Structure-preserving finite difference scheme for vortex filament motion - Ishiwata, Tetsuya; Kumazaki, Kota (Proceedings of the Conference Algoritmy, 2015)
Finite di®erence scheme for the model equation of vortex filament in three dimensional fluid is proposed. We show that the scheme inherits length-preserving and energy structures from the original model. We also show that solvability of the scheme since the scheme is implicit and nonlinear and give an error estimate of the iteration. Finally, numerical results are shown.