On Numerical Issues in Time Accurate Laminar Reacting Gas Flow Solvers

The numerical modeling of laminar reacting gas flows in thermal Chemical Vapor Deposition (CVD) processes commonly involves the solution of advectiondiffusion-reaction equations for a large number of reactants and intermediate species. These equations are stiffly coupled through the reaction terms, which typically include dozens of finite rate elementary reaction steps with largely varying rate constants. The solution of such stiff sets of equations is difficult, especially when timeaccurate transient solutions are required. In this study various numerical schemes for multidimensional transient simulations of laminar reacting gas flows with homogeneous and heterogeneous chemical reactions are compared in terms of efficiency, accuracy and robustness. One of the test cases is the CVD process of silicon from silane, modeled according to the classical 17 species, 26 reactions chemistry model for this process as published by Coltrin and coworkers [4]. It is concluded that, for time-accurate transient simulations the conservation of the non-negativity of the species concentrations is much more important, and much more restrictive towards the time step size, than stability. For this reason we restrict ourselves to the first order, unconditionally positive Euler Backward method. Since positivity of the solution is very important, the use of Newton methods to solve the nonlinear problems is only feasible in combination with direct solvers. When using iterative linear solvers, it appears that the approximate solutions may have small negative elements. To circumvent this, we introduce a projected Newton method. Choosing the best preconditioners, combined with our projected Newton method, enables us to reduce the computational time of the time accurate simulation of the classical 17 species, 26 reactions chemistry model by a factor 20 on a single processor.