Abstract: In the past decade, Wang's control volume approach hasbeen the dominated method to simulate the advancing front of melt ininjection molding. It demands one and only one control volume be filledwithin one time step no matter how fine or rough the mesh is. The time stepdecision deduced from geometry is lack of theory support and difficult totest its stability. This limitation results in the loss of simulatedprecision for rough mesh and tedious calculation for fine mesh. This workpresents a new method to simulate the advancing front of viscousincompressible fluid in injection molding. The governing equations are interms of generalized Hele-Shaw flow for the viscous, incompressible,non-Newtonian fluid under non-isothermal conditions. The moving fluiddescription is transformed into a transport equation about fill factor inthe whole domain to be filled. The fill factor at each time step isdetermined by Taylor expansion, while the derivatives in the expansion iscalculated with the recursive formula derived by Galerkin method. Differentfrom Wang's approach, the time step in this present method is determined by thepre-error and high order derivative of fill factor which involving velocityfield and the previous conditions of neighboring control volumes. This workproves that the method is stable if the time step is carefully chosen. Basedon this theory, a program was developed to simulate the advancing meltfronts in injection molding. For verification of the numerical resultsobtained from the developed program, the simulation results are comparedwith the experimental results obtained from the test mold set designed byHan in the current study using the same commercial-grade PP and processconditions. Comparisons are also carried out between this present method and thetraditional method. Compared with Wang's approach, this present method canimprove the simulated precision for rough mesh and reduce the calculationfor fine mesh.