Planar potential flow on Cartesian grids

Potential flow has many applications, including the modelling of unsteady flows in aerodynamics. For these models to work efficiently, it is best avoid Biot-Savart interactions. This presents a grid-based treatment potential two dimensions and its use vortex model for simulating aerodynamic flows. consisting elements, follows vortex-in-cell approach solves streamfunction-vorticity Poisson equation on Cartesian grid after transferring circulation from vortices onto grid. sources sinks, an analogous can be followed using scalar potential. The combined velocity field due vortices, then obtained Helmholtz decomposition. In this work, we several key tools that ensure works arbitrary geometries, with without sharp edges. Firstly, immersed boundary projection method used account bodies resulting body-forcing Lagrange multiplier identified as bound sheet strength. Secondly, edges are treated by decomposing strength into singular smooth part. To enforce Kutta condition, part constrained remove singularity introduced edge. These constraints formulated saddle-point system solved Schur complement method. lattice Green's function efficiently solve discrete unbounded conditions. accuracy demonstrated problems.