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

• Published in: Applied numerical mathematics Vol. 170; pp. 55 - 73
• Main Authors: Alves, Carlos J.S., Serrão, Rodrigo G., Silvestre, Ana L.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2021
• Subjects: [formula omitted]-density; Method of fundamental solutions; Mixed boundary conditions; Stokes problem; Stokeslets and Stresslets; Mixed boundary conditions; Stokes problem; Stokeslets and Stresslets; L2-density; Method of fundamental solutions
• ISSN: 0168-9274; 1873-5460
• DOI: 10.1016/j.apnum.2021.07.011

•Density results for very weak solutions with application to the method of fundamental solutions.•Implementation of mixed boundary conditions for non trivial Stokes problems.•Implementation of 2D and 3D numerical simulations and error estimates. 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 L2-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.