Comparison of two iterative schemes to solve the Chemotaxis– Biodegradation System.

Résumé

The mathematical model describing the biodegradation process in porous media by bacteria—
divided into planktonic and adherent types—incorporates the chemotaxis effect, wherein the flow velocity
depends on the concentration of adherent bacteria. This model consists of a system of five strongly
coupled nonlinear parabolic equations, including a nonlinear advection term. Using the fixed-point theorem,
we establish the existence, uniqueness, and non-negativity of the solution.
To approximate the solution, we employ the finite element (FE) method. To linearize the system at each
time step, we compare two iterative schemes. The first, called the Coupled Prediction Scheme (CPS), is shown
to converge, while the second is the conventional Fixed-Point Method (FPM). Theoretical and numerical results
show that CPS offers a faster and more efficient alternative to the conventional FPM.