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Volume 21, Issue 3
An Efficient Adaptive Rescaling Scheme for Computing Moving Interface Problems

Meng Zhao, Wenjun Ying, John Lowengrub & Shuwang Li

DOI: 10.4208/cicp.OA-2016-0040

Commun. Comput. Phys., 21 (2017), pp. 679-691.

Published online: 2018-04

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  • Abstract

In this paper, we present an efficient rescaling scheme for computing the long-time dynamics of expanding interfaces. The idea is to design an adaptive time-space mapping such that in the new time scale, the interfaces evolves logarithmically fast at early growth stage and exponentially fast at later times. The new spatial scale guarantees the conservation of the area/volume enclosed by the interface. Compared with the original rescaling method in [J. Comput. Phys. 225(1) (2007) 554–567], this adaptive scheme dramatically improves the slow evolution at early times when the size of the interface is small. Our results show that the original three-week computation in [J. Comput. Phys. 225(1) (2007) 554–567] can be reproduced in about one day using the adaptive scheme. We then present the largest and most complicated Hele-Shaw simulation up to date.

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@Article{CiCP-21-679, author = {Meng Zhao, Wenjun Ying, John Lowengrub and Shuwang Li}, title = {An Efficient Adaptive Rescaling Scheme for Computing Moving Interface Problems}, journal = {Communications in Computational Physics}, year = {2018}, volume = {21}, number = {3}, pages = {679--691}, abstract = {

In this paper, we present an efficient rescaling scheme for computing the long-time dynamics of expanding interfaces. The idea is to design an adaptive time-space mapping such that in the new time scale, the interfaces evolves logarithmically fast at early growth stage and exponentially fast at later times. The new spatial scale guarantees the conservation of the area/volume enclosed by the interface. Compared with the original rescaling method in [J. Comput. Phys. 225(1) (2007) 554–567], this adaptive scheme dramatically improves the slow evolution at early times when the size of the interface is small. Our results show that the original three-week computation in [J. Comput. Phys. 225(1) (2007) 554–567] can be reproduced in about one day using the adaptive scheme. We then present the largest and most complicated Hele-Shaw simulation up to date.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0040}, url = {http://global-sci.org/intro/article_detail/cicp/11255.html} }
TY - JOUR T1 - An Efficient Adaptive Rescaling Scheme for Computing Moving Interface Problems AU - Meng Zhao, Wenjun Ying, John Lowengrub & Shuwang Li JO - Communications in Computational Physics VL - 3 SP - 679 EP - 691 PY - 2018 DA - 2018/04 SN - 21 DO - http://doi.org/10.4208/cicp.OA-2016-0040 UR - https://global-sci.org/intro/article_detail/cicp/11255.html KW - AB -

In this paper, we present an efficient rescaling scheme for computing the long-time dynamics of expanding interfaces. The idea is to design an adaptive time-space mapping such that in the new time scale, the interfaces evolves logarithmically fast at early growth stage and exponentially fast at later times. The new spatial scale guarantees the conservation of the area/volume enclosed by the interface. Compared with the original rescaling method in [J. Comput. Phys. 225(1) (2007) 554–567], this adaptive scheme dramatically improves the slow evolution at early times when the size of the interface is small. Our results show that the original three-week computation in [J. Comput. Phys. 225(1) (2007) 554–567] can be reproduced in about one day using the adaptive scheme. We then present the largest and most complicated Hele-Shaw simulation up to date.

Meng Zhao, Wenjun Ying, John Lowengrub and Shuwang Li. (2018). An Efficient Adaptive Rescaling Scheme for Computing Moving Interface Problems. Communications in Computational Physics. 21 (3). 679-691. doi:10.4208/cicp.OA-2016-0040
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