A combination of parabolized Navier–Stokes equations and level-set method for stratified two-phase internal flow. (January 2017) - Rodríguez, Daniel
Highlights: First application of parabolized Navier–Stokes equations to internal flows with two immiscible phases. Computes flow fields with an accuracy comparable to expensive numerical simulations at a very low computational cost. Computations are performed on a personal computer in times of few minutes. Parabolic integration permits marching the solution to arbitrarily long distances in the streamwise direction. Abstract: A novel methodology is proposed for the numerical computation of pressure-driven gravity-stratified flows along channels comprising two immiscible phases. The parabolized Navier–Stokes equations are combined with the level set approach, resulting into a downstream-marching problem in which the solution is computed at each cross-section based on upstream information only. A main difficulty in the implementation of the approach for internal flows is the conservation of the mass flow rates, which is addressed by extending to two-phase flows the method proposed by Patankar and Spalding (1972) and Raythby and Schneider (1979), and by adding an explicit forcing term in the equation for the advection of the level function. The combination of high-order finite differences and sparse storage and algebra used here allows a fully-coupled integration of the parabolized equations, as opposed to the more classical segregated approaches. This enables a very efficient calculation of the complete downstream-developing flow field.