The explicit compact difference scheme, proposed in Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD by Lin et al., published in Applied Mathematics and Mechanics （English Edition）, 2007, 28（7）, 943-953, has the same performance as the conventional finite difference schemes. It is just another expression of the conventional finite difference schemes. The proposed expression does not have the advantages of a compact difference scheme. Nonetheless, we can more easily obtain and implement compared with the conventional expression in which the coefficients can only be obtained by solving equations, especially for higher accurate schemes.
The Brownian dynamics （BD） simulation of a dilute surfactant solution is conducted in a steady shear flow. The rodlike micelle is assumed as a rigid rod composed of lined-up beads. A novel intercluster potential model is introduced for describing the interactions between, micelles. In the model, the Lennard-Jones and the soft-sphere potentials are used as inter-bead potentials for end-end and interior-interior beads, respectively. The micelles are combined at their ends to form a network structure at lower shear rates and are disconnected to become more and more parallel to the shear flow direction with increasing shear rate. The change of micellar microstructures with the variation of the shear rate results in shear thinning characteristics of the computed shear viscosities and first normal stress difference coefficients. The effects of surfactant solution concentration on the micellar structures and rheological properties are also investigated. Results show that the shear viscosities and the first normal stress difference coefficients increase with increasing the viscosity of the surfactant solution.
