Higher-order time integration for weakly compressible subcycling

Develop higher-order time integration methods for the incompressible solver with weakly compressible subcycling while determining whether such extensions can be achieved without increasing computational cost.

Background

The proposed incompressible solver with weakly compressible subcycling uses first-order explicit Euler time integration. The authors state that this choice was made to construct a simple base framework and reduce computational cost, but they have not investigated whether the method can be extended to higher-order time integration. Such an extension is unresolved because it may require additional computational cost or introduce implementation difficulties.

References

We have not investigated extending our method to higher-order time integration methods, which may not be straightforward without increasing computational cost.

— Weakly Compressible Subcycling for Accelerating Simulations of Surface-Tension-Dominated Incompressible Two-Phase Flows  (2608.23110 - Yamashita et al., 24 Aug 2026) in Section ‘Conclusions,’ subsection ‘Limitations and Future Work,’ paragraph ‘Higher-Order Time Integration’