Generalized Newtonian fluid flow through a porous medium

• A new model for generalized Newtonian fluid flow through a porous medium.
• Existence and uniqueness of the solution to the new model is shown.
• An approximation algorithm for the new model is presented.
• Results from numerical experiments compared with theoretical estimates.

We present a model for generalized Newtonian fluid flow through a porous medium. In the model the dependence of the fluid viscosity on the velocity is replaced by a dependence on a smoothed (locally averaged) velocity. With appropriate assumptions on the smoothed velocity, existence of a solution to the model is shown. Two examples of smoothing operators are presented in the appendices. A numerical approximation scheme is presented and an a priori error estimate derived. A numerical example is given illustrating the approximation scheme and the a priori error estimate.