23 resultados para Meshless Method, Meshfree Method, Convection-Diffusion, Convection Dominated, Numerical Analysis
Resumo:
A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.
Resumo:
A two degrees of freedom (2-DOF) actuator capable of producing linear translation, rotary motion, or helical motion would be a desirable asset to the fields of machine tools, robotics, and various apparatuses. In this paper, a novel 2-DOF split-stator induction motor was proposed and electromagnetic structure pa- rameters of the motor were designed and optimized. The feature of the direct-drive 2-DOF induction motor lies in its solid mover ar- rangement. In order to study the complex distribution of the eddy current field on the ferromagnetic cylinder mover and the motor’s operating characteristics, the mathematical model of the proposed motor was established, and characteristics of the motor were ana- lyzed by adopting the permeation depth method (PDM) and finite element method (FEM). The analytical and numerical results from motor simulation clearly show a correlation between the PDM and FEM models. This may be considered as a fair justification for the proposed machine and design tools.
Resumo:
Alginate is widely used as a viscosity enhancer in many different pharmaceutical formulations. The aim of this thesis is to quantitatively describe the functions of this polyelectrolyte in pharmaceutical systems. To do this the techniques used were Viscometry, Light Scattering, Continuous and Oscillatory Shear Rheometry, Numerical Analysis and Diffusion. Molecular characterization of the Alginate was carried out using Viscometry and Light Scattering to determine the molecular weight, the radius of gyration, the second virial coefficient and the Kuhn statistical segment length. The results showed good agreement with similar parameters obtained in previous studies. By blending Alginate with other polyelectrolytes, Xanthan Gum and 'Carbopol', in various proportions and with various methods of low and high shear preparation, a very wide range of dynamic rheological properties was found. Using oscillatory testing, the parameters often varied over several decades of magnitude. It was shown that the determination of the viscous and elastic components is particularly useful in describing the rheological 'profiles' of suspending agent blends and provides a step towards the non-empirical formulation of pharmaceutical disperse systems. Using numerical analysis of equations describing planar diffusion, it was shown that the analysis of drug release profiles alone does not provide unambiguous information about the mechanism of rate control. These principles were applied to the diffusion of Ibuprofen in Calcium Alginate gels. For diffusion in such non-Newtonian systems, emphasis was placed on the use of the elastic as well as the viscous component of viscoelasticity. It was found that the diffusion coefficients were relatively unaffected by increases in polymer concentration up to 5 per cent, yet the elasticities measured by oscillatory shear rheometry were increased. This was interpreted in the light of several theories of diffusion in gels.
Resumo:
In this paper we examine the equilibrium states of periodic finite amplitude flow in a horizontal channel with differential heating between the two rigid boundaries. The solutions to the Navier-Stokes equations are obtained by means of a perturbation method for evaluating the Landau coefficients and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infini- tesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighbourhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable.
Resumo:
The diffusion and convection of a solute suspended in a fluid across porous membranes are known to be reduced compared to those in a bulk solution, owing to the fluid mechanical interaction between the solute and the pore wall as well as steric restriction. If the solute and the pore wall are electrically charged, the electrostatic interaction between them could affect the hindrance to diffusion and convection. In this study, the transport of charged spherical solutes through charged circular cylindrical pores filled with an electrolyte solution containing small ions was studied numerically by using a fluid mechanical and electrostatic model. Based on a mean field theory, the electrostatic interaction energy between the solute and the pore wall was estimated from the Poisson-Boltzmann equation, and the charge effect on the solute transport was examined for the solute and pore wall of like charge. The results were compared with those obtained from the linearized form of the Poisson-Boltzmann equation, i.e.the Debye-Hückel equation. © 2012 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.
Resumo:
The transport of a spherical solute through a long circular cylindrical pore filled with an electrolyte solution is studied numerically, in the presence of constant surface charge on the solute and the pore wall. Fluid dynamic analyses were carried out to calculate the flow field around the solute in the pore to evaluate the drag coefficients exerted on the solute. Electrical potentials around the solute in the electrolyte solution were computed based on a mean-field theory to provide the interaction energy between the charged solute and the pore wall. Combining the results of the fluid dynamic and electrostatic analyses, we estimated the rate of the diffusive and convective transport of the solute across the pore. Although the present estimates of the drag coefficients on the solute suggest more than 10% difference from existing studies, depending on the radius ratio of the solute relative to the pore and the radial position of the solute center in the pore, this difference leads to a minor effect on the hindrance factors. It was found that even at rather large ion concentrations, the repulsive electrostatic interaction between the charged solute and the pore wall of like charge could significantly reduce the transport rate of the solute.
Resumo:
A new 3D implementation of a hybrid model based on the analogy with two-phase hydrodynamics has been developed for the simulation of liquids at microscale. The idea of the method is to smoothly combine the atomistic description in the molecular dynamics zone with the Landau-Lifshitz fluctuating hydrodynamics representation in the rest of the system in the framework of macroscopic conservation laws through the use of a single "zoom-in" user-defined function s that has the meaning of a partial concentration in the two-phase analogy model. In comparison with our previous works, the implementation has been extended to full 3D simulations for a range of atomistic models in GROMACS from argon to water in equilibrium conditions with a constant or a spatially variable function s. Preliminary results of simulating the diffusion of a small peptide in water are also reported.