Shawn Wasserman posted on March 18, 2014 | | 3538 views

Solving CFD challenges with the adjoint method has theoretically been around for some time and is well known by experts in industries like Aerospace. What’s new is that this technology can now be applied to more common problems, like pressure drop simulation in ventilation systems or cast parts.

**What can adjoint solvers tell you?**

- What areas of your model geometry are causing

the greatest pressure drop - Which direction to modify the geometry to improve

the fluid or gas flow - A prediction of how much of an improvement to

expect from making the change

And it will do all that with surprisingly light computing resources and few iterations.

For example, on the left is a before and after image of an automotive ventilation system by Volvo. Note that the adjoint technology identified the y-junction area as the most restrictive area and recommended changes to the geometry of the duct, producing a 33% reduction in pressure drop from their original baseline.

If you are interested in the math behind the adjoint method, read this paper onGilles Eggenspieler Sr. Fluid Product Line Manager at **ANSYS** said, “With **adjoint solvers** you never define a parameter, you just define a goal. In Volvo’s case described above the goal was to minimize the pressure drop. First setup is to run the first simulation as usual. Then use the **adjoint solver** to determine what section of the geometry impacts (negatively) the pressure drop the most. In the same time, the **adjoint solver** will also suggest how to modify the geometry to reduce the pressure drop and estimate the effect this change will have on the goal.”

**Optimizing Parameterized Models takes a lot of Resources**

It’s not unusual for analysts to parameterize their designs and run multiple simulations to optimize for pressure drop or other desired outcomes. In many cases that means a work-flow process that looks like this:

Even when there are scripts running several iterations, this process still places a big demand on human and computing resources. “This is a good strategy,” says Eggenspieler, “but the iteration of modifying your geometry, mesh, and then restarting your simulation takes time. Additionally, how do you know you are testing all the parameters you need?”

**Adjoint Method is Fundamentally Different**

To iterate towards an optimal solution, one first solves the typical Navier-Stokes equations to determine a baseline solution. The **adjoint solver** then solves and converges an auxiliary field equation and determines a sensitivity gradient. This gradient will then tell the program the changes which, if implemented, will improve the system and by how much. The system can then be solved using the improved geometry.

This video on Youtube sets out how the **Ansys Adjoint software** works in a simple example. This aerospace example clearly shows how the software identifies the areas of improvements and recommends changes to morph the geometry. The video was recorded using a laptop and only one core. Ansys says the computing requirements for adjoint solving are no more than with traditional CFD.

“The added benefit to this method is that the program will not just suggest an improved geometry. The program can automatically morph the geometry to this improved shape (note: there is no meshing or re-meshing operation). Morphing takes the initial mesh and morphs it to the new shape. Assuming the initial mesh was optimal, your new one should be as well,” said Eggenspieler. He added, “What is even better is that your next simulation will have a perfect starting point for its iteration - the solution of the previous simulation. These two factors will reduce the optimization process considerably.”

**Optimizing with an Adjoint Method Solver**

**Who Should use an Adjoint Method Solver?**

“We see a very large market interest in minimizing pressure drop. Everything that can be made using casting and plastics is fair game for the **adjoint solver**. But there are other applications: for examples, applications where heat transfer needs to be optimized. Also automotive companies can use the **adjoint solver** to reduce car drags. Competitive racing companies (e.g. Formula One), can use the **adjoint solver** to maximize down forces,” clarified Eggenspieler.

However, if you don’t have control over the geometry, such as may be the case if you are working with piping, then an **adjoint solver** won’t speed your path to optimization.

The concept of **adjoint solvers** was once only a high-end solution for aerospace. Now this method is becoming more mainstream and can be applied to a wide range of design and engineering challenges in many industries.

*Ansys has sponsored promotion of their simulation solutions on ENGINEERING.com. They have no editorial input to this post - all opinions are mine, Shawn Wasserman.** *

Volvo Image courtesy of:

1. Wade, A. (2012). 52 ansys advantage volume vi | issue 1 | 2012 turning optimization on its head. Ansys Advantage, VI(1), 52-53. Retrieved from http://www.ansys.com/staticassets/ANSYS/staticassets/resourcelibrary/article/AA-V6-I1-Turning-Optimization-on-Its-Head.pdf

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