A pressure–velocity coupling approach for high void fraction free surface bubbly flows in overset curvilinear grids Jiajia Li, Alejandro M. Castro* ,† and Pablo M. Carrica IIHR-Hydroscience and Engineering, The University of Iowa, Iowa City, IA 52242, USA SUMMARY A methodology for improved robustness in the simulation of high void fraction free surface polydisperse bubbly flows in curvilinear overset grids is presented. The method is fully two-way coupled in the sense that the bubbly field affects the continuous fluid and vice versa. A hybrid projection approach is used in which staggered contravariant velocities at cell faces are computed for transport and pressure–velocity coupling while the momentum equation is solved on a collocated grid arrangement. Conservation of mass is formu- lated such that a strong coupling between void fraction, pressure, and velocity is achieved within a partitioned approach, solving each field separately. A pressure–velocity projection solver is iterated together with a predictor stage for the void fraction to achieve a robust coupling. The implementation is described for general curvilinear grids detailing particulars in the neighborhood to overset interfaces or a free surface. A balanced forced method to avoid the generation of spurious currents is extended for curvilinear grids. The overall methodology allows simulation of high void fraction flows and is stable even when strong packing forces accounting for bubble collisions are included. Convergence and stability in one-dimensional (1D) and two-dimensional (2D) configurations is evaluated. Finally, a full-scale simulation of the bubbly flow around a flat-bottom boat is performed demonstrating the applicability of the methodology to complex problems of engineering interest. Copyright © 2015 John Wiley & Sons, Ltd. Received 28 February 2015; Accepted 2 May 2015 KEY WORDS: pressure–velocity coupling; projection method; two-phase bubbly flow; curvilinear grids; overset; free-surface flows 1. INTRODUCTION It is well known that the staggered arrangement of pressure and velocity leads to a very stable pressure–velocity coupling that allows to preserve mass to machine precision. This scheme is attrac- tive because no special care on how fluxes are computed needs to be taken to obtain a strong pressure–velocity coupling. This is particularly important for applications with density changes and in particular for high density ratios as in the case of free surface flows [1, 2]. On the other hand, the collocated arrangement of velocity and pressure provides a configuration of simpler implemen- tation because only one grid for all variables can be used in contrast to having a different grid for each velocity component and pressure separately. While this does not represent a particular advantage for codes using Cartesian grids, it does make a significant difference for implementations using curvilin- ear grids for which significantly more complex geometric metrics are needed [3]. The evaluation of several metrics not only is cumbersome but also requires a significantly larger amount of computa- tions and memory. In addition, curvilinear grids can be body fitted allowing the representation of complex geometries and proper refinement normal to solid walls to resolve boundary layers. This technique has proven very effective in combination with overset methods [4, 5], allowing to *Correspondence to: Alejandro M. Castro, 100 C. Maxwell Stanley Hydraulics Laboratory, Iowa City, IA 52242, USA. † E-mail: alejandro-castro@uiowa.edu Copyright © 2015 John Wiley & Sons, Ltd. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids 2015; 79:343–369 Published online 18 June 2015 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/fld.4054