analytical estimation of the time step which is necessary for the convergence and then we study the behaviour of the…
A rigorous method for introducing the variational principle describing relativistic ideal hydrodynamic flows with all possible types of breaks (including shocks) is presented in the framework of an exact Clebsch type representation of the…
In spirit of the principle of least action, which means that when a perturbation is applied to a physical system its reaction is such that it modifies its state to "agree" with the perturbation by "minimal" change of its initial state. In…
We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial…
The problem of the description of two interacting particles is considered. It is shown that it can be reduced to the description of one particle in an external static potential even in a relativistic case. The method is based on the…
From Hamilton's principle of stationary action, we derive governing equations of two-fluid mixtures and extend the model to the dissipative case without chemical reactions. For both conservative and dissipative cases, an algebraic identity…
We will discuss various aspects of the incompressible Euler equation. We will discuss, in particular, problems related to the least action principle, the existence of special solutions, the problem of solvability, singularity formation, and…
We propose a two-fold approach to model reduction of fluid-structure interaction. The state equations for the fluid are solved with reduced basis methods. These are model reduction methods for parametric partial differential equations using…
Finite-volume numerical method for study shallow water flows over an arbitrary bed profile in the presence of external force is proposed. This method uses the quasi-two-layer model of hydrodynamic flows over a stepwise boundary with…