A mass-conservative control volume-finite element method for solving Richards’ equation in heterogeneous porous media

We present a mass-conservative vertex-centred finite volume method for efficiently solving the mixed form of Richards’ equation in heterogeneous porous media. The spatial discretisation is particularly well-suited to heterogeneous media because it produces consistent flux approximations at quadrature points where material properties are continuous. Combined with the method of lines, the spatial discretisation gives a set of differential algebraic equations amenable to solution using higher-order implicit solvers. We investigate the solution of the mixed form using a Jacobian-free inexact Newton solver, which requires the solution of an extra variable for each node in the mesh compared to the pressure-head form. By exploiting the structure of the Jacobian for the mixed form, the size of the preconditioner is reduced to that for the pressure-head form, and there is minimal computational overhead for solving the mixed form. The proposed formulation is tested on two challenging test problems. The solutions from the new formulation offer conservation of mass at least one order of magnitude more accurate than a pressure head formulation, and the higher-order temporal integration significantly improves both the mass balance and computational efficiency of the solution.

A Force-Balanced Control Volume Finite Element Method for Multi-Phase Porous Media Flow Modelling

Peer reviewed

A new control-volume finite-element scheme for heterogeneous porous media : application to the drying of softwood

An improved mesoscopic model is presented for simulating the drying of porous media. The aim of this model is to account for two scales simultaneously: the scale of the whole product and the scale of the heterogeneities of the porous medium. The innovation of this method is the utilization of a new mass-conservative scheme based on the Control-Volume Finite-Element (CV-FE) method that partitions the moisture content field over the individual sub-control volumes surrounding each node within the mesh. Although the new formulation has potential for application across a wide range of transport processes in heterogeneous porous media, the focus here is on applying the model to the drying of small sections of softwood consisting of several growth rings. The results conclude that, when compared to a previously published scheme, only the new mass-conservative formulation correctly captures the true moisture content evolution in the earlywood and latewood components of the growth rings during drying.

A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.

Numeric simulation of pollutant dispersion by a control-volume based on finite element method

The dispersion of pollutants in the environment is an issue of great interest as it directly affects air quality, mainly in large cities. Experimental and numerical tools have been used to predict the behavior of pollutant species dispersion in the atmosphere. A software has been developed based on the control-volume based on the finite element method in order to obtain two-dimensional simulations of Navier-Stokes equations and heat or mass transportation in regions with obstacles, varying position of the pollutant source. Numeric results of some applications were obtained and, whenever possible, compared with literature results showing satisfactory accordance. Copyright (C) 2010 John Wiley & Sons, Ltd.

NUMERICAL SIMULATION of CONVECTION-DIFFUSION PROBLEMS BY THE CONTROL-VOLUME-BASED FINITE-ELEMENT METHOD

This work presents a numerical study of the tri-dimensional convection-diffusion equation by the control-volume-based on finite-element method using quadratic hexahedral elements. Considering that the equation governing this problem in its main variable may represent several properties, including temperature, turbulent kinetic energy, viscous dissipation rate of the turbulent kinetic energy, specific dissipation rate of the turbulent kinetic energy, or even the concentration of a contaminant in a given medium, among others, the wide applicability of this problem is thus evidenced. Three cases of temperature distributions will be studied specifically in this work, in addition to one case of pollutant dispersion upon analysis of the concentration of a contaminant in a fixed flow point. Some comparisons will be carried out against works found in the open literature, while others will be done according to each phenomenon characteristics.

Modal analysis of anisotropic diffused-channel waveguide by a scalar finite element method

A procedure to model optical diffused-channel waveguides is presented in this work. The dielectric waveguides present anisotropic refractive indexes which are calculated from the proton concentration. The proton concentration inside the channel is calculated by the anisotropic 2D-linear diffusion equation and converted to the refractive indexes using mathematical relations obtained from experimental data, the arbitrary refractive index profile is modeled by a. nodal expansion in the base functions. The TE and TM-like propagation properties (effective index) and the electromagnetic fields for well-annealed proton-exchanged (APE) LiNbO3 waveguides are computed by the finite element method.

A finite element method for the Saint-Venant torsion and bending problems for prismatic beams

In this work, we present a finite element formulation for the Saint-Venant torsion and bending problems for prismatic beams. The torsion problem formulation is based on the warping function, and can handle multiply-connected regions (including thin-walled structures), compound and anisotropic bars. Similarly, the bending formulation, which is based on linearized elasticity theory, can handle multiply-connected domains including thin-walled sections. The torsional rigidity and shear centers can be found as special cases of these formulations. Numerical results are presented to show the good coarse-mesh accuracy of both the formulations for both the displacement and stress fields. The stiffness matrices and load vectors (which are similar to those for a variable body force in a conventional structural mechanics problem) in both formulations involve only domain integrals, which makes them simple to implement and computationally efficient. (C) 2014 Elsevier Ltd. All rights reserved.

Wave propagation analysis in laminated composite plates with transverse cracks using the wavelet spectral finite element method

This paper presents a newly developed wavelet spectral finite element (WFSE) model to analyze wave propagation in anisotropic composite laminate with a transverse surface crack penetrating part-through the thickness. The WSFE formulation of the composite laminate, which is based on the first-order shear deformation theory, produces accurate and computationally efficient results for high frequency wave motion. Transverse crack is modeled in wavenumber-frequency domain by introducing bending flexibility of the plate along crack edge. Results for tone burst and impulse excitations show excellent agreement with conventional finite element analysis in Abaqus (R). Problems with multiple cracks are modeled by assembling a number of spectral elements with cracks in frequency-wavenumber domain. Results show partial reflection of the excited wave due to crack at time instances consistent with crack locations. (C) 2014 Elsevier B.V. All rights reserved.

A three-dimensional self-adaptive hp finite element method for the characterization of waveguide discontinuities

We propose the use of a highly-accurate three-dimensional (3D) fully automatic hp-adaptive finite element method (FEM) for the characterization of rectangular waveguide discontinuities. These discontinuities are either the unavoidable result of mechanical/electrical transitions or deliberately introduced in order to perform certain electrical functions in modern communication systems. The proposed numerical method combines the geometrical flexibility of finite elements with an accuracy that is often superior to that provided by semi-analytical methods. It supports anisotropic refinements on irregular meshes with hanging nodes, and isoparametric elements. It makes use of hexahedral elements compatible with high-order H(curl)H(curl) discretizations. The 3D hp-adaptive FEM is applied for the first time to solve a wide range of 3D waveguide discontinuity problems of microwave communication systems in which exponential convergence of the error is observed.

Numerical analysis of the modal coupling at low resonances in a Colombian Andean Bandola in C using the finite element method

The work presented in this thesis is concerned with the dynamical behavior of a CBandola's acoustical box at low resonances -- Two models consisting of two and three coupled oscillators are proposed in order to analyse the response at the first two and three resonances, respectively -- These models describe the first resonances in a bandola as a combination of the lowest modes of vibration of enclosed air, top and back plates -- Physically, the coupling between these elements is caused by the fluid-structure interaction that gives rise to coupled modes of vibration for the assembled resonance box -- In this sense, the coupling in the models is expressed in terms of the ratio of effective areas and masses of the elements which is an useful parameter to control the coupling -- Numerical models are developed for the analysis of modal coupling which is performed using the Finite Element Method -- First, it is analysed the modal behavior of separate elements: enclosed air, top plate and back plate -- This step is important to identify participating modes in the coupling -- Then, a numerical model of the resonance box is used to compute the coupled modes -- The computation of normal modes of vibration was executed in the frequency range of 0-800Hz -- Although the introduced models of coupled oscillators only predict maximum the first three resonances, they also allow to study qualitatively the coupling between the rest of the computed modes in the range -- Considering that dynamic response of a structure can be described in terms of the modal parameters, this work represents, in a good approach, the basic behavior of a CBandola, although experimental measurements are suggested as further work to verify the obtained results and get more information about some characteristics of the coupled modes, for instance, the phase of vibration of the air mode and the radiation e ciency