COMSOL 4.0 multiphysics

Packages to solve boundary value problems are available on the Internet. On the NIST web page http //gams.nist.gov/, choose problem decision tree and then differential and integral equations and then ordinary differential equations and multipoint boundary value problems. On the Netlibweb site http //www.netlib.org/, search on boundary value problem. Any spreadsheet that has an iteration capability can be used with the finite difference method. Some packages for partial differential equations also have a capability for solving one-dimensional boundary value problems [e.g. Comsol Multiphysics (formerly FEMLAB)]. 

Computational fluid dynamics (CFD) programs are more specialized, and most have been designed to solve sets of equations that are appropriate to specific industries. They can then include approximations and correlations for some features that would be difficult to solve for directly. Four major packages widely used are Fluent (http //www.fluent.com/), CFX (now part of ANSYS), Comsol Multiphysics (formerly FEMLAB) (http //www.comsol.com/), and ANSYS (http //www.ansys.com/). Of these, Comsol Multiphysics is particularly useful because it has a convenient graphical-user interface, permits easy mesh generation and refinement (including adaptive mesh refinement), allows the user to add phenomena and equations easily, permits solution by continuation methods (thus enhancing... 

The modeling of the internal pore diffusion of a wax-filled cylindrical single catalyst pore was accomplished by the software Comsol Multiphysics (from Comsol AB, Stockholm, Sweden) as well as by Presto Kinetics (from CiT, Rastede, Germany). Both are numerical differential equation solvers and are based on a three-dimensional finite element method. Presto Kinetics displays the results in the form of diagrams. Comsol Multiphysics, instead, provides a three-dimensional solution of the problem. 

FIGURE 12.2 Concentration profiles of CO, H2, and H20 in a wax-filled pore (Lpore = 6.75-10 4 m > dpartlcle.yl = Lpore-4 = 2.7-10 m) modeled with Presto Kinetics (left) and a three-dimensional concentration profile of H2 modeled with Comsol Multiphysics (right)... 

Due to difficulty in implementing FEMs, commercial software packages like Comsol Multiphysics are often used, since they allow the application of these methods without implementing an in-house finite element code. Specific details of the working and potentialities of Comsol Multiphysics can be found in the programme manuals [6, 7],... 

It must be noted that the Comsol Multiphysics simulation does not take into account the electrochemical reactions occurring at the cathode-electrolyte and electrolyte-anode interfaces, with corresponding activation losses (which will be treated separately in Section 6.2.2). 

Finally, Figure 6.6 shows the colour map of the voltage obtained with Comsol Multiphysics the potential value is higher where the current enters the structure, on the left hand side, while it is lower where the current exits the cell, on the right hand side. 

Model with rotational symmetry for the analysis of materials for DTEGs.The dark grey area was simulated with the commercial FEM-software Comsol Multiphysics. Reprinted from Rettig and Moos (2008b) with permission from Elsevier. 

The normalized nonlinear partial differential equation (Equation [7.12]) was implemented for the rotational symmetric geometry according to Fig. 7.6 into the commercial FEM-program Comsol Multiphysics. The solution of this equation is the distribution of the reduced potential in a gas sensitive grain. 

In this work, the commercial software package Comsol Multiphysics 3.2 (Corn-sol AB, Stockholm, Sweden) was used to solve the system of nonlinear partial differential equations. Apart from predefined built-in applications, this tool enables the user to define and solve PDE systems by finite-element discretization. Taking advantage of the axial symmetry of the problem, the model domain can be simplified to two dimensions. In this domain, a structured quadrilateral mesh... 

In this work, we perform a sensitivity analysis of selected parameters of a commercial 26650 LiFePO/graphite cell and investigate their effect on the simulated impedance spectrum. Basic values such as layer thickness and particle radii are taken from literature and preceding measurements. The model implemented within the commercial Finite Element Method (FEM) software COMSOL Multiphysics is then solved in the frequency domain. To demonstrate the capabilities of this method, variations in state of charge, particle radius, solid state diffusion coefficient and reaction rate are analysed. These parameters evoke characteristic and also unusual properties of the observed impedance spectrum. 

The aforementioned equations are implemented in COMSOL Multiphysics. For the parameter variation the calculation was performed in the frequency domain. So the equations were transformed to frequency domain by applying FFT For implementing a harmonic stimulation, the boundary condition (Eq. 21) is set to a sinusoidal signal. The impedance of the entire cell is given by... 

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]. 

Pettersen, F.J., Hpgetveit, J.O., 2011. From 3D tissue data to impedance using Simpleware ScanFE+IP and COMSOL Multiphysics — a tutorial. J. Electr. Bioimp. 2, 13—32. 

An intrinsic time-dependent one-dimensional (ID) model and a macro two-dimensional (2D) model for the anode of the DMFC are presented in [178]. The two models are based on the dual-site mechanism, which includes the coverage of intermediate species of methanol, OH, and CO on the surface of Pt and Ru. The intrinsic ID model focused on the analysis of the effects of operating temperature, methanol concentration, and overpotential on the transient response. The macro 2D model emphasizes the dimensionless distributions of methanol concentration, overpotential and current density in the CL which were affected by physical parameters such as thickness, specific area, and operating conditions such as temperature, bulk methanol concentration, and overpotential. The models were developed and solved in the PDEs module of COMSOL Multiphysics, giving good agreement with experimental data. The dimensionless distributions of methanol concentration, overpotential, and current density and the efficiency factor were calculated quantitatively. The models can be used to give accurate simulations for the polarizations of methanol fuel cell. 

A short report for the numerical model developed in Chap. 7 is provided. The simulation environment is Comsol Multiphysics 4.4. 

Equations (16.14)-(16.16) are solved using COMSOL Multiphysics [32]. This simulation environment solves the governing conservation equations using the flnite element method [33]. It also readily accommodates introduction of the appropriate form for the permeation flux and its dependence on gas partial pressure. 

To relate the force in Eq. (2.41) to the physical bending of an IPMC sheet, a set of continuum mechanics equations were introduced. These equations are described in the Comsol Multiphysics structural mechanics... 

To validate the used direct- and reverse models, additionally to fitting the experimental data to theoretical (Dodd-Deeds etc) models, also a FEM simulation of the measurement setup (coil above the metal plate) has been done for RRl-3 coil above metal2 (Nordic gold). COMSOL multiphysics-FEM simulation software package has been sued for such simulation. Got by COMSOL impedance results were used as input to the reverse model of Dodd-Deeds etc, and the results (Fig. 16) show the good correspondence of the models. 

Figure 16. Back estimated conductivity from COMSOL multiphysics..

Table 11.1 Linear system solvers available in COMSOL Multiphysics.

COMSOL AB. COMSOL Multiphysics User s Guide, Version 3.4. COMSOL AB, Stockholm 2007. 

A simulative approach for the investigation of particulate induction heating in combination with pol5rmer-pol5rmer composites has been pursued with the help of Comsol Multiphysics... 

---