SUMMARYIn this work, a generalized Hele-Shaw approach is developed for non-isothermal, non-Newtonian and inelastic flows arising in injection molding. The advancing free surface of the injected fluid is predicted by a novel meshless front-tracking method coupled to control volume finite element solution for the pressure. A modified Cross constitutive model with Arrhenius temperature dependence is employed to describe the viscosity of the melt and the temperature field is solved by a semi-Lagrangian scheme with a finite volume method. The utility of the combined algorithm is demonstrated for a test problem that has complex 'obstacles' in the mold interior.