Numerical essays on the development of turing patterns under the effect of incompressible convective fields: An approach from the cavity problem

This work presents a number of numerical examples of reaction-difussion equations in Turing space, modified by convective fields in incompressible flows, using a Schnakenberg reaction mechanism. Examples were made in 2D using quad elements, which have an imposed advective field derived from the cavity problem solution. The developed model consists of an uncoupled system of equations including the reaction-advection-diffusion equations and the Navier-Stokes equations for incompressible flow. This system is solved simultaneously using the finite element method. Results illustrate that complex patterns are formed, mixing dots and stripes which reach a stable state. Changes in pattern concentration in both space and time are also shown due to the effect of the advective field. Numerical examples confirm that pattern formation is independent of initial conditions and mesh.