Champagne glasses are subjected to complex ascending bubble-driven flow patterns, which are believed to enhance the release of volatile organic compounds in the headspace above the glasses. Based on the Eulerian–Lagrangian approach, computational fluid dynamics (CFD) was used in order to examine how a column of ascending bubbles nucleated at the bottom of a classical champagne glass can drive self-organized flow patterns in the champagne bulk and at the air/champagne interface. Firstly, results from two-dimensional (2D) axisymmetric simulations were compared with a set of experimental data conducted through particle image velocimetry (PIV). Secondly, a three-dimensional (3D) model was developed by using the conventional volume-of-fluid (VOF) multiphase method to resolve the interface between the mixture’s phases (wine–air). In complete accordance with several experimental observations conducted through laser tomography and PIV techniques, CFD revealed a very complex flow composed of surface eddies interacting with a toroidal flow that develops around the ascending bubble column.