Journal of Theoretical
and Applied Mechanics

40, 4, pp. 825-846, Warsaw 2002

On the magnetization-based Lagrangian methods for 2D and 3D viscous flows. Part 2 – Numerical implementation and results

Piotr Duszyński, Piotr Olszewski, Marta Poćwierz, Andrzej Styczek, Jacek Szumbarski
The numerical implemcntation of the Lagrangian method using particles of the magnetization field (magnetons) has been considered. A detailed description of essential elements of the algorithm has been provided. The presentation has focused on computations of stretching, where a novel integral-based rather than point wise approach has been proposed. The results of test computations, carried out for viscous flows past 2D and 3D bodies, have been presented. Difficulties with obtaining stable large-time simulations have been encountered and discussed. It has also been shown that, in contrast to flows around solid bodies, the vortex dynamics in the absence of boundaries can be successfully simulated. However, some consistent remeshing technique niay be necessary to achieve appropriate resolution.
Keywords: viscous flow; Navier-Stokes equations; magnetization; stretching