Two-dimensional finite element methods

Futerko, P., Hsing, I-M. (2000). Two-dimensional finite-element method study of the resistance of membranes in polymer electrolyte fuel cells. Electrochimica Acta 45,... 

Keywords Differential movement, fall-off of exterior ceramic tile, honeycomb shaped woven net, polymer modified lightweight cement mortar, two dimensional finite element method, woven fiber net... 

For the design of FGM thermoelectric device, it is necessary to get optimum energy conversion efficiencies, and to decrease thermal stresses by the high temperatime difference within the device. In this paper, we describe about the electric property calculation using the band theory, and device efficiency calculation and thermal stress calculation using two dimensional finite element method. 

While most authors have used the finite-difference method, the finite element method has also been used—e.g., a two-dimensional finite element model incorporating shrinkable subdomains was used to de.scribe interroot competition to simulate the uptake of N from the rhizosphere (36). It included a nitrification submodel and found good agreement between ob.served and predicted uptake by onion on a range of soil types. However, while a different method of solution was used, the assumptions and the equations solved were still based on the Barber-Cushman model. 

A computational design procedure of a thermoelectric power device using Functionally Graded Materials (FGM) is presented. A model of thermoelectric materials is presented for transport properties of heavily doped semiconductors, electron and phonon transport coefficients are calculated using band theory. And, a procedure of an elastic thermal stress analysis is presented on a functionally graded thermoelectric device by two-dimensional finite element technique. First, temperature distributions are calculated by two-dimensional non-linear finite element method based on expressions of thermoelectric phenomenon. Next, using temperature distributions, thermal stress distributions are computed by two-dimensional elastic finite element analysis. 

Our current direction is to study dynamical processes in atomic and molecular two- and three-body systems. We use a technique which formally is based on the mathematical theory of dilation analytic functions. Numerically these results axe realized though a fully three-dimensional finite element method applied to a total angular-momentum representation. We here show how generalizations of our previously published two-body methods to three-body systems are possible without formal approximations. 

Abstract A newly developed numerical simulator of two-phase flow using three-dimensional finite element method is presented in this paper. It is described that the fundamental simultaneous equations, the deduction to implicit pressure explicit saturation formulation and their finite element discretization method. Furthermore, its practical application to the numerical simulation project of predicting Horonobe natural gas product is also introduced. 

Umitation by Hght (luminostat y = 1, or photo-limitation y < 1, see Comet, 2010) are presented in Table 2. They are compared with the predictive model calculations presented in this chapter, where the radiative transfer equation was solved using the one-dimensional two-flux approximation for all the simple geometric stmctures of photobioreactors except for reactor PBR 2 (as indicated in Table 2), for which we used the three-dimensional finite element method developed by Comet et al. (1994). As shown in the table, the mean deviation between the experimental results and the model calculation is less than 5% (ie, within the range of the experimental standard deviation), thus confirming the ability of the proposed predictive approach to quantify photobioreactor performance under many conditions of operation. 

The Finite Element Method (FEM) study was performed to calculate the potential distribution of the electric field caused by the change in geometry of the stimualtion site. The smdy was simulated with COMSOL Multiphysics 4.2 . A two dimensional finite element model was created with a cross section of the electrode array in perilymph to evaluate the electric field. For simplicity purpose the three dimensional study was avoided and all the cochlear tissues were considered purely resistive. More details of the FEM analysis study can be found elsewhere [47]. 

Elliptic Equations Elhptic equations can be solved with both finite difference and finite element methods. One-dimensional elhptic problems are two-point boundary value problems. Two- and three-dimensional elliptic problems are often solved with iterative methods when the finite difference method is used and direct methods when the finite element method is used. So there are two aspects to consider howthe equations are discretized to form sets of algebraic equations and howthe algebraic equations are then solved. 

In reality, heat is conducted in all three spatial dimensions. While specific building simulation codes can model the transient and steady-state two-dimensional temperature distribution in building structures using finite-difference or finite-elements methods, conduction is normally modeled one-... 

In the finite element method, Petrov-Galerkin methods are used to minimize the unphysical oscillations. The Petrov-Galerkin method essentially adds a small amount of diffusion in the flow direction to smooth the unphysical oscillations. The amount of diffusion is usually proportional to Ax so that it becomes negligible as the mesh size is reduced. The value of the Petrov-Galerkin method lies in being able to obtain a smooth solution when the mesh size is large, so that the computation is feasible. This is not so crucial in one-dimensional problems, but it is essential in two- and three-dimensional problems and purely hyperbolic problems. 

O.C. Zienkiewicz. Finite Element Methods in Stress Analysis, chapter 13 Iso-parametric and associate elements families for two and three dimensional analysis. Tapir Press, Trondheim, 1969. 

With the great strides in computational fluid mechanics made over the past decades, the current trend is toward applying sophisticated finite element methods. These include both two- and three-dimensional (10-15) methods, which in principle allow the computation of two- or three-dimensional velocity and temperature fields with a variety of boundary... 

The preceding expressions are approximate and based on the assumption of isothermal one-dimensional flow of a Newtonian fluid. Speur et al. (30) studied the full calender gap, two-dimensional flows using finite element methods (FEM), and concluded that the presence of vortices depends on the magnitude of the calender-gap leak flow. 

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