Fully-discrete provably Lyapunov consistent discretizations for convection-diffusion-reaction PDE systems

• DOI: 10.48550/arxiv.2410.11669
• Publication Date: 2024-10-15
• Authors: Rasha Al Jahdali; David C. Del Rey ...; Lisandro Dalcín; Matteo Parsani
• Keywords: Reaction–diffusion system

Convection-diffusion-reaction equations are a class of second-order partial differential widely used to model phenomena involving the change concentration/population one or more substances/species distributed in space. Understanding and preserving their stability properties numerical simulation is crucial for accurate predictions, system analysis, decision-making. This work presents comprehensive framework constructing fully discrete Lyapunov-consistent discretizations any order convection-diffusion-reaction models. We introduce systematic methodology that mimic analysis continuous using Lyapunov's direct method. The spatial algorithms based on collocated discontinuous Galerkin methods with summation-by-parts property simultaneous approximation terms approach imposing interface coupling boundary conditions. Relaxation Runge-Kutta schemes integrate time achieve Lyapunov consistency. To verify new schemes, we numerically solve governing dynamic evolution monomer dimer concentrations during dimerization process. Numerical results demonstrated accuracy consistency proposed discretizations. can enable further advancements control, understanding general systems.