An immersed boundary vector potential-vorticity meshless solver of the incompressible Navier-Stokes equation

George C. Bourantas, Benjamin F. Zwick, Theo Philippe Lavier, Vassilios C. Loukopoulos, Athanassios A. Dimas, Adam Wittek, Karol Miller

Research output: Contribution to journalArticlepeer-review

Abstract

We present a strong form meshless solver for numerical solution of the nonstationary, incompressible, viscous Navier-Stokes equations in two (2D) and three dimensions (3D). We solve the flow equations in their stream function-vorticity (in 2D) and vector potential-vorticity (in 3D) formulation, by extending to 3D flows the boundary condition-enforced immersed boundary method, originally introduced in the literature for 2D problems. We use a Cartesian grid, uniform or locally refined, to discretize the spatial domain. We apply an explicit time integration scheme to update the transient vorticity equations, and we solve the Poisson type equation for the stream function or vector potential field using the meshless point collocation method. Spatial derivatives of the unknown field functions are computed using the discretization-corrected particle strength exchange method. We verify the accuracy of the proposed numerical scheme through commonly used benchmark and example problems. Excellent agreement with the data from the literature was achieved. The proposed method was shown to be very efficient, having relatively large critical time steps.

Original languageEnglish
Pages (from-to)143-175
Number of pages33
JournalInternational Journal for Numerical Methods in Fluids
Volume95
Issue number1
Early online date16 Sep 2022
DOIs
Publication statusPublished - Jan 2023

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