Not knowing much about the subject myself, I did a quick search in our COMSOL Conference Papers and Presentations collection. (If you’re unfamiliar with the resource, you should really check it out; it contains papers and presentations covering a broad spectrum of applications that have been on display at our annual COMSOL Conference worldwide.)
The search brought me to a paper on modeling viscous fingering, presented by Ekkehard Holzbecher of Georg-August Universität Göttingen at the COMSOL Conference 2009 in Milan. As I scanned through it, I noticed that Ekkehard was using equations directly in his simulation. He based his model on work by Will Zimmerman and Bud Homsy, starting with the mathematical model described in their work and then using COMSOL Multiphysics to define his particular simulation.
A couple of neat things about Ekkehard’s model:
After getting a fairly good feel for the model, I went about attempting to repeat his simulation. What first looked like a challenging model to set up turned out to be quite easy in COMSOL. I simply chose a 2D, Coefficient Form PDE and implemented the model. I chose reasonable values for the physical parameters, and I was able to use the built-in random function that comes with COMSOL. You can see some of the results here:
Now for people like Ekkehard and I, equation-based modeling or, as I like to call it, DIY simulations, is a natural approach. But it’s not for everyone, and I get that. It was time for me to go back to my prospect with these results in hand.
It turns out that he loved the results. The approach was absolutely acceptable to him, primarily because he got good results. He was an experienced scientist and the equations suited him just fine. In this case, the flexibility of the software allowed him to do things he was unable to do elsewhere.
It’s interesting to me that I sometimes still get questions like, “what module do I need in order to use equations?” This is what COMSOL Multiphysics is based on. It’s in our essential structure. While you don’t have to enter your own equations, you always have that option — in all of our modules. After this experience, my confidence in COMSOL has never been higher, and I’m so impressed with the user-base we’ve developed. As we continue to roll out new product updates, rest assured that we’ll continue to support all of our DIY simulation enthusiasts.
One of the most famous fractals is the Mandelbrot Set, made popular by mathematician Benoit Mandelbrot. This recursively generated set is a great example of the most recognizable characteristic of fractals: self-similarity that persists at arbitrarily small scales. That is, you can look at the Mandelbrot Set and see the shape. Zoom in on the boundary, and, wow, there’s the Mandelbrot Set again! Zoom in again — yep, there it is.
The Mandelbrot Set. Image attribution: Agro1986.
The Koch Snowflake (shown below) is another well-known example of a fractal. It’s easy to understand because you can construct it by starting with an equilateral triangle, and then altering each line segment iteratively.
The Koch snowflake.
With the onset of computer graphics over the past thirty years, computational methods of generating fractals have made them a popular teaching tool that can open students’ eyes to the beauty of the mathematical sciences. Sure, fractals are beautiful, but it turns out that they’re more than just eye candy.
Fractal structures, in fact, have some desirable properties for engineers doing research in antennas and metamaterials. For RF applications, fractals can generate multiple resonances. Take, for instance, the Sierpinski triangle. This shape is generated by recursively removing the center sub-triangle in an equilateral triangle. The Model Library of the RF Module includes an in-depth analysis of such a fractal monopole antenna.
Sierpinski fractal monopole antenna, created using COMSOL Multiphysics and the RF Module.
Fractals also have their place in the emerging field of metamaterials (known in the popular science media for the many cloaking applications). The “magic” behind metamaterials is in the repeating structure that causes “normal” materials to take on “strange” properties (like negative refractive index). It’s pretty clear that the self-similar nature of fractals fits into this category. The precise details of one such example was presented at a recent COMSOL Conference and appears in the proceedings. In their paper, “Designing a Smart Skin with Fractal Geometry“, S. Ni, C.Y. Koh, S. Kooi, and E. Thomas from MIT use a repeating H structure to design a phononic metamaterial with applications to “smart skin” — a type of film with sensors throughout.
Repeating H pattern in the phononic material. Image courtesy of S.S. Ni, et al.
It might be a while before fractals find their way into everyday products, but these promising results show that beautiful things can be useful, too.
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First off, let me be clear about one thing: multiphysics is useful to all engineers regardless of their knowledge of theory. This is a fact demonstrated by the wide user-base of COMSOL Multiphysics. So if you don’t have a taste for equations, no problem. Just use the physics putting the material properties and other governing parameters that you’re used to. The equations will still be there, behind the scenes and doing their work, but you don’t have to worry about them.
I like to use the analogy of a car: most of us just drive it. Still, there is a segment of the population that can open the hood of a car, understand the technology, and achieve optimized performance by making changes.
Now, for those who want to understand, in broad terms, what makes COMSOL Multiphysics special “under the hood”, read on.
COMSOL Multiphysics is often thought of as a finite element method (FEM) code. Indeed it should be, since that is the primary method employed by COMSOL. However, the way COMSOL Multiphysics implements this to perform finite element analysis (FEA) is so clever that we patented it.
Traditional FEA focuses on “elements”. These are fixed discretizations, usually associated with a mesh, that describe certain physics or combinations of physics. If you want to analyze a combination of physics for which no elements have been created (a priori) you either have to couple multiple solvers or you’re out of luck. COMSOL, on the other hand, first allows the user to combine physics in any way. (You can think of writing down any system of equations you want.) Then, just before solving, COMSOL initiates discretization “on-the-fly”. So really, it’s like having an infinite number of “element” types.
The Coefficient Form Settings Window. | The Coefficient Form is one of the ways in which equations can be freely entered into COMSOL Multiphysics. |
What’s the benefit? Full flexibility in your modeling. That is why, when it comes to pioneering applications in multiphysics, COMSOL Multiphysics users have always come first. Just have a look through the COMSOL Conference papers and presentations, and you’ll see an incredibly broad range of combinations of physics and mathematical models.
When you look at the big picture, there are even more benefits: a uniform workflow and the cross-pollination of innovative ideas, just to mention two. It is the patented multiphysics technology of COMSOL that makes this all possible, and will continue to provide a platform of innovation for computational scientists and engineers everywhere.
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Schematic showing orthogonal fracture propagation. From the paper “Investigation of Hydraulic Fracture Re-Orientation Effects in Tight Gas Reservoirs“. Image courtesy of B. Hagemann^{1} J. Wegner^{1} L. Ganzer^{1}
^{1}Clausthal University of Technology, Clausthal-Zellerfeld, Germany.
Fracturing is simple to describe; it’s just cracks in the earth. The mechanics involved, however, are complicated, especially when you consider fluid flow through formations within the earth. Moreover, it’s not easy to observe what’s happening hundreds or thousands of meters beneath the surface of the earth. These facts have made hydraulic fracturing a hot topic of active research, and since the underlying phenomena are relatively unknown, it is ideal for multiphysics simulation.
That fracturing is ideal for multiphysics modeling is evidenced by the number of papers and posters related to the topic presented at the COMSOL Conference earlier this year. Consider the following:
3D Modeling of Fracture Flow in Core Samples Using μ-CT Data, S. Hoyer^{1} U. Exner^{2} M. Voorn^{1} A. Rath^{3}
^{1}Department of Geodynamics and Sedimentology, University of Vienna, Austria
^{2}Museum of Natural History, Vienna, Austria
^{3}OMV ESG-D Production Geology, Vienna, Austria
Here the authors used CT scans of fractured samples of rock to perform simulations measuring permeability without destroying the samples — a difficult task using physical experiments.
3D Simulations of an Injection Test Done Into an Unsaturated Porous and Fractured Limestone, A. Thoraval^{1} Y. Guglielmi^{2} F. Cappa^{3}
^{1}INERIS, Nancy, France
^{2}CEREGE, Aix-en-Provence, France
^{3}GEOAZUR, Valbonne, France
The researchers behind this paper developed an advanced COMSOL model including stress-strain constitutive law, two-phase flows, and hydro-mechanical coupling, then applied it to an actual slope location in France.
A Coulomb Stress Model to Simulate Induced Seismicity Due to Fluid Injection and Withdrawal in Deep Boreholes, G. Perillo^{1} G. De Natale^{2} C. Troise^{2} A. Troiano^{2} M.G. Di Giuseppe^{2} A. Tramelli^{2}
^{1}University of Naples Parthenope, Naples, Italy
^{2}INGV, Osservatorio Vesuviano, Naples, Italy
This paper presents a stress model to account for cases of fluid injection in deep boreholes, with particular application to a geothermal site in northeastern France.
Finite Element Solution of Nonlinear Transient Rock Damage with Application in Geomechanics of Oil and Gas Reservoirs, S. Enayatpour^{1} T. Patzek^{1}
^{1}The University of Texas at Austin, Austin, TX, USA
A novel script was written for a first-principles PDE model of rock damage until fracture.
Fracture-Matrix Flow Partitioning and Cross Flow: Numerical Modeling of Laboratory Fractured Core Flood, R. Sanaee^{1} G.F. Oluyemi^{1} M. Hossain^{1} B.M. Oyeneyin^{1}
^{1}Robert Gordon University, Aberdeen, United Kingdom
This paper is part of an effort to better understand subsurface flow that includes both fractures and matrix flow. Under certain stress conditions (fracture closure and overburden), the flow was studied and further physical experiments were suggested.
Investigation of Hydraulic Fracture Re-Orientation Effects in Tight Gas Reservoirs, B. Hagemann^{1} J. Wegner^{1} L. Ganzer^{1}
^{1}Clausthal University of Technology, Clausthal-Zellerfeld, Germany
Not just fracturing, but re-fracturing! This is an important consideration for tight gas formations where the critical question is: when should you perform re-fracturing for optimal productivity?
Poroelastic Models of Stress Diffusion and Fault Re-Activation in Underground Injection, R. Nopper^{1} J. Clark^{2} C. Miller^{1}
^{1}DuPont Company, Wilmington, DE, USA
^{2}DuPont Company, Beaumont, TX, USA
Flow plus poroelastic deformation models developed in COMSOL point toward promising criteria for rock failure.
No matter where you might stand on the issue, it’s great to see that COMSOL is enabling those who are at the forefront of fracture modeling to simulate, understand, and advance the technology. Knowledge, I think we can agree, is the key to understanding the risks and rewards of fracking.
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But not everyone likes equations. In fact, many become engineers in spite of equations. Common complaints are that equations are too abstract, too complicated, and just too dull. They have little to do with actually putting things together and making them work, which is a big part of engineering.
On the other hand, some engineers are theoretical experts who are more comfortable with equations than with the actual thing they’re making or fixing. And in any engineering organization, you’ll likely both sorts of professionals at least to some degree.
With COMSOL, we’re sympathetic to both points of view, and we believe we can satisfy both. You might be more comfortable describing things in terms of the physics: loads, constraints, fields, conductivity, currents, etc. For you, we use specialized terminology specific to the sort of your application. This goes for everything from the material properties to the boundary conditions and other model inputs.
Context menu for solid mechanics boundary conditions.
Or you might be like me, “just show me the equation and I’ll figure it out…” We have a section in the settings window (hidden so as not to scare anyone) just for you. It opens the “black box” of simulation and reveals exactly the system of equations that is being solved.
Governing equations for thermal stress.
So how about you? What category would you place yourself in? We welcome your comments and discussion in the comment field below.
In either case, it is our aim to make multiphysics modeling accessible to all serious engineers from researchers to designers and manufacturing. We still have some work to do, and we’ll continue to find new ways toward this goal. Your feedback is indeed important.
Note from the editor: A follow-up to this blog post titled Multiphysics versus FEA was published on 2/14/2013.
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Let’s have a look at the physics settings for one of the models in the Model Library: Heat Sink with Surface-to-Surface Radiation. This model is interesting in its own right (think three modes of heat transfer) but I’ll focus on the icons.
Conjugate Heat Transfer node plus sub-nodes.
(Bonus Tip: I used the new “Sort by Space Dimension” feature.)
If you have experience with COMSOL, you probably recognize this structure. But have you noticed the details of the symbols?
Node icon designs indicate different space dimensions.
If a node has an icon with a fuchsia patch, you can be sure it’s a boundary condition. If it’s just the shaded “peanut” shape, it’s a domain (or 3D volume). How about some more info? The capital “D” indicates a default condition, which is automatically applied and cannot be deleted.
“D” means “Default”.
The icons are actually dynamic, meaning they change depending on what node is selected in the Model Builder. Check this out:
Selecting “Temperature 1” shows how this condition overrides “Thermal Insulation 1” and contributes with “Inlet 1”. Note how the icons change.
When I select the “Temperature 1” condition, a (soon-to-be-not) mysterious triangle appears near the bottom of the “Thermal Insulation 1” icon. This triangle and its position indicate that “Thermal Insulation 1” has been overridden by the selected node, namely “Temperature 1”. There is also a circle that appears next to “Inlet 1”. This indicates contribution. You can confirm all this in the setting window of “Temperature 1” by expanding the “Override and Contribution” section:
Contents of the “Override and Contribution” section of the “Temperature 1” node.
What if you now selected “Thermal Insulation 1” you ask? The icons change and look like this:
Icons change to indicate that “Thermal Insulation 1” is overridden by “Temperature 1” and “Outflow 1”.
Now the red triangle is on the “Temperature 1” and “Outlet 1” nodes, above the peanut-shaped icon. This indicates that both the “Temperature 1” and “Outlet 1” conditions override the selected node “Thermal Insulation 1”.
There’s even more to the story, but you can read all about it in the documentation. While you may actually get away without being aware of these features, as you advance in using COMSOL, knowing this can really be a time saver.
What’s your favorite COMSOL convenience feature? The Player or Report Generator? Feel free to post your experience to comments.
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There are several types of linear solvers, but I won’t go into that now. (Maybe later if there’s enough demand.) Instead, I want to point out a little-known fact: linear solvers have improved at the same rate (or better) than hardware. Or put another way, Moore’s law holds for solver algorithms, too.
Most are familiar with Moore’s law, which states that “computer power doubles every two years”. Most associate this with hardware, whether it’s transistors on a chip or their speed. But back in 2005, the U.S. President’s Information Technology Advisory Committee (PITAC) issued a report that showed how solver algorithms have improved just as quickly.
We featured this graph in the COMSOL Product Booklet some years ago because such information really matters. There is a significant amount of intellectual capital invested in this technology, and it’s good to be recognized. Just as pertinently, these solver algorithms are some of the very same ones you’ll find in COMSOL Multiphysics.
If anyone knows of an updated graph (this one is 7 years old), please share it with us in the comments below.
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One direct benefit multiphysics provides is unifying simulation projects. Say you have a widget that needs mechanical, thermal, and electromagnetic simulations — yet all uncoupled. Having one multiphysics environment for multiple single physics puts your simulations in one place. There is then no need to switch between software or try to get uniform output. It’s all automatic if you’re using one multiphysics environment. You only need to be proficient in one software environment for geometry, meshing, materials, solver settings, and postprocessing. You no longer need to learn different workflows. It’s all right there.
These benefits are amplified when considering simulations performed in an organization. Efficiency is certainly increased when all participants in a large-scale analysis “speak the same language”.
Another huge, but somewhat hidden, benefit is the cross-pollination of simulation technology. Certain advances in one field can directly benefit another. Let’s take for example perfectly matched layers (PMLs). This was a technology developed to perfectly damp out electromagnetic waves propagating in an infinite domain. Previous to their introduction, engineers used various sorts of boundary conditions to approximately absorb the waves when they hit the end of a computational domain. PMLs completely changed the game because they did a perfect job of damping the waves (both theoretically and practically). Acoustic engineers quickly realized that what was good for EM waves was also good for sound waves. And PMLs have been a standard tool in acoustics and any other wave-based physics ever since. This sort of shared advancement is spontaneous in a software environment like COMSOL Multiphysics.
Left: Model depicting scattering from a dielectric object and the absorption of the scattered wave by PMLs.
Right: Far-field analysis of a piezo-acoustic device.
Finally, I’d also like to point out one more benefit of multiphysics: innovation. I squirm at using such a mushy term, but it’s warranted here. If your software environment is limited to a single physics, there’s no possibility of thinking “outside the box”. More precisely, you can’t take into account everything the real world throws at you. And if you’re in a competitive marketplace, this can mean the difference between success and failure.
So all in all, even if multiphysics is “not your style”, you might want to consider trying it on for size. You just might find the benefits make a big difference.
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In order to understand the term, let’s take it in context. First off, “multiphysics” is a descriptor of computer simulation for physical phenomena. We’re talking using computers to understand heat, flow, EM currents and waves, sound, to name a few. It was one of the first applications of digital computers back in the 1940s and continues to be a contributing factor in the progress of scientific computing.
In those early days, computing resources were scarce. (Think vacuum tubes and room-sized machines and you get the picture.) Not only so, but the theoretical foundation for taking continuum mathematical models to digital was still being formed. So those pioneering researchers had to get a start on performing these simulations. They did so, primarily, through a divide-and-conquer approach. That is, they segregated physics into categories that could then be more easily solved. Then, computational scientists could become more specialized in their expertise. From this approach, fields like computational fluid dynamics (CFD) and finite element analysis (FEA) for mechanics were born.
Over the years, solvers improved, the theory was solidified, and hardware gained speed and capacity. Fast forward to today, and we have at our finger tips very powerful machines matched with powerful software algorithms. This begs the question: Why settle for artificially segregated categories of physics, when the real-world applications of engineers and scientists require more? The answer is: You don’t.
Enter COMSOL Multiphysics: the true leader in real-world simulations. With COMSOL Multiphysics you can combine any (yes, I mean any) set of physics together in one model. Want to model the acoustics of miniature loudspeakers that take into account thermal and structural effects? You can, with COMSOL software. How about electrical heating underground to decrease viscosity of fluids and increase well production? With COMSOL, you can do that too. The list goes on and on.
From left, models of: a loudspeaker, a Rossler attractor, and NOx reduction in a monolithic reactor.
We encourage you to think outside the lines of traditional engineering simulation. It might bring a new perspective to you and your technical organization.
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Another complementary type of flexibility is what I would call “multidimensional modeling”. This, of course, implies that you can model in 3-, 2-, 1, and even 0D. Even more, you can combine models across dimensions. For instance, you can solve for one physics on a boundary (2D) and use it as a condition for a 3D simulation. This approach not only saves precious computational power but also reflects the real physical effects based on where they are actually taking place. While this capability has been built into COMSOL for quite some time, it has not been among the most-used features. That might change with the release of the Pipe Flow Module.
The new Pipe Flow Module automatically builds in multidimensional modeling. Here’s why: one characteristic of modeling flow in pipes is that the geometry is typically uniform along the length of a pipe. The physics of the problem can then be simplified so that its discretization results in a more efficient computation. In other words, you can make the flow along the pipe a 1D simulation. This can save hours (or more) of computation time.
Now the real innovation here is the ability to couple back the flow in a pipe to a higher dimension model. Consider the example of the cooling of a steering wheel mold.
In this model, the curved pipes are modeled in 1D, while the steering wheel along with the surrounding mold (the box) was modeled in 3D. So as the heat flow through the pipe cools, it affects the mold and eventually the steering wheel. The results are as accurate as if you were to model the cooling pipes in 3D, yet the computational savings is two orders of magnitude. Big!
While there are other features in COMSOL that take advantage of multidimensional modeling (coupling with circuits, port conditions, laminar flow profiles, etc.), the Pipe Flow Module is the first full product that is based on this feature. I expect it won’t be the last.
There is more to the Pipe Flow Module, and I encourage you to delve into the details if you’re interested. I think it’s an important breakthrough, and now you know why.
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Electric field near borehole generated by a galvanic resistivity logging tool.
There are several types of tools including sonic (which use piezoelectric transducers), resistivity (using electromagnetic currents), and nuclear magnetic resonance (NMR). The technology has been around since the 1920’s, but has arguably never been more important.
The workshop started with a general introduction to COMSOL. Then, guest speaker Tina Zhao from Schlumberger presented her work; “Using Superposition Principle and Edge Current Model to Compute Impedance of Coil in Logging Tool”. Everyone appreciated the insight she showed in using COMSOL to design better inductive logging tools, focusing on the coil placement on the tool. Several follow up questions were asked, from the general context to the particular COMSOL implementation.
A demonstration of the performance of sonic tool near a wellbore followed. Step-by-step, the audience got to see COMSOL in action. The end result was an analysis of the measured pressure in the frequency domain.
After a short break, the workshop reconvened for the “main event”: a hands-on minicourse of building a simulation of the near-wellbore performance of a galvanic tool. One of the audience members, Sushant Dutta of Baker Hughes, provided the inspiration for many aspects of the exercise, including reasonable arrangement of the electrodes. Everyone collaborated, asking questions and helping each other through the model.
In the end, everyone completed a model of the electric current flowing through a formation that varied in resistivity. They even completed a parametric sweep of the tool as the depth varied from 10 to 35 meters.
The response was very positive. It was great seeing attendees quickly pick up on the benefits of using COMSOL Multiphysics in their design work. Zhong Wang of Bitswave Tech echoed the response of many; “Thanks for the workshop yesterday. It was a good chance to know how people use COMSOL in well logging industries.”
COMSOL Workshops are held every week throughout the world. See www.comsol.com/events for one near you.
If you’re interested in well logging, contact the author at david.kan@comsol.com. The workshop material is available upon request.
Animated version of the above model: