Variational Finite Element Analysis Research Articles

Soret and Dufour effects on MHD heat and mass transfer flow of a micropolar fluid with thermophoresis particle deposition

The effect of thermophoresis on heat and mass transfer flow of a micropolar fluid in the presence of Soret and Dufour effects past a vertical porous plate have been investigated . The transformed conservation equations are solved numerically using an optimized, extensively validated, variational finite element analysis. The influence of important non-dimensional parameter, Suction parameter ( ), Soret parameter (Sr), Dufour parameter (Du) and thermophoretic parameter (?) on velocity, angular velocity (micro-rotation), temperature and concentration fields as well as shear stress, Nusselt number and Sherwood number are examined in detail and the results are shown in graphically and in tabular form to know the physical importance of the problem. It is found that the imposition of wall fluid suction (V0>0) in this present problem of flow has the effect of depreciating the velocity, micro-rotation, temperature and concentration boundary layer thicknesses at every finite value of ?.

Virtual anthropology meets biomechanics

A meeting in Vienna in October 2010 brought together researchers using Virtual Anthropology (VA) and Finite Element Analysis (FEA) in order to explore the benefits and problems facing a collaboration between the two fields. FEA is used to test mechanical hypotheses in functional anatomy and VA complements and augments this process by virtue of its tools for acquiring data, for segmenting and preparing virtual specimens, and for generating reconstructions and artificial forms. This represents a critical methodological advance because geometry is one of the crucial inputs of FEA and is often the variable of interest in functional anatomy. However, we currently lack tools that quantitatively relate differences in geometry to differences in stress and strain, or that evaluate the impact on FEA of variation within and between biological samples. Thus, when comparing models of different geometry, we do not currently obtain sufficiently informative answers to questions such as “How different are these models, and in what manner are they different? Are they different in some anatomical regions but not others?" New methodologies must be developed in order to maximize the potential of FEA to address questions in comparative and evolutionary biology. In this paper we review these and other important issues that were raised during our Vienna meeting.

Variational analysis for simulating free‐surface flows in a porous medium

A variational formulation has been developed to solve a parabolic partial differential equation describing free‐surface flows in a porous medium. The variational finite element method is used to obtain a discrete form of equations for a two‐dimensional domain. The matrix characteristics and the stability criteria have been investigated to develop a stable numerical algorithm for solving the governing equation. A computer programme has been written to solve a symmetric positive definite system obtained from the variational finite element analysis. The system of equations is solved using the conjugate gradient method. The solution generates time‐varying hydraulic heads in the subsurface. The interfacing free surface between the unsaturated and saturated zones in the variably saturated domain is located, based on the computed hydraulic heads. Example problems are investigated. The finite element solutions are compared with the exact solutions for the example problems. The numerical characteristics of the finite element solution method are also investigated using the example problems.

Variational finite element analysis of dielectric waveguides with no spurious solutions

A new variational formulation for the analysis of dielectric waveguides is presented. This formulation provides a direct solution for the propagation constant using only the transverse components of the magnetic field and avoids spurious solutions. It allows treatment of lossy anisotropic dielectrics and leads to a canonical sparse matrix eigenvalue problem.