Further development of a combustion Large Eddy Simulation (LES) code for the design of advanced gaseous combustion systems is described in this fourth quarterly report. CFD Research Corporation (CFDRC) is developing the LES module within the parallel, unstructured solver included in the commercial CFD-ACE+ software. In this quarter, in-situ adaptive tabulation (ISAT) for efficient chemical rate storage and retrieval was further tested in the LES code. A more efficient PK binary tree data structure is being developed and implemented to replace the original BSP-tree structure. Implementation of the Linear Eddy Model (LEM) for subgrid chemistry has also started. In addition, Georgia Tech has shown that a chemical neural net (1-step chemistry) trained at certain turbulent conditions can be used at different turbulent conditions without expensive chemical kinetic integrations. Initial evaluations of the code accuracy have also been carried out. The evaluations cases included the unstable DOE-NETL combustor and a lid-driven cavity. Next quarter, the ISAT algorithm for efficient chemistry will be tested for the unstable DOE-NETL combustor. Initial flame calculations, with the LEM subgrid chemistry model are planned. Also, demonstration of the neural net approach, for chemical kinetics speed-up, should be demonstrated for more advanced chemistry (8-species and 19-species mechanisms).