Numerical Solution of Navier-Stokes Equations with Non-Linear Source Terms Nikolova, Ivanka Petkova, University of Pittsburgh, USA Among the varieties of methods applied in numerical modeling of fluid flows the Semi-Implicit Finite Differences Alternative Directions(Splitting Operators) techniques ocupies special place. It was created in 1978 in Moscow for numerical solving of the Navier-Stockes equations along the energy and species conservation equations. Non-linearity here arrises because of the presence of convective terms. But real strong non-linearity is due to the source terms representing heat or mass source respectivelly. The method allows to reduce a system of 5 or more PDE (usually coupled) for the velocity, density (pressure), temperature and species concentrations to a large system of algebraic equations, which is solved by forward-backward matrix procedure. It realization is quite difficult and computer time consuming. As compensation to this obstacles one gets detailed picture of flow behavior, namely the velocity, the temperature, the heat fluxes, other special profiles and time-dependent characteristics. Examples will be given for solving low Mach number flows with high temperature gradients as they frequently ocure in compustion processes.