CES for transonic shocks
A widely cited University of Wyoming paper demonstrating Continuous Eddy Simulation (CES) for transonic shock‑induced flow separation was highlighted on social media as useful for transonic shock simulation. The post emphasized CES as a modelling approach for complex shock-separation interactions. (x.com)
Air over a wing can stay subsonic in one spot and turn supersonic in another, then hit a sudden pressure jump called a shock. A 2024 University of Wyoming paper tested a simulation method called Continuous Eddy Simulation on that problem and is now being recirculated online as a tool for transonic shock cases. (mdpi.com) The paper, by Adeyemi Fagbade and Stefan Heinz, was published in *Applied Sciences* on March 23, 2024. It compares Continuous Eddy Simulation, or CES, with Reynolds-averaged Navier–Stokes, detached eddy simulation, wall-modeled large eddy simulation, and wall-resolved large eddy simulation. (mdpi.com) Those methods all try to predict turbulence, which is the swirly, unsteady motion that gets harder to compute near a wall. The Wyoming authors say CES changes its model contribution up or down based on how much motion the grid actually resolves, instead of fixing that split in advance. (mdpi.com; uwyo.edu) The test case was the Bachalo-Johnson axisymmetric transonic bump, a benchmark used for decades to check whether turbulence models can handle shock-wave and boundary-layer interaction. NASA’s reference page says the original experiment used a circular-arc bump 1.905 centimeters high and 20.32 centimeters long on a 15.24-centimeter-diameter cylinder. (nasa.gov) That bump matters because it produces the sequence engineers worry about on transonic aircraft: local acceleration, a shock, boundary-layer separation, and then reattachment downstream. NASA and the Turbulence Model Benchmarking Working Group both list the case as a validation problem for shock-induced separation. (nasa.gov; tmbwg.github.io) In the paper’s abstract, the authors write that CES “performs better” than the comparison methods and does so at “a little fraction” of the computational cost of wall-resolved large eddy simulation. They also argue that CES avoids some of the setup constraints that standard hybrid methods face. (mdpi.com; nsf.gov) That claim lands in a field where cost is a central problem. A NASA report on wall-resolved large eddy simulation for the same bump case says calculations used as many as 24 billion grid points at Mach 0.875 and Reynolds number 2.763 million. (ntrs.nasa.gov) Other researchers have also reported that established large-eddy approaches can struggle on this benchmark. A 2017 *Flow, Turbulence and Combustion* paper said wall-modeled large eddy simulations of the Bachalo-Johnson flow were “disappointing,” including on shock position, even on grids with 4.7 × 10^8 and 1.6 × 10^9 cells. (link.springer.com) The social-media post that revived the Wyoming paper did not announce a new result; it pointed readers back to an existing 2024 study. What changed is attention: CES is being recirculated as another option for simulating the shock-separation interactions that still make transonic flows expensive and difficult to predict. (x.com; mdpi.com)
