Hybrid grid-particle method for fluid mixing simulation

Abstract

In this paper, we propose a hybrid grid-particle method for the numerical simulation of fluid mixing problem. The method solves the incompressible Navier–Stokes equations using a grid method and the advection–diffusion equation of chemical species concentration using a particle method. With this framework, the fluid mixing problem at moderate Reynolds number ( $$\sim $$ 10 $$^2$$ ) and high Peclet number ( $$\sim $$ 10 $$^5$$ ), which is typical for liquid–liquid mixing in microsystem, can efficiently be solved utilizing the characteristics of each approach; the flow field is stably solved even with long time step, and the concentration field is accurately solved with minimal numerical diffusion. The proposed hybrid method is examined through three test cases, and the results show that the hybrid method provides substantial accuracy for simulating the fluid mixing problem at high Peclet number.