Analysis of time integration methods for the compressible two-fluid model for pipe flow simulations

The strong performance of BDF2 is illustrated via several test cases related to the Kelvin-Helmholtz instability. A novel concept called Discrete Flow Pattern Map (DFPM) is introduced which describes the effective well-posed unstable flow regime as determined by the discretization method. Backward Euler introduces so much numerical diffusion that the theoretically well-posed unstable regime becomes numerically stable (at practical grid and timestep resolution). BDF2 accurately identifies the stability boundary, and reveals that in the nonlinear regime ill-posedness can occur when starting from well-posed unstable solutions. The well-posed unstable regime obtained in nonlinear simulations is therefore in practice much smaller than the theoretical one, which might severely limit the application of the two-fluid model for simulating the transition from stratified flow to slug flow. This should be taken very seriously into account when interpreting results from any slug-capturing simulations.