Influence of numerical diffusion on the growth rate of viscous fingers in the numerical implementation of the Peaceman model by the finite volume method

A numerical model of oil displacement by a mixture of water and polymer based on the Peaceman model is considered. Numerical experiments were carried out using the $\rm DuMu^x$ package, which is a software library designed for modeling nonstationary hydrodynamic problems in porous media. The software package uses the vertex-centered variant of finite volume method. The effect of diffusion on the growth rate of “viscous fingers” has been studied. The dependencies of the leading front velocity on the value of model diffusion are obtained for three viscosity models. It is shown that the effect of numerical diffusion on the growth rate of “viscous fingers” imposes limitations on calculations for small values of model diffusion.