Discontinuous Galerkin hp-adaptive methods for multiscale chemical reactors: Quiescent reactors

We present a class of chemical reactor systems, modeled numerically using a fractional multistep method between the reacting and diffusing modes of the system, subsequently allowing one to utilize algebraic techniques for the resulting reactive subsystems. A mixed form discontinuous Galerkin method is presented with implicit and explicit (IMEX) timestepping strategies coupled to dioristic entropy schemes for hp-adaptivity of the solution, where the h and p are adapted based on an L1-stability result. Finally we provide some numerical studies on the convergence behavior, adaptation, and asymptotics of the system applied to a pair of equilibrium problems, as well as to general three-dimensional nonlinear Lotka-Volterra chemical systems.