Density Wave Instability Verification of 1-D Computational Two-Fluid Model

A new dynamic verification of the one-dimensional (1-D) computational Two-Fluid Model (TFM) using the Type II density wave instability (DWI) theory of Ishii is presented. Verification requires convergence in the sense of the Lax Equivalence Theorem and dynamic comparison with the DWI theory. Rigorous verification of the computational TFM must be performed with a computational model that is well posed without regularization because, otherwise, since the theory of Ishii is well posed, regularization would make the TFM incompatible with it. Furthermore, since the TFM is well posed, it was possible to implement a second-order numerical method with a flux limiter that, together with a fine mesh, achieves numerical convergence. This is significant because numerical convergence and consistency, both of which are demonstrated, are prerequisites for the rigorous dynamic verification according to the Lax Equivalence Theorem. Thus, the apparent but previously unproven numerical verification of the 1-D TFM to simulate the two-phase long wave DWI instability is hereby performed.