Accuracy comparison of SSPRK2 and BDF2 DTS schemes

Determine whether the second-order SSPRK2 scheme is more efficient and assess its accuracy relative to the implicit BDF2 dual time-stepping positivity-preserving scheme on the specified three-dimensional Taylor–Green vortex test problem.

Background

The paper compares the implicit BDF2 dual time-stepping scheme with explicit SSPRK3 and reports that BDF2 DTS is more efficient in wall-clock time. The authors also run SSPRK2 on the same grid and find that it is slightly slower than BDF2 DTS, but explicitly note that its accuracy was not assessed. Consequently, the relative accuracy and overall efficiency of SSPRK2 versus BDF2 DTS remain unresolved in the presented study.

References

A reasonable question is to ask whether the second-order SSPRK2 scheme would be more efficient than the BDF2 DTS scheme. The SSPRK2 scheme was also run on the same grid using the exact settings. The total number of explicit steps for the SSPRK2 scheme is $3868$, while the wall clock time average over three runs is $51,648$ seconds. When compared to the BDF2 DTS scheme, the SSPRK2 scheme shows a $\%5.8$ increase in the wall clock time. Therefore, it is still less efficient than the BDF2 DTS scheme without assessing its accuracy.

— Implicit BDF2 dual time-stepping positivity-preserving entropy-stable schemes for unsteady compressible viscous flows  (2608.20103 - Sayyari et al., 20 Aug 2026) in Remark in Section 5.2, “3D supersonic Taylor–Green vortex flow”