COMSOL software

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. 

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],... 

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. 

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. 

Most solutions found by solving the complete set of piezoelectric material equations are very simple approximations. Computation, typically using finite element analysis software, is often necessary for practical cases. The ability to handle piezoelectric materials in commercially available finite element analysis software varies, though ANSYS (ANSYS Inc., Canonsburg, PA, USA) and COMSOL (COMSOL Inc.,... 

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. 

The emergence of personal computing toward the end of the 1980s marks the beginning of widespread CFD-based software modeling tools. Such software tools, popular in scientific and engineering communities, are commercial software tools, such as ACE+ Suite, ANSYS CFX , ANSYS Fluent , ANSYS Multiphysics , COMSOL Multiphysics , FLOW-3D , STAR-CD and STAR-CCM+ , and an open-source software tool OpenFOAM . Other CFD-based software tools, such as AVL FIRE or ANSYS Polyflow , are also available on the market, but they are... 

Commercially available discretization methods for solving complex real-world physical systems are predominantly based on finite volume method and finite element method. The most widely used commercial software tools, such as ANSYS Fluent , STAR-CD , and STAR-CCM+ , are based on finite volume method, whereas ANSYS CFX uses finite element-based control volume method. On the other hand, COMSOL Multiphysics is based on finite element method. Both methods have advantages and disadvantages, but nevertheless they give enough comparable computational results with real-world physical systems. 

With the advance of software engineering, commercially available CFD and multiphysics-based software modeling tools, such as ANSYS CFX , ANSYS Fluent , ANSYS Multiphysics , COMSOL Multiphysics , STAR-CD , or STAR-CCM-t , have sophisticated postprocessing and visualization units incorporated in their products. There are also available stand-alone visualization units, such as ANSYS CFD-Post , AVS/Express , EnSight , or Tecplot 360 , developed by software companies with a specialism in visualization software tools. 

This section applies conservation equations, explained in Section 6.2, to three real-world physical systems. It shows a step-by-step computational modeling approach of three conventional chemical multiphysics systems. The first case study is a 3D computational model of a laminar static mixer with twisted blades, the second case study is a 3D computational model of a porous reactor with injection needle, and the last case study is a 3D model of an isothermal heat exchanger. All three case studies are computationally modeled and simulated with one of the commercial software tools COMSOL Multiphysics , the CFD and multiphysics modeling software tool developed by COMSOL AB from Sweden. 

The solution of the steady state problem described above was performed using the commercial software COMSOL Multiphysics v 3.5a. The numerical technique used by that software is the Finite Element Method (FEM). The shape functions, chosen for the simulation, are Lagrange quadratic shape functions. 

For a sufficiently fine subdivision of the body, it is possible to find a suitably exact solution of the heat conduction problem. Several FEM software packages are available on the market. The ANSYS and the COMSOL systems are often used by calorimeter-developing corporations. The software can be used to define the time-dependent heat flux curves at any site of the calorimeter system and also to indicate the temperature field if this is necessary for the purposes of the discussion and for a better understanding including heat leaks of all kinds. 

Fortunately there are software programs these days that can be given the PDEs, boundary conditions, and input parameters, and will set up and solve the required equations. One such program, used for the examples in this chapter, is Comsol Multiphysics (Stockholm, Sweden). 

The MEMEPhys numerical algorithm was developed by combining a C language code with Matlab-Simulink and Comsol Multiphysics commercial software. This algorithm contains an in-house temporal multi-scale solver (variable time step) developed by the author, which allows management of simultaneously simulated processes occurring at different time scales (e.g. 

The IDA generator-collector system has been simulated using the Laasonen (BI) scheme [374], explicit FD [375, 376], hopscotch and conformal mapping [220], the finite analytic numerical method [152], extrapolation using expanding space intervals [332] and ADI with expanding space intervals [348, 377]. Commercial FEM software packages Flux-Expert [324] and COMSOL Multiphysics [378] have also been employed. 

For more complex geometries in two- and three-dimensional space FEM or BEM might be a choice, especially if one has access to commercial FEM software such as ANSYS or COMSOL Multiphysics . In any case, for commercial packages, convergency tests are still necessary to gain insight into the quality of the simulation. 

Dickinson EJF, Ekstrdm H, Fontes E (2014) COMSOL Multiphysics finite element software for electrochemical analysis. A mini-review. Electrochem Commun 40 71-74... 

One have calculated temperature in the computing cell with a finite element software Comsol using a steady state heat conduction model. Using eq.(l), ETC values are deduced (fig. 5). For simple cubic arrangement of particles, it is shown that the ETC increase cannot be more than 14 times higher than the matrix conductivity and that having a matrix /filler thermal conductivity ratio smaller than 10 is not worth for ETC improvment. 

COMSOL. The COMSOL Multiphysics software is a partial differential equation solver that is used with DVD Chapter 15 to view both axial and radial temperature and concentration profiles. For users of this text, COMSOL has provided a special Web site that includes a step-by-step tutorial, along with examples. See wH w.comsol.com/ecre. 

---