Abstract: The lineal approximation of the line continuous distribution method of singularities is proposed to treat the creeping motion of the arbitrary prolate axisymmetrical body. The analytic expressions in closed form for the flow field are obtained. The numerical results for the prolate spheroid and Cassini oval demonstrate that the convergence and the accuracy of the proposed method are better than the constant density approximation. Furthermore, it can be applied to greater slender ratio. In this paper the example is yielded to show that the linear approximation of the singularities for the density on the partitioned segments can be utilized to consider the creeping motion of the arbitrary pointed prolaue axisymmetrical body.

Key words: convection-diffusion equation, alternating segment method, Crank-Nicolson scheme, asymmetries difference scheme, unconditionally stable, parallel computing