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A novel approach to rigid spheroid models in viscous flows using operator splitting methods

Tapley, Benjamin; Celledoni, Elena; Owren, Brynjulf; Andersson, Helge Ingolf
Peer reviewed, Journal article
Accepted version
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URI
https://hdl.handle.net/11250/2654492
Date
2019
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  • Institutt for energi og prosessteknikk [2622]
  • Institutt for matematiske fag [1390]
  • Publikasjoner fra CRIStin - NTNU [19694]
Original version
Numerical Algorithms. 2019, 81 (4), 1423-1441.   10.1007/s11075-019-00666-1
Abstract
Calculating cost-effective solutions to particle dynamics in viscous flows is an important problem in many areas of industry and nature. We implement a second-order symmetric splitting method on the governing equations for a rigid spheroidal particle model with torques, drag and gravity. The method splits the operators into a vector field that is conservative and one that takes into account the forces of the fluid. Error analysis and numerical tests are performed on perturbed and stiff particle-fluid systems. For the perturbed case, the splitting method greatly improves the solution accuracy, when compared to a conventional multistep method, and the global error behaves as (𝜀�ℎ2) for roughly equal computational cost. For stiff systems, we show that the splitting method retains stability in regimes where conventional methods blow up. In addition, we show through numerical experiments that the global order is reduced from (ℎ2/𝜀�) in the perturbed regime to (ℎ) in the stiff regime.
Publisher
Springer
Journal
Numerical Algorithms

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