Turbulent mixing of single or multi-phase flows is common in diverse research fields, and direct numerical simulation is useful for understanding such phenomenon. To study the scaler transport in turbulence, the computational grids must resolve the Batchelor scale, which is smaller than the Kolmogorov scale by a factor of √Sc. This would commonly lead to the over-resolving of the Navier-Stokes equation, making DNS even more expensive. To overcome this issue, this thesis presents a method to reduce the computational cost in scalar turbulent flows, by using a coarse grid for the velocity and a fine grid for the scalar. A divergence-free Hermite interpolation is implemented for the velocity field to ensure the continuity equation is fulfilled on the fine grid. The interpolation scheme is validated by cases of Arnold–Beltrami–Childress flow and Taylor–Green vortex. For the active scaler, the integration schemes are included for fine-to-coarse integration. The multi-resolution method is parallelised by MPI and integrated into the open-source multiphase flow solver FluTAS. For the diffuse interface modelling in FluTAS, the indicator function is updated on the fine grid, and the surface tension force is then calculated and extrapolated back to the coarse grid for momentum equation update. The method is evaluated against the single-resolution method at different refinement factors.