Joel Davison, CD-adapco Product Manager for STAR-CCM+ will conduct a webinar on Adjoint Solvers.
What is it? How does it work?
“The adjoint solver is a method of forming a sensitivity analysis for fluid based simulations. Essentially it tells you where and how your results are going to be influenced by the flow and also the geometry that you analyze,” said Joel Davison, CD-adapco Product Manager for STAR-CCM+.
The adjoint solver provides information on how changes in flow might affect the cost functions of interest.
Sabine Goodwin, Sr. Engineer at CD-adapco explains that the solver is based on a mathematical technique called optimal control theory. The cost functions are defined using Lagrange multipliers, the flow solution and the mesh. Once you take the derivative of the cost function you can solve for the Lagrange multipliers. This then produces the sensitivity of the function based on mesh coordinates, and flow variables such as momentum, mass and energy. The final result is then determined using simple matrix algebra.
Traditionally, this was done by a method called finite difference. An analyst would determine a gradient based on multiple alterations of the mesh processed one alteration at a time. This would entail a large number of simulations for each cost function, and section being altered. The more variables and sections being tested, the more simulations that were needed. “Whereas the cost of running an adjoint solver to determine this gradient is approximately one normal solve,” assures Davison.
So what does this do for me?
With an adjoint solver “you can optimize many cost functions at once,” explained Davison. “The output of the adjoint solver is the influence on the flow patterns and geometry on each of the cost functions independently. It will tell you how changing the shape of your wing will change your lift on an aircraft for example and you would have a different result for say the drag.”
With this guidance, analysts can tweak their designs based on the cost functions to better optimize the final product. One issue is that this can get a little tricky with multiple competing cost functions. Fortunately, version v9.04 of STAR-CCM+ is set to release with a method to link cost functions together mathematically for more sophisticated optimization problems. Continuing his flight example, Davison explains that “the ability to actually tie two cost functions together will allow you to look at the sensitivity of lift and drag independently as well as being able to see the lift to drag ratio.”
Perhaps the most useful part of the adjoint solver is when it is used with the mesh morpher to drive geometric change. As the adjoint solver produces a gradient with respect to the mesh’s positions and potential morphing, the mesh morpher can be used to change the shape of your design based on the gradient.
Optimization of a Formula SAE front wing.
“This isn’t a case of pushing a button and everything happens while you have no control over the process,” assures Davison. “What the solver gives you is information on how changing the shape will change the cost function and then you use that information to change the mesh using the morpher. You can, however, easily automate the process using java macros to read the results and make the deformations based on the results automatically.”
The adjoint solver can save simulation time in another way too. “As the solver gives you a sensitivity of the mesh with respect to position, you are able to ensure your mesh is well suited to you engineering objectives of interest. You are able to use your mesh in a more efficient manner to ensure the areas of your interest are suitably defined and structured,” said Davison. Therefore, the solver can tell you which areas of the design require fewer cells, saving computational time.
How does it compare?
CD-adapco isn’t the only game in town for adjoint solvers; however, Davison stresses the ability of their solver to “handle non-linear solutions, multiple constraints on your geometry, incompressible or compressible fluids, moving reference frames (MRF) for rotating objects such as fans and wheels and high speed flows.”
He continues that CD-adapco “has made a strong commitment to the adjoint solver as a company. We have a dedicated team of 3.5 developers to ensure the technology is easy to use, widely applicable and our customers are satisfied with the capabilities STAR-CCM+ provides. We released the adjoint solver a year ago and already we have made an array of new developments with more to come in future versions.”
Though vague on the comparisons, users should feel more at ease knowing that should an issue arise the dedicated development team is looking for a solution.
Where can I learn more?
Optimization of a IC engine port to improve swirl ration for steady state port flow.
Demand for the adjoint solver came from a very vocal user base, whose comments led to new developments and questions about the product.
For more information on the adjoint solvers, join Joel Davison in his global webinar on May 22nd at 10am (Los Angeles), 1pm (New York), 10am (London), 11am (Berlin/Paris), and 2:30pm (Bangalore).
According to Davison “In the webinar we will look at several examples of how the adjoint solver can be used, such as with the steady state port flow in an internal combustion engine.” Considering how much work the solver can save you, it’s definitely worth an hour of your time.
CD-adapco has sponsored promotion of their Adjoint Solvers on ENGINEERING.com. They have no editorial input to this post - all opinions are mine. Shawn Wasserman