相关论文: On pressure boundary conditions for thermoconvecti…

Nonlinear partial differential equations are central to physics, engineering, and finance. Except in a limited number of integrable cases, their solution generally requires numerical methods whose cost becomes prohibitive in…

We consider a boundary value problem for the parabolic Lam\'e type operator being a linearization of the Navier-Stokes' equations for compressible flow of Newtonian fluids. It consists of recovering a vector-function, satisfying the…

We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. The approach is based on the minimization on an integral functional which arises from…

A new formulation of the immersed boundary method, which facilitates accurate simulation of incompressible isothermal and natural convection flows around immersed bodies and which may be applied for accurate linear stability analysis of the…

In this paper, we investigate the effect of boundary surface roughness on numerical simulations of incompressible fluid flow past a cylinder in two and three spatial dimensions furnished with slip boundary conditions. The governing…

The global existence of strong solution to the initial-boundary value problem of the three-dimensional compressible viscoelastic fluids near equilibrium is established in a bounded domain. Uniform estimates in $W^{1,q}$ with $q>3$ on the…

We study the long-time behaviour of the temperature-driven compressible flows. We show that numerical solutions of a structure-preserving finite volume method generate a discrete attractor that consists of entire discrete trajectories.…

We develop an immersed boundary (IB) method for modeling flows around fixed or moving rigid bodies that is suitable for a broad range of Reynolds numbers, including steady Stokes flow. The spatio-temporal discretization of the fluid…

We study unsteady internal flows in a sessile droplet of capillary size evaporating in constant contact line mode on a heated substrate. Three-dimensional simulations of internal flows in evaporating droplets of ethanol and silicone oil…

Recently there has been an increasing interest for a better understanding of ultra low Reynolds number flows. In this context we present a new setup which allows to efficiently solve the stationary incompressible Navier-Stokes equations in…

Despite the physical importance, there are limited mathematical theories for the compressible Navier-Stokes equations with strong boundary layers. This is mainly due to the absence of a stream function structure, unlike the extensively…

We consider an infinite system of quasilinear first-order partial differential equations, generalized to contain spacial integration, which describes an incompressible fluid mixture of infinite components in a line segment whose motion is…

In this paper we establish the incompressible limit for the compressible free-boundary Euler equations with surface tension in the case of a liquid. Compared to the case without surface tension treated recently, the presence of surface…

The exhaustive classification of stationary incompressible flows with constant total pressure of ideal infinitely electrically conducting fluid is given. By introduction of curvilinear coordinates based on streamlines and magnetic lines of…

Rayleigh-Benard convection in a cylindrical container can take on many different spatial forms. Motivated by the results of Hof, Lucas and Mullin [Phys. Fluids 11, 2815 (1999)], who observed coexistence of several stable states at a single…

By means of topological methods, we provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of perturbed Hammerstein integral equations. In order to illustrate our theoretical…

We study boundary conditions applied to the macroscopic dynamics of Newtonian liquids from the view of microscopic particle systems. We assume the existence of microscopic boundary conditions that are uniquely determined from a microscopic…

We consider a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are respectively piecewise constant and affine. We use a projection…

This work is devoted to the theoretical study of the stability of two superposed horizontal liquid layers bounded by two solid planes and subjected to a horizontal temperature gradient. The liquids are supposed to be immiscible with a…

We study coupled non-linear parabolic equations for a fluid described by a material density and a temperature, both functions of space and time. In one dimension, we find some stationary solutions corresponding to fixing the temperature on…