In the mixing systems of high Schmidt fluids, calculation of a precise concentration distribution is difficult because numerical diffusion becomes appreciable. In this paper, a new calculation model is proposed that allows the representation of the fine lamellar mixing pattern without using extremely small lattice cells, to attain both high speed calculation and a numerically stable scheme. This model has the following characteristics. (1) Advection is expressed by a Lagrangian method using one-to-one mapping in order to suppress numerical diffusion. (b) Each lattice cell is divided into subcells. This suppresses, numerical diffusion effects even when the cell sizes are large. (3) For the speed-up of calculation and the numerical stabilization, the processes of advection, molecular diffusion and chemical reaction are calculated sequentially, and local analytical solutions are used in these schemes.