A new upscaling method for the solute transport equations

This paper proposes a new upscaling method in the simulations of solute transport in heterogeneous media. We provide a detailed convergence analysis of the method under the assumption that the oscillating coefficients are periodic. While such a simplifying assumption is not required by our method, it allows us to use homogenization theory to obtain the asymptotic structure of the solutions. Numerical experiments are carried out for solute transport in a porous medium with a random log-normal relative permeability to demonstrate the efficiency and accuracy of the proposed method.