A fast, decomposed pressure correction method for an intrusive stochastic multiphase flow solver

Abstract

Solution of the pressure Poisson equation is often the most expensive aspect of solving the incompressible form of Navier–Stokes. For a single phase deterministic model the pressure calculation is costly. Expanded to an intrusive stochastic multiphase framework, the simulation expense grows dramatically due to coupling between the stochastic pressure field and stochastic density. To address this issue in a deterministic framework, Dodd and Ferrante (“A fast pressure-correction method for incompressible two-fluid flows” Journal of Computational Physics, 273, 416–434, 2014) discuss a decomposed pressure correction method which utilizes an estimated pressure field and constant density to modify the standard pressure correction method. The resulting method is useful for improving computational cost for one-fluid formulations of multiphase flow calculations. In this paper, we extend the decomposed pressure correction method to intrusive uncertainty quantification of multiphase flows. The work improves upon the original formulation by modifying the estimated pressure field. The new method is assessed in terms of accuracy and reduction in computational cost with oscillating droplet, damped surface wave, and atomizing jet test cases where we find convergence of results with the proposed method to those of a traditional pressure correction method and analytic solutions, where appropriate.