On the DLM/FD methods for simulating neutrally buoyant swimmers moving in non‐Newtonian shear thinning fluids

Abstract

In this article we discuss the generalization of a Lagrange multiplier based fictitious domain (DLM/FD) method to simulating the motion of neutrally buoyant particles of non‐symmetric shape in non‐Newtonian shear‐thinning fluids. Numerical solutions of steady Poiseuille flow of non‐Newtonian shear‐thinning fluids are compared with the exact solutions in a two‐dimensional channel. Concerning a self‐propelled swimmer formed by two disks, the effect of shear‐thinning makes the swimmer moving faster and decreases the critical Reynolds number (for the moving direction changing to the opposite one) when decreasing the value of the power index n in the Carreau‐Bird model.