A Semi-Lagrangian Vortex Penalization Method for 3D Incompressible Flows (Journal of Mathematical Study, 2019)
A remeshed Vortex method is proposed in this work to simulate three-dimensional incompressible flows. The convection equation is solved on particles,using a Vortex method, which are then remeshed on a Cartesian underlying grid. Theother differential operators involved in the governing incompressible Navier-Stokesequations are discretized on the grid, through finite differences method or in spectralspace. In the present work, the redistribution of the particles on the Cartesian meshis performed using a directional splitting, allowing to save significant computationalefforts especially in the case of 3D flows. A coupling of this semi-Lagrangian methodwith an immersed boundary method, namely the Brinkman penalization technique, isproposed in this paper in order to efficiently take into account the presence of solidand porous obstacles in the fluid flow and then to perform passive flow control using porous medium. This method, which combines the robustness of particle methodsand the flexibility of penalization method, is validated and exploited in the context ofdifferent flow physics.
Keywords: Semi-Lagrangian method; remeshed Vortex method; penalization approach; bluff body flows; DNS.