A global version of the Method of Approximate Particular Solutions (MAPS) is developed to solve two-dimensional Stokes flow problems in bounded domains. The velocity components and the pressure are approximated by a linear superposition of particular solutions of the non-homogeneous Stokes system of equations with a Multiquadric Radial Basis Function as forcing term. Although, the continuity equation is not explicitly imposed in the resulting formulation, the scheme is mass conservative since the particular solutions exactly satisfy the mass conservation equation. The present scheme is validated by comparing the obtained numerical result with the analytical solution of two boundary value problems constructed from the Stokeson exterior fundamental solution, i.e. regular everywhere except at infinity. For these two cases, convergence of the method and the influence of the value of the Multiquadric's shape parameter on the numerical results are studied by computing the relative Root Mean Square (RMS) error for several homogeneous distributions of collocation points and values of the shape parameter. From this analysis is observed that the proposed MAPS results are stable and accurate for a wide range of shape parameter values. In addition, the lid-driven cavity and backward-facing step flow problems are solved and the obtained results compared with the solutions found with more conventional numerical schemes, showing good agreement between them.
Bibliographical noteFunding Information:
The present work is partially supported by COLCIENCIAS and Empresas Públicas de Medellín (EPM) , Colombia, as part of the funding provided to the project Energetic assessment of the San Fernando plant bio-solids which has been developed by the consortium of some Colombian academic institutions from Medellín and the public utility company EPM, known as the Energy Research and Innovation Centre (CIIEN).
- Meshless methods
- Particular solutions
- Radial Basis Functions
- Stokes flows