A bi-phasic model is necessary for the simulation of phase segregation effects in PIM, which results in the solution of two coupled Navier-Stokes equations. Based on the previous explicit algorithms realized by the authors, a new explicit and vectorial algorithm for bi-phasic filling flow has been proposed and developed. By virtue of the new algorithm, all the global solutions are removed to provide the purely vectorial operations with a very efficient feature. The only matrix operations are strictly limited at the element level. Moreover, only the elements of equal-order interpolations are necessary with this new algorithm. In the filled domain, Incompressibility of the mixture is retained by a specially designed corrective feedback operation, with a systematic smoothing procedure to avoid the possibility of mesh lock. As all the global solutions are performed in vectorial forms, the computational cost is merely about proportional to the degree of freedom level. So the simulation of filling processes and phase segregation effects can be carried out with high efficiency, which provides the good suitability for simulation of the industrial problems in large scale. It is furthermore easy to be parallelized on a high performance multi-cluster system. The comparison of numerical results with the experiments proves the validity and efficiency of newly proposed algorithm.