H(div)-Conforming DG Method for the Coupled Generalized Convective Brinkman–Forchheimer and Double-Diffusion Equations

Speaker: Kallol Ray

Venue: Room 203, Haina Building 2, Zijingang Campus

Abstract: This work investigates both steady and unsteady nonlinear systems that couple the generalized convective Brinkman-Forchheimer model with a system of advection-diffusion equations, commonly referred to as double-diffusion equations. The existence and uniqueness of weak solutions to the governing equations are established using Galerkin’s method. Subsequently, H(div)-conforming discontinuous Galerkin (DG) discretizations are formulated for the considered models, yielding exactly divergence-free velocity approximations. For the unsteady model, a second-order semi-implicit backward differentiation formula (BDF2) scheme is employed for temporal discretization. A rigorous analysis is then carried out to establish the well-posedness of the discrete problems. Optimal a priori error estimates are derived, ensuring that the velocity errors are pressure-robust. Furthermore, when the diffusion coefficients are constant, the velocity error estimates are Re-semi-robust at high Reynolds numbers. Numerical experiments are presented to corroborate the theoretical results and to demonstrate the performance of the proposed methods.