A thermo-chemo-electro-mechanical formulation of quasi-static finite deformation of swelling incompressible porous media is derived from a mixture theory including the volume fraction concept. The model consists of an electrically charged porous solid saturated with an ionic solution. Incompressible deformation is assumed. The mixture as a whole is assumed locally electroneutral. Different cons...

Lattice Boltzmann equations using multiple relaxation times are intended to be more stable than those using a single relaxation time. The additional relaxation times may be adjusted to suppress non-hydrodynamic modes that do not appear directly in the continuum equations, but may contribute to instabilities on the grid scale. If these relaxation times are fixed in lattice units, as in previous ...

Statement of problem on vortical inviscid flow of barotropic and incompressible fluids. Abstract The question what information is necessary for determination of a unique solution of hydrodynamic equations for ideal fluid is investigated. Arbitrary inviscid flows of the barotropic fluid and of incompressible fluid are considered. After integrating hydrodynamic equations, all information on the f...

In this paper we will present a numerical method for computing incompressible free surface ows in irregular ge ometries in three dimensions The approach we are taking is based on three ideas The rst is the second order ac curate projection method of Bell Colella and Glaz Bell et al for computing nite di erence approximations to the incompressible ow equations on rectangular grids The second is ...

We describe probably the simplest 3-manifold which contains closed separating incompressible surfaces of arbitrarily large genus. Two applications of this observation are given. (1) For any closed, orientable 3-manifold M and any integer m> 0, a surgery on a link inM of at most 2m+1 components will provide a closed, orientable, irreducible 3-manifold containing m disjoint, non-parallel, separat...

Experimental results of sharp edge potentials in the quantum Hall (QH) regime of a two-dimensional electron system are presented. First the general QH edge state picture is reviewed, including recent theory which explains the importance of incompressible strips at the sample edge. Then two sharp edge geometries are presented where incompressible strips are predicted to vanish below the scale of...

This paper presents the development of a 2D high-order solver with spectral difference method for unsteady incompressible Navier–Stokes equations accelerated by a p-multigrid method. This solver is designed for unstructured quadrilateral elements. Time-marching methods cannot be applied directly to incompressible flows because the governing equations are not hyperbolic. An artificial compressib...

Abstract: In this paper, we consider the inviscid limit of the incompressible Navier-Stokes equations in a smooth, bounded and simply connected domain Ω ⊂ R, d = 2, 3. We prove that for a vortex patch initial data the weak Leray solutions of the incompressible Navier-Stokes equations with Navier boundary conditions will converge (locally in time for d = 3 and globally in time for d = 2) to a vo...

We prove that there exists no self-similar finite time blowing up solution to the 3D incompressible Euler equations. The proof uses the vorticity transport formula represented in terms of the back to label map. By similar method we also show nonexistence of self-similar blowing up solutions to the divergence-free transport equation in R. This result has direct applications to the density depend...

The paper demonstrates that enhanced stability properties of some finite element methods on barycenter refined meshes enables efficient numerical treatment of problems involving incompressible or nearly incompressible media. One example is the linear elasticity problem in a pure displacement formulation, where a lower order finite element method is studied which is optimal order accurate and ro...