Abstract: Anisotropic unstructured mesh adaptation was developed to improve the accuracy of the numerical solutions of the complicated turbulent combustions in practical gas turbine combustors. Numerical solutions of four benchmark problems (oblique shock on a 15° wedge at Mach 2.5; one-dimensional premixed laminar flame; two-dimensional opposed flame; and three-dimensional premixed Bunsen flame) demonstrate the applicability of the proposed anisotropic mesh adaptation. The proposed method has been used to study the combustion in a low emission RQL(rich-burn, quick-mix, lean-burn) combustor and the underlying mixing process. The complex thermo-acoustic instabilities were captured well.