spectrally accurate boundary integral method is developed for solving the velocity of the film flow with suspended particles down an inclined... Show morespectrally accurate boundary integral method is developed for solving the velocity of the film flow with suspended particles down an inclined plane in Stokes flow. The problem is a two-dimensional gravity-driven film flow with a rigid particle flowing down an inclined plane. We present the governing equations and the numerical methods for solving it with the help of periodic Green’s function. To obtain the system of discretized equations, we discuss the smoothness of each integrand appearing in the boundary integral formulation and use the composite trapezoidal rule for smooth periodic integrands to achieve the spectral accuracy. For the weakly singular integral, we approximate it by a special spectrally accurate quadrature. The Krylov subspace iterative method GMRES is employed to solve the resulting linear system. This method can be also applied to compute the velocity of interface in some other cases of film flow. M.S. in Applied Mathematics, May 2011 Show less
