Solving Moving-Boundary Problems with the Wavelet Adaptive Radial Basis Functions Method
Moving boundaries are associated with the time-dependent problems where the momentary position of boundaries needs to be determined as a function of time. The level set method has become an effective tool for tracking, modeling and simulating the motion of free boundaries in fluid mechanics, computer animation and image processing. This work extends our earlier work on solving moving boundary problems with adaptive meshless methods. In particular, the objective of this paper is to investigate numerical performance the radial basis functions (RBFs) methods, with compactly supported basis and with global basis, coupled with a wavelet node refinement technique and a greedy trial space selection technique. Numerical simulations are provided to verify the effectiveness and robustness of RBFs methods with different adaptive techniques.
L. Vrankar et al., "Solving Moving-Boundary Problems with the Wavelet Adaptive Radial Basis Functions Method," Computers and Fluids, vol. 86, pp. 37 - 44, Elsevier Ltd., Nov 2013.
The definitive version is available at https://doi.org/10.1016/j.compfluid.2013.06.029
Civil, Architectural and Environmental Engineering
Keywords and Phrases
Adaptive greedy algorithm; Compactly supported RBFs; Global RBFs; Level set method; Moving-boundary problems; Partial differential equations; Wavelet method
International Standard Serial Number (ISSN)
Article - Journal
© 2013 Elsevier Ltd., All rights reserved.
01 Nov 2013