Weakening accuracy dependence with the regularization parameter in the Method of Regularized Stokeslets

In this paper we present a simple modification of the Method of Regularized Stokeslets, which significantly reduces the dependence of the accuracy on the regularization parameter and achieves accurate solutions with low computational effort. Thanks to the modification introduced, the regularization parameter is no longer a free-tuning parameter. This new approach is based on a special treatment of the near-singular kernel evaluations, where spatially averaged quantities are considered. Numerical tests for both exterior and interior Stokes flows are presented, showing both accurate results and good conditioning of the matrix kernel.