A modified phase-field model is presented to numerically study the dynamics of flowing foam in an obstructed channel. The bubbles are described as smooth deformable fields interacting with one another through a repulsive potential. A strength of the model lies in its ability to simulate foams with wide range of gas fraction. The foam motion, composed of about hundred two-dimensional gas elements, was analyzed for gas fractions ranging from 0.4 to 0.99, that is below and beyond the jamming transition. Simulations are preformed near the quasi-static limit, indicating that the bubble rearrangement in the obstructed channel is primarily driven by the soft collisions and not by the hydrodynamics. Foam compression and relaxation upstream and downstream of the obstacle are reproduced and qualitatively match previous experimental and numerical observations. Striking dynamics, such as bubbles being squeezed by their neighbors in negative flow direction, are also revealed at intermediate gas fractions.