A relatively simple approximate single-phase model (SPM) was developed for flow simulation of viscous liquid motion generated by a chain of rising bubbles. The complete detailed information about the gas-liquid two-phase flow was obtained with help of the full multi-phase model (MPM) using the direct numerical simulation (DNS) approach of the volume of fluid method (VOF), as implemented in the Fluent software. The overall driving effect of the bubble chain was expressed with an approximate buoyancy force closure formula, obtained in form of correlations of the MPM numerical data This formula was compared with other published closures and used as a source term in SPM. SPM was solved and the results compared with MPM. Good agreement was found. SPM worked well in a range of bubbling frequency, liquid viscosity, and with temperature gradients. The replacement of the highly demanding and complex MPM with SPM is a great simplification of the flow modelling. SPM can be readily used for simulating the flow structure in containers with pneumatic mixing and design of equipment, where several rows of bubbling nozzles are installed. In this work, our modelling was done for the case of glass melts in glass furnaces. (C) 2015 Elsevier Ltd. All rights reserved.