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Fundamental solutions for the Stokes equations: Numerical applications for 2D and 3D flows

Alves, Carlos J. S.; Serrão, Rodrigo G.; Silvestre, Ana Leonor

Appl. Numer. Math., 170 (2021), 55-73

We consider the application of the Method of Fundamental Solutions (MFS)
to homogeneous force Stokes problems in 2 and 3 space dimensions. The choice of the main basis functions for the implementation of the MFS is justified by a new density result of linear combinations of Stokeslets in the $L^2$-setting. This is convenient for Stokes flows with low degree of regularity which are found in many applications. In the case of mixed boundary conditions, Stresslets are added as basis functions in order to enforce the Neumann boundary condition.
The accuracy of the method is investigated through a series of numerical tests, which
include comparison between exact and numerical solutions and the
application of the method to benchmark problems.