Search results for "equation"
showing 10 items of 4219 documents
Influence of Confining Walls on the Dynamics of Supercooled Simple Liquids
2003
The relaxation dynamics of supercooled liquids in the bulk shows many features that are not seen in the dynamics of liquids at elevated temperatures, such as a very slow decay of the time-correlation functions, stretching, etc. The dynamics of liquids that are close to a surface (free space, confining wall, etc.) is even more complex in that the stretching is increased and in that there is evidence for the presence of multiple time scales. In this paper we review some results of recent molecular dynamics computer simulations in which we investigated the dynamics of a simple glass forming liquid in the vicinity of a wall. Two types of walls axe studied: A rough one and a smooth one. We find …
Thermal deformations of inhomogeneous elastic plates
1995
We consider thermal deformations of transversally inhomogenous elastic plates. Thin plate equations are derived as limits of full three-dimensional models both in the linear was well as in the non-linear case with appropriate convergence proofs. In the non-linear case also the corresponding von Karman equations are formulated. Its is obtained that the inhomogeneity leads to the loss of some symmetry properties at the von Karman equations
Mathematical and Numerical Analysis of Some FSI Problems
2014
In this chapter we deal with some specific existence and numerical results applied to a 2D/1D fluid–structure coupled model, for an incompressible fluid and a thin elastic structure. We will try to underline some of the mathematical and numerical difficulties that one may face when studying this kind of problems such as the geometrical nonlinearities or the added mass effect. In particular we will point out the link between the strategies of proof of weak or strong solutions and the possible algorithms to discretize these type of coupled problems.
Electrokinetic Phenomena Revisited: A Lattice—Boltzmann Approach
2003
The Lattice-Boltzmann method (LBM) is an efficient tool to solve the Navier-Stokes equations. Based on this method we have developed a scheme to investigate electrokinetic phenomena in charged colloidal suspensions. The equations of motion that are solved are the so-called electrokinetic equations, i.e. a set of partial differential equations that couple the gradient of the electrostatic potential to the hydrodynamic flow by means of a mean field theory. These equations have been extensively used to study electroviscous phenomena for the limit of a weakly charged sphere in an unbounded electrolyte. We demonstrate that our method can be applied beyond these limit. As an example we discuss th…
Coupled Multi-Field Continuum Methods for Porous Media Fracture
2015
The focus of the present contribution is on the numerical modelling of hydraulic fracture in fluid-saturated heterogeneous materials, which can be carried out on a macroscopic scale using extended continuum porous media theories. This accounts for the crack nucleation and propagation, deformation of the solid matrix and change in the flow of the interstitial fluid. In particular, fluid-saturated porous materials basically represent volumetrically interacting solid-fluid aggregates, which are modelled using the Theory of Porous Media. The hydraulic- or tension-induced fracture occurs in the solid matrix and is simulated using a diffusive phase-field modelling approach. This way of fracture t…
Statistical Modeling for the Flow of Short Fibers Composites
1994
Numerical results are given for the flow of fiber composites modelled as suspensions of non spherical particles. In this framework, because the many particles rotate, their state of orientation is described with a statistical approach. We used these methods to compute coupled solutions in which the orientation of the particles is affected by the flow and the flow itself depends on the orientation of the particles. The computation methods involve an augmented lagrangian approach and a streamline upwind petrov galerkin formulation to solve the convective orientation equation.
Collective Excitations in Simple Liquids
2014
The dynamics of simple liquid is discussed by starting from the linearized Navier-Stokes equations. Using these equations expicit formulas for the density- and current-correlation functions are given. Mode-coupling theory is introduced, which gives a constitutive equation between the current-relaxation memory function and the density correlation function. This theory is shown to accurately describe the collective-excitation behavior of simple liquids like liquid metals.
Numerical simulation and analysis of heat and mass transfer processes in metallurgical induction applications
2009
Comprehensive knowledge of the heat and mass transfer processes in the melt of induction applications is required to realize efficient metallurgical processes. Experimental and numerical studies of the melt flow in induction furnaces show that the flow pattern, which comprise several vortexes of the mean flow, and the temperature distribution in the melt are significantly influenced by low-frequency large scale flow oscillations. Two- and three-dimensional hydrodynamic calculations of the melt flow, using two-equation turbulence models based on Reynolds Averaged Navier-Stokes approach, do not predict the large scale periodic flow instabilities obtained from the experimental data. That's why…
Travelling Panels Interacting with External Flow
2013
This chapter is devoted to the analysis of the travelling panel, submerged in axially flowing fluid. In order to accurately model the dynamics and stability of a lightweight moving material, the interaction between the material and the surrounding air must be taken into account somehow. The light weight of the material leads to the inertial contribution of the surrounding air to the acceleration of the material becoming significant. In the small displacement regime, the geometry of the vibrating panel is approximately flat, and hence flow separation is unlikely. We will use the model of potential flow for the fluid. The approach described in this chapter allows for an efficient semi-analyti…
Solving the heat-flow problem with transient relativistic fluid dynamics
2014
Israel-Stewart theory is a causal, stable formulation of relativistic dissipative fluid dynamics. This theory has been shown to give a decent description of the dynamical behavior of a relativistic fluid in cases where shear stress becomes important. In principle, it should also be applicable to situations where heat flow becomes important. However, it has been shown that there are cases where Israel-Stewart theory cannot reproduce phenomena associated with heat flow. In this paper, we derive a relativistic dissipative fluid-dynamical theory from kinetic theory which provides a good description of all dissipative phenomena, including heat flow. We explicitly demonstrate this by comparing th…