Workshop on Numerical Methods and Analysis in CFD - Abstract

Gazca Orozco, Pablo Alexei

Nonlinear iterative approximation of steady flow of chemically reacting fluids

In this talk, I will present some recent results obtained in collaboration with P. Heid and E. Süli on an iterative scheme for computing the solutions of a system describing an incompressible fluid with power-law-like rheology, with a power-law exponent depending on a scalar variable that solves an advection-diffusion PDE; in particular, this exponent varies in space. Under small data assumptions, we prove that a Zarantonello-type iteration converges to the (unique) solution of the problem. The proposed iteration scheme is remarkably simple and it amounts to solving a linear Stokes-Laplace system at each step. I will conclude with numerical experiments and some discuss possible uses as a nonlinear preconditioner.