Vortex particle method with iterative Brinkman penalization for simulation of flow past sharp-shape bodies

This paper presents a Lagrangian vortex method combined with iterative Brinkman penalization for the simulation of incompressible flow past a complex geometry. In the proposed algorithm, particle and penalization domains are separately introduced. The particle domain is for the computation of particle convection and diffusion, while the penalization domain is the enforcement of the wall boundary conditions. In iterative Brinkman penalization, the no-slip boundary condition is enforced by applying penalization force in multiple times within each time step. This enables large time step size reducing computational cost and maintains the capability in handling complex geometries. The method is validated for benchmark problems such as an impulsively started flow past a circular cylinder, normal to a flat plate, and a symmetric airfoil at Reynolds numbers ranging from 550 to 1000. The vorticity and streamline contours, drag, and lift coefficients show a good agreement with those reported in literature.