The following work have been accepted for publication on Communications in Nonlinear Science and Numerical Simulation (CNSNS; https://www.sciencedirect.com /journal/communications-in-nonlinear-science-and-numerical-simulation) and is now available online:

A relaxation approach to modeling properties of hyperbolic-parabolic type models

Eduardo Abreu, Wanderson Jose Lambert, Arthur Miranda do Espírito Santo and John Perez.

LINK: https://doi.org/10.1016/j.cnsns.2024.107967

Highlights:
• We propose a novel relaxation approach for modeling convection-diffusion problems via a hyperbolic system.
• The new system satisfies Liu’s sub-characteristic condition, ensuring solution stability.
• We apply the relaxation modeling to both classical and non-classical models.
• From numerical experiments, we verify the new system’s solutions converge to those of the original equations.

Keywords: Modeling using PDEs via Relaxation; Liu sub-characteristic condition; Convection-diffusion problems; Discontinuous flux function; Discontinuous coefficient in space; Numerical validation of models.