After the implementation of local mesh refinement (LMR) in solution of Euler equations and detonation simulation, the technique has been used to optimize the simulation of viscid flow. In this paper, LMR has been implemented in Navier-Stokes (NS) equations and LES turbulent model. In order to implement LMR in the simulation of viscid flow accurately and efficiently, hybrid interpolation and coarse flux limiter are established. At the same time, implementation of LMR maintains the temporal refinement in solution of NS equations. In practical application, 2D advection diffusion is used to show the advantages of LMR and verify the implementation.

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