On the Horizontal Method of Lines for Nonlinear Adsorption Problems
We consider a nonlinear transport problem to model the chromatography
process of high-capacity multimodal membranes. The absorption model
for this process is nonlinear and can be represented by either
explicitly or implicitly defined isotherms. Through the utilization of
the horizontal method of lines, a variety of time-integration schemes
are developed. The main advantage of this method is its flexibility in
the manipulation of the nonlinear term when compared to the
traditional method of lines. Preliminary stability and solvability
results are presented for selected schemes. We use the FEniCSx
environment to generate approximate solutions, employing its parallel
capabilities to evaluate different temporal integration schemes
coupled with nonlinear solution algorithms. Numerical verification of
a priori error estimates is also provided.
Last modified: Tue Apr 2 11:05:37 EDT 2024