A single domain velocity - vorticity Fast Multipole Boundary Domain Element Method for three dimensional incompressible fluid flow problems, part II

Engineering Analysis with Boundary Elements, vol 114, pages 74-93 (2020), https://doi.org/10.1016/j.enga
https://doi.org/10.1016/j.enganabound.2020.02.006

In the present work, the Fast Multipole Boundary Element Method (FMM / BEM) for solving three-dimensional incompressible fluid flow problems governed by the Navier-Stokes equations is proposed. The velocity-vorticity form is selected, and the pressure gradient is eliminated from the equations. The kinematics equation, related to the velocity field satisfies continuity and provides a direct boundary condition for the vorticity equation. The single-domain approach is used for the discretization of the entire computational volume. The system of equations is compressed into two vectors and a preconditioner matrix, which is negligible in size. The involved unknowns are velocities, vorticities, and boundary vorticity fluxes. The two governing equations are coupled together in a convergent Newton-Raphson iteration scheme, successfully used for the solution of 3D fluid flow problems on a 32 GB memory computer. The degrees of freedom of the benchmark problems are above to 300000, which is an unreachable limit for the conventional single-domain BEM.