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Show .... pIc. ha\'e been ana1yzed for major species composition. Comparison of centerline va1ues of Ar, CO and CO2 concentrations as measured and as predicted by the three simulat ions are shown in Figure 5. Temperat ure predictions have been shown for (ompari~on. In this furnace Ar tracer has been doped into the primary (coa1 carrier) stream to track the gaseous mixing. Mixing properties clearly do not change dramatically with heat transfer or with increased fluid turbulence. The discrepancy between data and predictions in the early part of the furnace depict data collection problems since the inlet condition of the predictions is that reported for the experiment. The variability in the CO and CO2 predictions quantifies the impact of the local heat loss and of the turbulent fluctuations on the flame structure. The heat loss results in differences of around 50% in CO concentrations at the centerline and CO2 concentration differences of 70%. Although the fluid turbulence results in a smaller variability, it is clearly significant. Radial profiles at an axial location ~ of the distance from the burner to the outlet are shown in Figure 6. 5 Ad\anced Numerical Methods 5.1 General Description One of the observations that results from the preceding discussion is tbat current numerical methods are unacceptable for con1prehensive, industrial coal furnace computer models. To make meaningful predictions in reasonable computational times for these complex furnaces , dran1atic improvements must be made in coDvergence properties while expanding capabilities for increased grid resolution. 1\1 ucb work bas been performed in this area in recent years , and several candidate metbods provide \arying degrees of success. Some examples of these advanced techniques are: preconditioned conjugate gradient methods [12]; adaptive grid algorithms, of which there are a number of variations [13)4,15]' and multigrid methods [16,17,18]. \\'e have chosen to concentrate our numerical efforts on implementing multi grid or multilevel methods. These techniques are thought to have more applicability to these codes : and pro\'ide the greatest potential impact in terms of computational run times. The derivation and full description of multigrid methods is contained fully in several publications [16,17,18]. The essence of multigrid methods is that tbe error of an iterative solution is approximated by making calculations on a coarser grid , and then is used to correct the existing solution OD the fine grid. This requires three steps: 1) interpolation of the solution from the fine to the coarse grid 2) error calculations. and 3) interpolat.ion and correction of errors from the coarse to fine grid. The coarse grid usually contains half as many nodes as the fine grid for each dimension. The abo\'e error correction algorithnl can be applied recursively, so that this error calculation 11 |