Wavelet-based upscaling of advection equations

A method for upscaling the transport equation for flow in porous media is presented. This is a new application of the wavelet-based renormalization method for absolute permeability in Darcy’s elliptic equation for flow in porous media, described in Pancaldi et al. [V. Pancaldi, K. Christensen, P.R. King, Transp. Porous Media 67 (3) (2007) 395]. This formalism can be applied to any parabolic equation, such as the heat equation or other advection and diffusion transport equations. We present the method for a tracer transport problem.