Abstract： To study the diffusion mechanism of expansible grouting material, a calculation method for solving two-dimensional flow field of variable density grout was developed based on the modern computational fluid dynamics theory. The structured collocated grid was used for partitioning the computational domain. The finite volume method (FVM) was employed to discretize the governing equations of grout. The momentum interpolation method (MIM) was adopted to establish the pressure correction equation. The semi-implicit method for pressure-linked equations (SIMPLE) was utilized for iteratively solving discrete momentum equations, pressure correction equations and velocity correction equations. By using it to solve an example of variable density grout freely expanding in a two-dimensional rectangular slot, the validity and high calculation accuracy of the proposed method was verified, laying a foundation for developing the numerical method for simulating the flow and diffusion process of expansible polymer grouting material in two-dimensional fractures.