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 - <p style="text-align: justify;">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.</p>