## Guidelines for Equation-Based Modeling in Axisymmetric Components

##### Temesgen Kindo October 5, 2016

Cylindrical coordinates are useful for efficiently solving and postprocessing rotationally symmetric problems. The COMSOL Multiphysics® software has built-in support for cylindrical coordinates in the axisymmetry physics interfaces. When defining custom partial differential equations (PDEs) using the mathematical interfaces, paying close attention to their meaning is important. The PDE interfaces assume partial differentiation in a Cartesian system, requiring manual coordinate transformations to change to a cylindrical system. See how to account for such coordinate transformations when using your own PDEs.

Read More##### Caty Fairclough May 9, 2016

Have you ever wondered how tigers develop their stripes? Alan Turing’s theory of morphogenesis offers one possible explanation for this occurrence, suggesting that patterns, such as stripes, develop naturally from initially homogeneous states. Today, we’ll take a closer look at Turing’s theory and explore some modern research on this topic, including the modeling of branching morphogenesis in COMSOL Multiphysics.

Read More##### Walter Frei March 24, 2016

In today’s blog post, we will introduce a procedure for thermally modeling a material with hysteresis, which means that the melting temperature is different from the solidification temperature. Such behavior can be modeled by introducing a temperature-dependent specific heat function that is different if the material has been heated or cooled past a certain point. We can implement this behavior in COMSOL Multiphysics via the Previous Solution operator and a little bit of equation-based modeling. Let’s find out how…

Read More##### Walter Frei March 16, 2016

Thermal curing is the process of temperature-induced chemical change in a material, such as the polymerization of a thermoset resin. This process is relevant, for example, when a precursor resin is heated and hardens during the manufacturing of composites. You can often assume that the material does not flow during curing, which simplifies the analysis. Thermal curing is very easy to model within the core functionality of COMSOL Multiphysics, as we will show in this blog post.

Read More##### Nikola Strah January 25, 2016

Surely you remember the last time you were stuck in bed with the flu. Influenza, commonly known as the flu, can be at the very least an unpleasant experience, but it also claims a lot of casualties every year. Today, public health officials use mathematical modeling techniques to study the flu and other infectious diseases to predict their spread and make informed decisions about public health.

Read More##### Temesgen Kindo July 27, 2015

How do we check if a simulation tool works correctly? One approach is the Method of Manufactured Solutions. The process involves assuming a solution, obtaining source terms and other auxiliary conditions consistent with the assumption, solving the problem with those conditions as inputs to the simulation tool, and comparing the results with the assumed solution. The method is easy to use and very versatile. For example, researchers at Sandia National Laboratories have used it with several in-house codes.

Read More##### Chien Liu April 16, 2015

Previously in our weak form series, we discretized the weak form equation to obtain a matrix equation to solve for the unknown coefficients in our simple example problem. Following the same procedure as in this previous blog post, we will implement the equation in the COMSOL Multiphysics® software with additional steps included to examine the matrices. We will find it more convenient to use a COMSOL® software application to display all relevant matrices at once, arranged logically on one screen.

Read More##### Chien Liu April 1, 2015

Over half a century ago, Mark Kac gave an interesting lecture on a question that he had heard from Professor Bochner ten years earlier: “Can one hear the shape of a drum?” He focused on the (then undetermined) uniqueness of the set of eigenvalues given the shape of a vibrating membrane. The eigenvalue problem has since been solved and here we explore the “hearing” part of the question by considering some interesting physical effects.

Read More##### Chien Liu February 9, 2015

This post continues our blog series on the weak formulation. In the previous post, we implemented and solved an exemplary weak form equation in the COMSOL Multiphysics software. The result was validated with simple physical arguments. Today, we will start to take a behind-the-scenes look at how the equations are discretized and solved numerically.

Read More##### Chien Liu January 6, 2015

This blog post is part of a series aimed at introducing the weak form with minimal prerequisites. In the first blog post, we learned about the basic concepts of the weak formulation. All equations were left in the analytical form. Today, we will implement and solve the equations numerically using the COMSOL Multiphysics simulation software. You are encouraged to follow the steps with a working copy of the COMSOL software.

Read More##### Chien Liu November 19, 2014

This is an introduction to the weak form for those of us who didn’t grow up using finite element analysis and vector calculus in our daily lives, but are nevertheless interested in learning about the weak form, with the help of some physical intuition and basic calculus.

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