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In our work, we mainly use a lattice Boltzmann method (LBM) to simulate the underlying dynamics of miscible mixtures in binary fluid simulation called TFLBM. However, it suffers from the limitation of only resolving mixture flows with low Reynolds number, and it would blow up when the Reynolds number gets higher. In order to resolve such mixture flows with higher Reynolds number, by further investigation, we proposed to use a subgrid method to stabilize the computation of two fluid mixtures. The idea of the subgrid method is to split the actual velocity field into large-scale (resolved) and small-scale (unresolved) components. The effect of the unresolved motion on the resolved one is included by introducing a so-called eddy viscosity, and the method is also referred to as large eddy simulation (LES).