An Efficient Rescaling Algorithm for Simulating the Evolution of Multiple Elastically Stressed Precipitates
Year: 2013
Communications in Computational Physics, Vol. 14 (2013), Iss. 4 : pp. 940–959
Abstract
In this paper, we propose a space-time rescaling scheme for computing the long time evolution of multiple precipitates in an elastically stressed medium. The algorithm is second order accurate in time, spectrally accurate in space and enables one to simulate the evolution of precipitates in a fraction of the time normally used by fixed-frame algorithms. In particular, we extend the algorithm recently developed for single particle by Li et al. (Li, Lowengrub and Leo, J. Comput. Phys., 335 (2007), 554) to the multiple particle case, which involves key differences in the method. Our results show that without elasticity there are successive tip splitting phenomena accompanied by the formation of narrow channels between the precipitates. In presence of applied elastic field, the precipitates form dendrite-like structures with the primary arms aligned in the principal directions of the elastic field. We demonstrate that when the far-field flux decreases with the effective radius of the system, tip-splitting and dendrite formation can be suppressed, as in the one particle case. Depending on the initial position of the precipitates, we further observe that some precipitates grow while others may shrink, even when a positive far field flux is applied.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.251012.271212a
Communications in Computational Physics, Vol. 14 (2013), Iss. 4 : pp. 940–959
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
-
A Kernel-Free Boundary Integral Method for 2-D Magnetostatics Analysis
Jin, Zichao | Cao, Yue | Li, Shuwang | Ying, Wenjun | Krishnamurthy, MaheshIEEE Transactions on Magnetics, Vol. 59 (2023), Iss. 4 P.1
https://doi.org/10.1109/TMAG.2023.3247444 [Citations: 1] -
Pattern formation of the three-layer Saffman-Taylor problem in a radial Hele-Shaw cell
Zhao, M. | Anjos, Pedro H. A. | Lowengrub, J. | Li, ShuwangPhysical Review Fluids, Vol. 5 (2020), Iss. 12
https://doi.org/10.1103/PhysRevFluids.5.124005 [Citations: 20] -
Sharp-interface problem of the Ohta-Kawasaki model for symmetric diblock copolymers
Barua, Amlan K. | Chew, Ray | Li, Shuwang | Lowengrub, John | Münch, Andreas | Wagner, BarbaraJournal of Computational Physics, Vol. 481 (2023), Iss. P.112032
https://doi.org/10.1016/j.jcp.2023.112032 [Citations: 1] -
Boundary integral simulations of boundary layers in linear viscoelastic flow
Feng, Hualong | Barua, Amlan | Li, Shuwang | Li, XiaofanPhysics of Fluids, Vol. 35 (2023), Iss. 2
https://doi.org/10.1063/5.0138344 [Citations: 1] -
An Efficient Adaptive Rescaling Scheme for Computing Moving Interface Problems
Zhao, Meng | Ying, Wenjun | Lowengrub, John | Li, ShuwangCommunications in Computational Physics, Vol. 21 (2017), Iss. 3 P.679
https://doi.org/10.4208/cicp.OA-2016-0040 [Citations: 14]