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

On the DLM/FD methods for simulating neutrally buoyant swimmer motion in non-Newtonian shear thinning fluids