New paper on implicit time stepping in Computer Physics Communications

A scale-resolving simulation at high Reynolds number is usually held back by the time step rather than by the mesh: the CFL condition on an explicit scheme ties the step to the smallest cell, and a boundary-layer mesh around a complex geometry has very small cells indeed. In a new paper in Computer Physics Communications, H. Wüstenberg, A. Liosi, S. J. Sherwin, J. Peiró and D. Moxey compare two implicit forms of the velocity correction scheme, a linear-implicit one and a sub-stepping semi-Lagrangian one, against the standard semi-implicit formulation, in an implicit large-eddy simulation of the Imperial Front Wing.

A bigger stable step is not the same as a faster answer, and the paper separates the two. Sub-stepping extends the stable step by a factor of 20 and the linear-implicit scheme by up to 100, but each step costs more, so the time to solution improves by a factor of 8.7 for the linear-implicit scheme and by only 12% for sub-stepping. Holding to accuracy targets of 1% in mean lift and 5% in mean drag, the fastest acceptable case runs 1.53 times faster than the CFL-limited one.

The more interesting result is the one that argues for caution. At the larger steps the main-plane laminar separation bubble is already substantially shortened, which means the integrated forces can agree while the transition-sensitive structure underneath them has changed. Matching lift and drag is not on its own evidence that the flow is the same.