The solution of very large non-linear algebraic systems

The manuscript discusses the feasibility and the methods for solving systems of non-linear algebraic equations, the main numerical subjects being convergence tests, stop criteria, and expedients for large and sparse systems. After a detailed discussion on the features of large non-linear systems, the paper focuses on the numerical simulation of complex combustion devices and on the formation of macroand micro-pollutants. This quantification is not possible by simply introducing a detailed kinetic scheme into a fluid dynamics (CFD) code, especially when considering turbulent flows. Actually, the resulting problem pplied numerical analysis ery large non-linear algebraic systems ixed CFD and detailed kinetics would reach a so huge dimension that is still in orders of magnitude larger than the feasible one (by means of modern computing devices). To overcome this obstacle it is possible to implement a separate and dedicated kinetic post-processor (KPP) that, starting from the CFD output data, allows simulating numerically the turbulent reactive systems by means of a detailed kinetic scheme. The resulting numerical problem consists of a very large, non-linear algebraic system comprising a few millions of unknowns and equations. The manuscript describes the KPP organization and structure as well as the numerical s that challenges and difficultie