Numerical Simulation of a Class of PDAEs with a Separation of Time Scales

Abstract

Modeling and simulation of dynamic systems with a separation of time-scales leads naturally to sing ular perturbation models. For systems of PDEs in time and one spatial dimension, the corresponding quasi-steady-state models yields a reduced set of PDEs (slow variables), subject to a set of (impli cit) ODEs in the spatial dimension (fast variables). In this presentation, we shall consider those problems wherein the slow variables are lumped and th e fast variables are hyperbolic with all the characteristics pointing in the same direction. Under these assumptions, the quasi-steady-state model yields two decoupled subsystems, (i) a set of ODEs in time, subject to a set of ODEs in the spatial dimension, i.e., ODEs embedded ODEs. A numerical integrator can then be used to solve for the spatial profile of the fast variables at e ach time step for the slow variables. The ability to use an adaptive spatial mesh is highly advanta geous to the relibiality and accuracy of the simulation. This is demonstrated on applications relat ed to the start-up of micro-scale chemical processes for portable power generation, where shock and fronts can develop and move around the spatial domain.