A single domain velocity - vorticity Fast Multipole Boundary Domain Element Method for two dimensional incompressible fluid flow problems.

Engineering Analysis with Boundary Elements, 106 (2019), 359-370
https://www.sciencedirect.com/science/article/pii/S095579971930092X

In the present paper, a fast multipole boundary domain element method for the solution of the two dimensional Navier-Stokes equations is proposed. The velocity-vorticity formulation is adopted and the pressure gradient is eliminated from the governing equations. The non-linear system of velocity kinematics and vorticity kinetics is solved using a Newton-Raphson iteration procedure. The computational domain is discretized by a single region which is common for both equations. Qualitative results for low, moderate and high Reynolds number problems, that are not possible to be obtained on a 32 Gb memory computer by an equivalent conventional one domain BEM solver, are presented.