Abstract: A detailed description of turbulent fluids based on numerical simulation is an important research topic required by many visual effects. We propose a novel method to simulate fluids with turbulent small-scale details. By inserting diffusive derivatives and divergence-free constraints to moving least-squares (MLS) fitting, we upgrade the velocity interpolation method for existing fluid solvers to enhance the subgrid accuracy. The time-step restriction of asymptotic property of diffusive derivatives is resolved by means of coupling to the constrained interpolation profile (CIP) advection framework. The proposed constrained moving least-squares interpolation profile (CMIP) method provides intuitive control over turbulence through the adjustment of one parameter as though controlling the Reynolds number with an inviscid model. The proposed method generates improved visuals of the highly turbulent fluid and is complementary to existing techniques that are currently being used.