AbstractsMathematics

For finding the solution to Stokes flow due to motion of an immersed particle, we introduce two different methods based on boundary integral equations (BIE). For the first method, which is based on the first kind BIE, we prove the compactness of the integral operator of which the kernel is the Stokeslet, which implies that the BIE of the first kind in this method are ill-posed problems. For the second method, which is based on the second kind BIE which are well-posed problems, it is shown that the kernel functions in the BIE are generally not smooth. Finally, using the known numerical schemes, we compare the computational cost of these two method for finding the velocity of a given point in the domain in terms of the number of numerical integrations over triangles. It is show that theses two schemes are of same order while the computational cost of the second method is more expensive than that of the first one.