An adaptive error-controlled hybrid fast solver for regularized vortex methods

• Published in: Journal of computational physics 2022-11, Vol.468, p.111504, Article 111504
• Main Authors: Salloum, Samer, Lakkis, Issam
• Format: Article
• Language: English
• Subjects: Accuracy; Adaptive control; Adaptive fast solver; Cell division; Computational physics; Computer architecture; Criteria; Fast multipoles; Fields (mathematics); Mathematical analysis; Multipoles; Optimization; Parameters; Regularization; Solvers; Vortex methods; Vortex rings; Vortices
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2022.111504

In this paper, an adaptive error-controlled hybrid fast solver that combines both O(N) and O(Nlog⁡N)schemes is proposed. For a given accuracy, the adaptive solver is used in the context of regularized vortex methods to optimize the speed of the velocity and vortex stretching calculation. This is accomplished by introducing criteria for cell division in building of the tree, conversion of multipole to local expansion in the downward pass, stopping of the downward pass and choosing between direct and fast summation to compute the vector fields. These criteria are based on key parameters (p,nF,nT,dσ) which take into account the elements distribution, choice of the regularization function, and the computer architecture. The proposed solver automatically adapts to the evolving flow-field by periodically updating the optimal values of these parameters to maximize the speed, while meeting the accuracy constraints, by balancing far and near-field calculations. Performance of the proposed scheme is investigated in terms of the dependence of cost and accuracy on the various controlling parameters. The evolution of the optimal values of these parameters along with the associated computational savings are presented for the case of collision of two vortex rings over a reasonable time span. •We present an adaptive error-controlled fast solver for Vortex Methods.•Velocity and vortex stretching computing cost is minimized for a given accuracy.•Key parameters are used to divide and balance far and near field calculations.•They account for elements distribution, regularization and computer architecture.•Optimal parameter values are periodically updated to adapt to the evolving flow.