This paper aims to describe the 2D meshless local boundary integral equation (LBIE) method for solving the Navier–Stokes equations.
The velocity–vorticity formulation is selected to eliminate the pressure gradient of the equations. The local integral representations of flow kinematics and transport kinetics are derived. The integral equations are discretized using the local RBF interpolation of velocities and vorticities, while the unknown fluxes are kept as independent variables. The resulting volume integrals are computed using the general radial transformation algorithm.
The efficiency and accuracy of the method are illustrated with several examples chosen from reference problems in computational fluid dynamics.
The meshless LBIE method is applied to the 2D Navier–Stokes equations. No derivatives of interpolation functions are used in the formulation, rendering the present method a robust numerical scheme for the solution of fluid flow problems.
This work has been supported by FCT – Fundação para a Ciência e a Tecnologia (www.fct.pt), through the grant SFRH/BPD/109574/2015 and the Research Project UID/Multi/04621/2013 of the CEMAT – Center for Computational and Stochastic Mathematics, Instituto Superior Técnico, University of Lisbon.
Sellountos, E.J., Tiago, J. and Sequeira, A. (2019), "Meshless velocity – vorticity local boundary integral equation (LBIE) method for two dimensional incompressible Navier-Stokes equations", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 29 No. 11, pp. 4034-4073. https://doi.org/10.1108/HFF-06-2018-0310
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