IN RESPONSE TO ROA-2011 APPENDIX A-2 SUBSONIC FIXED WING (SFW1) SECTION 2.2: NUMERICAL METHODS FOR TURBULENT FLOW COMPUTATIONS WE PROPOSE TO PERFORM RESEARCH ON HIGH ORDER DISCONTINUOUS GALERKIN (DG) AND WEIGHTED ESSENTIALLY NON-OSCILLATORY (WENO) ALGORITHMS FOR COMPRESSIBLE TURBULENCESIMULATIONS. THE OBJECTIVE OF THIS RESEARCH IS THE CONSTRUCTION OF EFFICIENT AND HIGHLY ACCURATE SOLVERSBOTH FOR DIRECT NUMERICAL SIMULATIONS AND FOR SIMULATIONS WITH TURBULENCE MODELS FOR COMPRESSIBLE FLOWS. WE WILL EMPHASIZE RESEARCH ON A FEW CRUCIAL ALGORITHM DEVELOPMENT EFFORTS TO FACILITATE THE CONSTRUCTION OF ROBUST DG AND WENO SCHEMES FOR COMPRESSIBLE TURBULENCE SIMULATIONS INCLUDING THE DESIGN OF COMPACT WENO SCHEMES WITH SMALL DISPERSION AND DISSIPATION ERRORS A TECHNIQUE TOMAINTAIN POSITIVITY OF DENSITY AND PRESSURE WITHOUT AFFECTING HIGH ORDER ACCURACY FOR BOTH HIGH ORDERWENO AND DG SCHEMES THE DESIGN OF EFFICIENT AND RELIABLE HIGH ORDER WENO LIMITERS FOR DG SCHEMES TO STABLY RESOLVE STRONG DISCONTINUITIES WITHOUT LOSING ACCURACY AND AN EFFECTIVE TREATMENT OF STIFF SOURCE TERMS TO OBTAIN CORRECT SHOCK LOCATIONS ON COARSE MESHES FOR HIGH ORDER WENO AND DGSCHEMES. AT THE LATER STAGE COLLABORATIONS WITH NASA SCIENTISTS ARE ENVISIONED TO DEVELOP AND TESTCODES USING THE NEW TECHNIQUES AND PERFORM SIMULATION ON BENCHMARK PROBLEMS IN COMPRESSIBLE TURBULENCE TO VERIFY THE ADVANTAGE OF THESE NEW TECHNIQUES. THE ENVISIONED BENCHMARK PROBLEMS INCLUDE HOMOGENEOUS TURBULENCE BOUNDARY EFFECTS AND SHOCK INTERACTION WITH VORTICES. IT IS EXPECTEDTHAT THE WENO AND DG ALGORITHMS WITH FEATURES RESULTING FROM THIS RESEARCH WILL BE MORE ROBUST MORE ACCURATE AND MORE EFFICIENT IN COMPRESSIBLE FLOW SIMULATIONS THAN THE CURRENT WENO AND DG ALGORITHMS WHICH ARE ALREADY AMONG THE POPULAR CHOICES OF SIMULATION ALGORITHMS FOR COMPRESSIBLETURBULENCE.