Three dimensional combustor calculations are currently stretching the computer hardware capabilities and the computing budgets of gas turbine manufacturers. One of the main reasons for this relates to the large number of complex physical processes occurring in the combustor. Airflow, fuel spray, reaction kinetics, flame radiation, and not the least of which, turbulence must be modeled and the related differential equations solved. Discussions in this conference will address methods to improve the accuracy of combustor flow field calculations and methods to speed the convergence of the modeled equations. This report will focus on aspects of merging these two new technologies. The improved accuracy discretization schemes have a negative impact on the speed of convergence of the modeled equations that the improved solution algorithms may not overcome. A description of the causes of this problem and potential solutions will be examined