DRBEM formulation for transient Stokes flow with slip boundary condition

In this study, the effect of linear and nonlinear slip boundary conditions on the flow of a slow viscous fluid is investigated numerically. The boundary integral representation of the transient Stokes equations is given in primitive variables form. The fundamental solution to the steady Stokes equations is employed in the boundary element method (BEM) formulation. The time derivative is taken to the boundary with the dual reciprocity method and approximated by the finite difference method (FDM) until a steady-state is achieved. It is assumed that the fluid is capable of slip, with the slip velocity expressed as a function of shear rate at the wall. In the numerical tests, the fluid is initially assumed to be stationary; at each time step, the velocity boundary conditions along the walls are updated as the shear forces vary with time