Abstract
We consider a large time step (LTS) Roe scheme, originally suggested by LeVeque [Comm. Pure Appl. Math., 37 (1984), pp. 463-477] which has attained increased popularity in recent years. The scheme is based on a wave formulation of the ordinary Roe scheme, and the assumption that waves interact linearly. This assumption lets us propagate waves over more than one cell, thereby violating the ordinary CFL condition requiring the Courant number to be less than one. The LTS Roe scheme is applied to a two-phase flow model with phase transfer, modelled using the stiffened-gas equation of state. Results from various test cases show that the LTS Roe scheme with moderate Courant numbers is significantly more efficient than the ordinary Roe scheme, measured by an error-to-runtime ratio. The optimal Courant number is mainly a trade-off between reduced runtime due to fewer time steps, and increased error due to the assumption of linear wave interactions.
