18. New Trends on Multiphase Flow Simulations Using Slug Capturing Approach

It is well known that the 4-equation formulation of the two-fluid model is ill-posed. As a result, it is impossible to differentiate between the errors originating from uncertainty in the empirical closure models and the nonphysical oscillations due to ill-posedness of the equations. The present work uses a 5-equation formulation, by adding a volume fraction evolution equation, which is unconditionally hyperbolic. To solve the resulting system of equations, a high-resolution Roe’s scheme is developed, and to keep the solution time practical, an adaptive mesh refinement algorithm is implemented. To obtain the wall shear stresses, a novel set of analytically developed friction equations is used for the non-Newtonian liquid phase. Finally, the capability of the developed code has been examined for the terrain slugging cases.