Multiple-Precision Arithmetic of Biot-Savart Integrals for Reconnections of Vortex Filaments

• Published in: Computational Science and Its Applications - ICCSA 2021 Vol. 12953; pp. 191 - 201
• Main Authors: Lee, Yu-Hsun, Fujiwara, Hiroshi
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2021; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Computational fluid dynamics; Multiple-precision arithmetic; Numerical instability and reliability; Vortex reconnection
• ISBN: 303086975X; 9783030869755
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-86976-2_13

In this paper, we show an efficient application of multiple-precision arithmetic to numerical computation of the Biot-Savart integral, which is a mathematical model of motion of vortex filaments. Since it is a non-linear integro-differential equation, numerical methods play a significant role in analysis. Hence reliable schemes are desired even though their computational costs are high. Multiple-precision arithmetic enables us to estimate rounding errors quantitatively, and comparing various precision arithmetic. Thus we conclude reliability of numerical results. In particular, reconnection of vortex filaments is investigated, and we meet oscillation of numerical solutions due to singularity. The proposed method clarifies that the divergence immediately after reconnection is still reliable in terms of rounding errors.