Related papers: Geometric microcanonical theory of two-dimensional…
Fluid turbulence is a far-from-equilibrium phenomenon and remains one of the most challenging problems in physics. Two-dimensional, fully developed turbulence may possess the largest possible symmetry, the conformal symmetry. We focus on…
In the present paper, microcanonical measures for the dynamics of three dimensional (3D) axially symmetric turbulent flows with swirl in a Taylor-Couette geometry are defined, using an analogy with a long-range lattice model. We compute the…
A simplified thermodynamic approach of the incompressible 2D Euler equation is considered based on the conservation of energy, circulation and microscopic enstrophy. Statistical equilibrium states are obtained by maximizing the…
An ensemble model of turbulence is proposed. The ensemble consists of flow fields in which the flux of an inviscid conserved quantity, such as energy (or enstrophy in two-dimensional flow fields), across the wavenumber $k$ is a constant…
In this paper, we will provide the the finite element method for the electro-osmotic flow in micro-channels, in which a convection-diffusion type equation is given for the charge density $\rho^e$. A time-discrete method based on the…
Using numerical simulations, we show that the asymptotic states of two-dimensional (2D) Euler turbulence exhibit large-scale flow structures due to nonzero energy transfers among small wavenumber modes. These asymptotic states, which depend…
We prove the conservation of energy for weak and statistical solutions of the two-dimensional Euler equations, generated as strong (in an appropriate topology) limits of the underlying Navier-Stokes equations and a Monte Carlo-Spectral…
An inviscid two-dimensional fluid model with nonlinear dispersion that arises simultaneously in coarse-grained descriptions of the dynamics of the Euler equation and in the description of non-Newtonian fluids of second grade is considered.…
We develop structure-preserving numerical methods for the compressible Euler equations, employing potential temperature as a prognostic variable. We construct three numerical fluxes designed to ensure the conservation of entropy and total…
This paper introduces multidimensional algorithms for simulating multiphase flows, leveraging the wave structure of the Euler equations in characteristic space and the physical properties of variables in physical space. The algorithm…
Numerical simulations of large scale geophysical flows typically require unphysically strong dissipation for numerical stability. Towards energetic balance various schemes have been devised to re-inject this energy, in particular by…
In this paper, we first construct a model for free surface flows that takes into account the air entrainment by a system of four partial differential equations. We derive it by taking averaged values of gas and fluid velocities on the cross…
The aim of this article is to study the limiting behavior of the solutions for the scaled generalized Euler equations of compressible fluid flow. When the initial data is of Riemann type, we showed the existence of solution which consists…
Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the…
The 2D Euler equations is the basic example of fluid models for which a microcanical measure can be constructed from first principles. This measure is defined through finite-dimensional approximations and a limiting procedure. Creutz's…
We consider the Euler equation of quasi-geostrophic fluids which is widely used in weather forecast. Our goal is to study explicit volume-preserving numerical methods for very long simulations on an energy and enstrophy preserving…
General conservation equations are derived for 2D dense granular flows from the Euler equation within the Boussinesq approximation. In steady flows, the 2D fields of granular temperature, vorticity and stream function are shown to be…
We consider Canonical Gibbsian ensembles of Euler point vortices on the 2-dimensional torus or in a bounded domain of R 2 . We prove that under the Central Limit scaling of vortices intensities, and provided that the system has zero global…
In this paper, we proved the well-posedness theory of compressible subsonic jet flows for two-dimensional steady Euler system with {\it general} incoming horizontal velocity as long as the flux is larger than a critical value. One of the…
It has recently been shown, by application of statistical mechanical methods to determine the canonical ensemble governing the equilibrium distribution of operator initial values, that complex quantum field theory can emerge as a…