Abstract

Green’s functions (also called fundamental solutions) can be used to construct solutions to several differential equations arising in physics. These solutions, however, cannot be easily implemented on a computer due to the divergence of Green’s functions. One popular way to overcome this difficulty is to remove the singularities in Green’s functions, a process known as regularization or mollification. The amount of regularization is often controlled by a parameter, called the regularization parameter. The significance of the parameter and the physical change to the Green’s function are often not well understood. Nevertheless, they are essential to a good understanding of the error introduced in the regularization process. In this talk, I will discuss a specific Green’s function in fluid mechanics – the Stokeslet. Its regularized versions, called regularized Stokeslets, have been extensively used in many flow problems since the early 2000s. I will elucidate the physical significance of regularized Stokeslets for various regularization schemes. If time permits, I will explain the implication for computation.