Communications in Mathematical Sciences
Volume 16 (2018)
Data-driven modeling for the motion of a sphere falling through a non-Newtonian fluid
Pages: 425 – 439
In this paper, we will introduce a mathematical model of the jerk equation to simulate the unstable oscillations of the motion of a falling sphere in the wormlike micellar solution. This differential/algebraic equation (DAE) is established only by learning the experimental data of time vs. velocity with the sparse optimization method. To simulate the solutions of the DAE, four discretization schemes are proposed and compared. Periodic and damped harmonic motion, and nonuniform transient and sustaining oscillations can be observed for the sedimentation of a sphere through the non-Newtonian fluid in the numerical experiments. It successfully presents chaos consistent with the physical behavior, which are highly sensitive to the initial values and experimentally nonreproducible. We can conclude that our model has the ability to capture the primary pattens of the dynamics, which is more meaningful than predict an individual trajectory for the chaotic systems.
falling sphere, non-Newtonian fluid, data-driven modeling, sparsity, differential/algebraic equation (DAE), jerk
2010 Mathematics Subject Classification
34B60, 34K28, 41A30, 65P20, 65Z05
This work is supported by NSFC Key Project (11631015), NSFC (91330201), NSFC(11571078), and Joint Research Fund by National Science Foundation of China and Research Grants Council of Hong Kong (11461161006).
Received 21 October 2017
Accepted 22 November 2017
Published 14 May 2018