3D dynamic model for channeled model flows with nonlinear rheology

In this work we studied the effect of a power-law rheology on a gravity driven lava flow. We consider a viscous fluid flowing in the x direction in an inclined rectangular conduct. The flow is assumed steady, laminar and subjected to the gravity force. The fluid is assumed isothermal, isotropic and incompressible, with constant density and power law rheology. Analytical solution for the equation of the motion does not seem to be possible, so an approximated solution was found. We used the finite volume method to obtain the discretized equation that was solved with a classical iterative technique. The convergence, the stability and the order of approximation were tested for the case n =1 comparing the numerical solution with the analytical solution available for the Newtonian rheology. The results indicate that, for a lava flow with constant flow rate, the power-law rheology produces important differences as to the height of the channel and the average flow velocity with respect to the Newtonian case.