## Methods for Dealing with Numerical Issues in Constraint Enforcement

##### Temesgen Kindo September 11, 2018

In the first part of this blog series, we discussed how to solve variational problems with simple boundary conditions. Next, we proceeded to more sophisticated constraints and used Lagrange multipliers to set up equivalent unconstrained problems. Today, we focus on the numerical aspects of constraint enforcement. The method of Lagrange multipliers is theoretically exact, yet its use in numerical solutions poses some challenges. We will go over these challenges and show two mitigation strategies: the penalty and augmented Lagrangian methods.

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### Evaluating a Schottky Diode with a Semiconductor Benchmark Model

##### Bridget Paulus September 10, 2018

Schottky diodes are one of the oldest semiconductor components, but they are still found in many modern applications, including computers and radar systems. To ensure that a Schottky diode performs well, it’s important for engineers to accurately analyze factors like current density and barrier height in the design. As a benchmark model demonstrates, the COMSOL Multiphysics® software and add-on Semiconductor Module are well suited for this type of analysis.

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### Specifying Boundary Conditions and Constraints in Variational Problems

##### Temesgen Kindo September 7, 2018

In the first part of this blog series, we discussed variational problems and demonstrated how to solve them using the COMSOL Multiphysics® software. In that case, we used simple built-in boundary conditions. Today, we will discuss more general boundary conditions and constraints. We will also show how to implement these boundary conditions and constraints in the COMSOL® software using the same variational problem from Part 1: (the soap film) — and just as much math.

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### How to Model the Compression of a Hyperelastic Foam

##### Chandan Kumar September 5, 2018

To characterize hyperelastic materials, we need experimental data from a variety of tests, including subjection to uniaxial tension and compression, biaxial tension and compression, and torsion. Here, we show how to model the compression of a sphere made of an elastic foam using tension and compression test data obtained via uniaxial and equibiaxial tests. We demonstrate the use of the compressible Storakers hyperelastic material model for computation as well as how force-versus-stretch relationships are calculated for uniaxial and equibiaxial tests.

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### Introduction to Modeling Soap Films and Other Variational Problems

##### Temesgen Kindo September 4, 2018

What do soap films, catenary cables, and light beams have in common? They behave in ways that minimize certain quantities. Such problems are prevalent in science and engineering fields such as biology, economics, elasticity theory, material science, and image processing. You can simulate many such problems using the built-in physics interfaces in the COMSOL Multiphysics® software, but in this blog series, we will show you how to solve variational problems using the equation-based modeling features.

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### Happy Birthday, Hermann von Helmholtz

##### Thomas Forrister August 31, 2018

Hermann von Helmholtz was a German scientist, doctor, and philosopher who made advances in many scientific fields, including electrodynamics, optics, and thermodynamics. He invented several devices, such as the ophthalmoscope and the polyphonic siren, and is also known for the Helmholtz coil. By exploring the philosophy of science, Helmholtz made accurate connections about the laws of nature, perception, and empiricism.

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### Seeing Through Solids: Discovery and Applications of Photoacoustics

##### Brianne Costa August 30, 2018

In 1880, Alexander Graham Bell wrote a letter to his father, saying: “I have heard articulate speech by sunlight! I have heard a ray of the sun laugh and cough and sing!” He was talking about his latest success, the photophone, which he called his “greatest invention” shortly before his death. The photophone did not revolutionize the field of imaging, but an unintended effect Bell noticed while developing it did…

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### How to Model Ion-Exchange Membranes and Donnan Potentials

##### Henrik Ekström August 29, 2018

Ion-exchange membranes are widely employed within the field of electrochemical engineering. In polymer electrolyte fuel cells and vanadium flow batteries, they are used to conduct ions and at the same time prevent reactants and electrons from crossing between the two flow compartments. The ability to promote the passage of ions of either positive or negative charge is also used in electrodialysis for cleaning water from ions. In this blog post, we will explore the ion-selective capabilities of ion-exchange membranes.

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### How to Model Sparging in COMSOL Multiphysics®

##### Siva Sashank Tholeti August 22, 2018

Sparging, a mass transfer process between a gas and a liquid, is commonly encountered in industrial applications such as beverage carbonation and photobioreactors, or even at home for aeration in aquariums. In this blog post, we detail how to model a type of sparging, carbonation, using the COMSOL Multiphysics® software.

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### Examining Vibration in a Lumped Model of the Human Body

##### Bridget Paulus August 21, 2018

If you’ve ever gone on a road trip, you know that it’s a bit of a pain — literally. Part of why your body aches after driving long distances is due to whole body vibration (WBV), which can cause fatigue; motion sickness; and, eventually, serious health problems. To design systems that reduce WBV for cars and other applications, engineers need an efficient way to visualize the effect of vibrations on the human body. That’s where simulation comes in.

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### How to Place Inlet and Outlet Boundary Conditions in CFD Simulations

##### Mats Nigam August 20, 2018

When setting up fluid flow simulations, we typically focus on a single (possibly a few) components in a larger system, such as a pump or sedimentation tank in a water treatment plant. Naturally, this raises a question: At what distance can we apply boundary conditions without interfering with the process? In this blog post, we look at the effects of the proximity of inlet and outlet boundaries for interior and exterior flows of a homogeneous fluid with negligible compressibility.

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