A class of projected Newton methods to solve laminar reacting flow problems

The numerical modeling of the transport phenomena and the multispecies, multireaction chemistry in laminar reacting gas flow processes such as chemical vapor deposition typically involves the solution of large numbers of advection-diffusion-reaction equations, which are stiffly coupled through the reaction terms. Stability and positivity requirements of the solution basically reduce the time integration to be first order Euler Backward. This paper is devoted to the reduction of the computational costs within Newton’s method by means of introducing preconditioned iterative linear solvers. However, solving nonlinear systems in an iterative way does not guarantee the positivity of the solution. In particular when the linear systems within Newton’s method are not solved exactly, the nonlinear solution may have many small negative elements. To circumvent this, we introduce a projected Newton method. We conclude by comparing various preconditioners for the acceleration of the internal linear algebra problem.