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Volume 33, Issue 6
An Adaptive Fast Interface Tracking Method

Yana Di, Jelena Popovic & Olof Runborg

DOI: 10.4208/jcm.1503-m4532

J. Comp. Math., 33 (2015), pp. 576-586.

Published online: 2015-12

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  • Abstract

An adaptive numerical scheme is developed for the propagation of an interface in a velocity field based on the fast interface tracking method proposed in [2]. A multiresolution stategy to represent the interface instead of point values, allows local grid refinement while controlling the approximation error on the interface. For time integration, we use an explicit Runge-Kutta scheme of second-order with a multiscale time step, which takes longer time steps for finer spatial scales. The implementation of the algorithm uses a dynamic tree data structure to represent data in the computer memory. We briefly review first the main algorithm, describe the essential data structures, highlight the adaptive scheme, and illustrate the computational efficiency by some numerical examples.

  • Keywords

Interface tracking, Multiresolution, adaptivity, Fast algorithms

  • AMS Subject Headings

42C40, 65D10.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yndi@lsec.cc.ac.cn (Yana Di)

jelenap@csc.kth.se (Jelena Popovic)

olofr@nada.kth.se (Olof Runborg)

  • BibTex
  • RIS
  • TXT
@Article{JCM-33-576, author = {Di , YanaPopovic , Jelena and Runborg , Olof}, title = {An Adaptive Fast Interface Tracking Method}, journal = {Journal of Computational Mathematics}, year = {2015}, volume = {33}, number = {6}, pages = {576--586}, abstract = {

An adaptive numerical scheme is developed for the propagation of an interface in a velocity field based on the fast interface tracking method proposed in [2]. A multiresolution stategy to represent the interface instead of point values, allows local grid refinement while controlling the approximation error on the interface. For time integration, we use an explicit Runge-Kutta scheme of second-order with a multiscale time step, which takes longer time steps for finer spatial scales. The implementation of the algorithm uses a dynamic tree data structure to represent data in the computer memory. We briefly review first the main algorithm, describe the essential data structures, highlight the adaptive scheme, and illustrate the computational efficiency by some numerical examples.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1503-m4532}, url = {http://global-sci.org/intro/article_detail/jcm/9861.html} }
TY - JOUR T1 - An Adaptive Fast Interface Tracking Method AU - Di , Yana AU - Popovic , Jelena AU - Runborg , Olof JO - Journal of Computational Mathematics VL - 6 SP - 576 EP - 586 PY - 2015 DA - 2015/12 SN - 33 DO - http://doi.org/10.4208/jcm.1503-m4532 UR - https://global-sci.org/intro/article_detail/jcm/9861.html KW - Interface tracking, Multiresolution, adaptivity, Fast algorithms AB -

An adaptive numerical scheme is developed for the propagation of an interface in a velocity field based on the fast interface tracking method proposed in [2]. A multiresolution stategy to represent the interface instead of point values, allows local grid refinement while controlling the approximation error on the interface. For time integration, we use an explicit Runge-Kutta scheme of second-order with a multiscale time step, which takes longer time steps for finer spatial scales. The implementation of the algorithm uses a dynamic tree data structure to represent data in the computer memory. We briefly review first the main algorithm, describe the essential data structures, highlight the adaptive scheme, and illustrate the computational efficiency by some numerical examples.

Di , YanaPopovic , Jelena and Runborg , Olof. (2015). An Adaptive Fast Interface Tracking Method. Journal of Computational Mathematics. 33 (6). 576-586. doi:10.4208/jcm.1503-m4532
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