Comparison of ODE methods for laminar reacting gas flow simulations

Abstract

Two-dimensional transient simulations are presented of the transport phenomena and multispecies, multireaction chemistry in chemical vapor deposition (CVD). The transient simulations are run until steady state, such that the steady state can be validated against the steady state solutions from literature. We compare various time integration methods in terms of efficiency and robustness. Besides stability, which is important due to the stiffness of the problem, preservation of non-negativity is crucial. It appears that this latter condition on a time integration method is much more restrictive toward the time step size than stability.

On projected Newton–Krylov solvers for instationary laminar reacting gas flows

“…In [18] we have shown that careful numerical analysis results in successful determination of time accurate solutions. However, in [18] we did not discuss efficient linear solvers. This is one of the topics of this paper.…”

“…doi:10.1016/j.jcp.2009. 11.004 details are given in Section 4 of this paper and in [18]. Under these circumstances most of the computing work is consumed by solving the system of Eq.…”

“…Moreover, virtually all published multi-species, multi-reaction CVD simulations have been limited to two spatial dimensions and steady state. In our prior work [18] and this paper we aim at two-dimensional and three-dimensional instationary CVD simulations. In [18] we have shown that careful numerical analysis results in successful determination of time accurate solutions.…”

“…In our prior work [18] and this paper we aim at two-dimensional and three-dimensional instationary CVD simulations. In [18] we have shown that careful numerical analysis results in successful determination of time accurate solutions. However, in [18] we did not discuss efficient linear solvers.…”

“…For stability, temporal discretization of (1) has to be implicit, and for positivity of species concentrations it has to be first order [18]. We therefore use the first order Euler backward method.…”